CN109376493B - Particle swarm optimization radial basis function neural network vehicle speed tracking method - Google Patents

Particle swarm optimization radial basis function neural network vehicle speed tracking method Download PDF

Info

Publication number
CN109376493B
CN109376493B CN201811541341.4A CN201811541341A CN109376493B CN 109376493 B CN109376493 B CN 109376493B CN 201811541341 A CN201811541341 A CN 201811541341A CN 109376493 B CN109376493 B CN 109376493B
Authority
CN
China
Prior art keywords
time
neural network
radial basis
pid controller
basis function
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201811541341.4A
Other languages
Chinese (zh)
Other versions
CN109376493A (en
Inventor
尹智帅
何嘉雄
聂琳真
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan University of Technology WUT
Original Assignee
Wuhan University of Technology WUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Wuhan University of Technology WUT filed Critical Wuhan University of Technology WUT
Priority to CN201811541341.4A priority Critical patent/CN109376493B/en
Publication of CN109376493A publication Critical patent/CN109376493A/en
Application granted granted Critical
Publication of CN109376493B publication Critical patent/CN109376493B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks

Abstract

The invention discloses a particle swarm optimization-based radial basis function neural network vehicle speed tracking method. The method comprises the steps of constructing an automobile dynamics model through an engine model, a transmission system model, a vehicle model and a brake model; calculating parameters of the radial basis function neural network model through a gradient descent method, and adaptively adjusting the parameters through the radial basis function neural network model by the PID controller; performing offline optimization through a particle swarm optimization algorithm to obtain parameters after particle swarm optimization; initializing and assigning the parameters after particle swarm optimization to a radial basis function (PID) controller; obtaining the initial throttle opening or the initial brake pedal position through the initialized radial basis function neural network PID controller, and inputting the initial throttle opening or the initial brake pedal position into an automobile dynamics model to calculate the actual tracking speed; the actual tracking vehicle speed and the PID controller output are input into the neural network, and the parameters of the radial basis neural network and the PID controller are adjusted according to the feedback error of the speed. The invention realizes safe and stable target tracking speed.

Description

Particle swarm optimization-based radial basis function neural network vehicle speed tracking method
Technical Field
The invention belongs to the technical field of tracking control of an automatic driving automobile, and particularly relates to a particle swarm optimization-based radial basis function neural network vehicle speed tracking method.
Background
Vehicle speed tracking is a hot spot problem in the field of automatic driving, and is also a difficult problem in the technology of automatic driving vehicles due to the characteristics of nonlinearity, time-varying property, uncertainty and the like of longitudinal motion of the vehicles. At present, the research on the problem is more at home and abroad, and a plurality of solutions are also provided, wherein the methods comprise Adaptive Cruise Control (ACC), PID control, fuzzy control, sliding mode structure control and the like. The methods can effectively solve some practical problems, but still have some defects when the methods are applied to the driving of the automatic driving vehicle under the dynamic urban road working condition, such as the problems that the methods cannot be well adapted to the complex scene of dynamic change, the uncertainty of parameters and the like. Queensland et al use a single incremental PID control strategy to achieve automatic cruise, but research finds that a controller manufactured by using a single control algorithm in Adaptive Cruise Control (ACC) cannot perfectly achieve all vehicle working modes, the control effect is very ideal in certain driving modes, and once the mode is switched to another mode, the problems of large speed fluctuation, long reflection time, increased error and the like, which obviously reduce the control quality, occur. Chien and the like adopt a PID longitudinal controller to solve the real-time problem of vehicle longitudinal control under intelligent traffic, but because the control parameters are obtained by a trial and error method, the optimal control of intelligent longitudinal motion is difficult to realize. Establishing a dynamic model of an automobile by the aid of juveniles, macros and the like, designing a cruise controller by a fuzzy control method, designing an inter-vehicle distance controller by an adaptive neural network fuzzy inference system ANFIS, optimizing by means of simulation, and controlling a train by means of speed and inter-vehicle distance combined control. Guozhihua and the like adopt a classical PID control method to design an upper controller of a speed tracking system, adopt an adaptive fuzzy sliding mode control (AFLSMC) method to design a lower controller of the speed tracking system, and the sliding mode variable structure controller can improve the dynamic response capability of the system, effectively overcome the characteristics of vehicle nonlinearity, parameter uncertainty, external interference and the like, but can enable the control system to generate oscillation or instability due to the discontinuity of control gain.
The complexity of vehicle speed tracking is: non-linearity, time-varying and uncertainty of the control object; safety and control stability; the neural network is widely concerned about on-line learning ability, does not depend on the control characteristic of an accurate mathematical model, has incomparable advantages on two aspects of a complex nonlinear system with unknown models or a control object with constantly changing dynamic characteristics, and provides a PID controller parameter optimization method based on the ant colony neural network aiming at the safety and stability problems of vehicle speed tracking, complaining and willingness and the like, so that a better control effect can be obtained. The improved particle swarm optimization algorithm searches for the optimal PID gain for position control, and intelligent selection of initial parameters is achieved.
Disclosure of Invention
The invention aims to solve the problems of overshoot and instability caused by the fact that a traditional control method cannot be well adaptive to a complex scene with dynamic change and initial parameter selection is improper, and provides a vehicle tracking method with high-precision tracking and stable control.
The invention provides a particle swarm optimization-based radial basis function neural network vehicle speed tracking method based on the difficult problems of the background art, which utilizes a particle swarm optimization PSO to realize the offline optimization intelligent selection of initial parameters, and combines a radial basis function neural network RBFNN and a PID to realize the online adaptive adjustment of the parameters, thereby achieving higher control precision and stable tracking control effect.
The implementation steps of the technical scheme summarized by the invention are as follows:
step 1: constructing an automobile dynamics model through an engine model, a transmission system model, a vehicle model and a brake model;
step 2: establishing a radial basis function neural network model, calculating parameters of the radial basis function neural network model through a gradient descent method, and adaptively adjusting the parameters through the radial basis function neural network model by the PID controller to construct a radial basis function neural network PID controller;
and step 3: performing offline optimization through a particle swarm optimization algorithm to obtain parameters after particle swarm optimization;
and 4, step 4: initializing and assigning the parameters after particle swarm optimization to a radial basis function (PID) controller;
and 5: obtaining initial throttle opening or initial brake pedal position through an initialized radial basis function neural network PID controller, inputting the initial throttle opening or the initial brake pedal position into an automobile dynamic model to calculate actual tracking vehicle speed V (tau), wherein tau belongs to 0 MAX ]τ is the simulation time, T MAX The simulation maximum time;
step 6: actually tracking vehicle speed V (tau) and PID controller output to obtain tau-1 time A (tau-1) and inputting into neural network according to speedThe feedback error of the method adjusts the parameters of the radial basis function neural network and the PID controller, the simulation time tau is increased by the time step length and transferred to the step 5, and the loop execution is carried out until the simulation time tau reaches the simulation maximum time T MAX 。
Preferably, the engine model in step 1 is:
Figure BDA0001908158700000021
wherein, T e (t) effective torque of engine at t, N e (t) is the rotational speed of the crankshaft at time t, A T (T) is the opening of the throttle valve at time T, T i (t) impeller torque requested for crankshaft shift at time t, I e Is the rotational inertia of the engine crankshaft;
in the step 1, the transmission system model is as follows:
Figure BDA0001908158700000022
wherein, N e (T) is the speed of rotation of the crankshaft at time T, K (T) is the capacity factor at time T, T i (T) impeller torque requested for crankshaft shift at time T, T q (t) is the torque of the output shaft of the torque converter at time t, R TQ (t) is the torque factor at time t, R TR (T) is the transmission ratio of the variator at time T, T o (t) is the output shaft torque of the automatic transmission at time t, η t Is the efficiency of the automatic transmission, N m (t) is the input shaft rotational speed of the automatic transmission at time t, N o (t) is the rotational speed of the output shaft of the automatic transmission at time t, N w (t) is the wheel speed at time t, R fd Is the main reducer transmission ratio, K (t) and R TQ (t) is determined by the following expression:
Figure BDA0001908158700000031
wherein f2 is a capacity coefficient, and f3 is a variableCoefficient of moment rate, N m (t) the input shaft rotation speed of the automatic transmission at time t, N e (t) the rotational speed of the crankshaft at time t;
the vehicle model in step 1 is:
Figure BDA0001908158700000032
wherein, I v Is the moment of inertia of the rotor and,
Figure BDA0001908158700000034
is the derivative of the rotational speed of the wheel at time t, R fd Is the main reducer transmission ratio, T o (T) is the output shaft torque of the automatic transmission at time T, T load (t) is the torque of the load at time t, V (t) is the actual tracking vehicle speed at time t, r is the radius of the wheel, N w (t) is the wheel speed at time t, R load,0 Is the coefficient of friction resistance, R load,2 Is the aerodynamic drag coefficient, T u (t) torque of braking at time t;
in the step 1, the brake model is as follows:
Figure BDA0001908158700000033
wherein r is the radius of the wheel, A B (T) position of the brake pedal at time T, T u (t) is the braking torque at time t;
preferably, the establishing of the radial basis function neural network model in the step 2 is as follows:
the input vector of the radial basis function neural network is:
X＝(x 1 ,x 2 ,x 3 ) T
wherein x is 1 Is the output A (t-1), x of the PID controller at time t-1 2 Is the actual tracking vehicle speed V (t), x at time t 3 Actual tracking vehicle speed V (t-1) at time (t-1);
the number of nodes of the input layer of the radial basis function neural network is 3;
the number of nodes of the hidden layer of the radial basis function neural network is 6;
the output of the radial basis function neural network is the model output V at the time t R (t), the number of nodes of the output layer of the radial basis function neural network is 1;
in the radial basis function neural network structure, X = [ X ] 1 ,x 2 ,…,x n ] T As input vector, x, of the radial basis function neural network i (i =1,2, \8230; (n) is the ith input quantity of X, and the number of nodes of the input layer of the radial basis function neural network is n =3,h = [ h = [ (/) 1 ,h 2 ,…,h m ] T Hiding layer node radial basis vectors, h, for a radial basis function neural network j (j =1,2, \8230; m) is a radial basis of the node of the hidden layer of the jth neuron, the number of the nodes of the hidden layer of the radial basis neural network is m =6, and a radial basis function is a Gaussian function:
Figure BDA0001908158700000041
wherein, X = [ X = 1 ,x 2 ,…,x n ] T Is the input vector, x, of the radial basis function neural network i (i =1,2, \8230; n) is the ith input quantity of X, c j ＝[c j,1 ,c j,2 ,…,c j,n ] T Is the central vector of the node of the hidden layer of the jth neuron, c j,i (i =1,2, \8230n) is the i-th central value of the j-th neuron hidden layer node, b = [ b = 1 ,b 2 ,…,b m ] T A base width vector of nodes of the hidden layer, b j (j =1,2, \8230; m) is the base width of the hidden layer node of the jth neuron, w = [ w = ] 1 ,w 2 ,…,w m ] T Is a weight vector, w, for the connection of the hidden layer to the output layer j (j =1,2, \8230; m) is the weight of the connection of the ith hidden layer neuron to the output layer, V R (t) is the output of the neural network, the number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
the output of the radial basis function neural network at the time t is V R (t) steamThe output of the vehicle dynamics model is the actual tracking vehicle speed V (t) at the time t stated in the step 1, and the performance index function of the radial basis function neural network is as follows:
Figure BDA0001908158700000042
the radial basis function neural network adopts supervised learning, and in order to minimize the value of J (t) at the time t, a gradient descent method is adopted to continuously update the central vector c of the hidden layer node j ＝[c j,1 ,c j,2 ,…,c j,n ] T And a base width vector b = [ b ] of hidden layer node 1 ,b 2 ,…,b m ] T And weight vector w = [ w ] for hidden layer to output layer connection 1 ,w 2 ,…,w m ] T The number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
in the step 2, the parameters of the radial basis function neural network model calculated by the gradient descent method are as follows:
Figure BDA0001908158700000043
the number of nodes of the input layer of the radial basis function neural network is n =3, the number of nodes of the hidden layer of the radial basis function neural network is m =6, beta is the learning rate of the neural network, alpha is a momentum factor, beta, alpha is an element (0, 1), c is j,i (t) is the ith central value of the jth neuron hidden layer node at the time t, c j,i (t-1) is the ith central value of the jth neuron hidden layer node at time t-1, c j,i (t-2) is the ith central value, Δ c, of the jth neuron hidden layer node at time t-2 j,i (t) an increment of an ith center value of a jth neuron hidden layer node at time t;
X＝[x 1 ,x 2 ,…,x n ] T is the input vector of the radial basis function neural network, c j ＝[c j,1 ,c j,2 ,…,c j,n ] T Is that the jth neuron is hiddenCenter vector of reservoir node, b j (j =1,2, \ 8230; m) is the base width of the hidden layer node of the jth neuron, w j (j =1,2, \8230; m) is the weight of the connection of the ith hidden layer neuron to the output layer, Δ c j (t) is the increment of the weight of the jth neuron hidden layer node at time t, V R (t) is the output of the radial basis function neural network at the time t, and V (t) is the actual tracking vehicle speed at the time t in the step 1;
b j (t) base width of the jth neuron hidden layer node at time t, b j (t-1) is the base width of the hidden layer node of the jth neuron at the time t-1, b j (t-2) base width of the hidden layer node of the jth neuron at time t-2, Δ b j (t) is the increment of the base width of the jth neuron hidden layer node at the time t, h j (j =1,2, \8230m) is the radial basis of the hidden layer node of the jth neuron;
w j (t) is the weight of the hidden layer node of the jth neuron at time t, w j (t-1) is the weight of the hidden layer node of the jth neuron at time t-1, w j (t-2) is the weight of the hidden layer node of the jth neuron at time t-2, Δ w j (t) is the increment of the weight of the jth neuron hidden layer node at time t;
in the step 2, the PID controller adaptively adjusts parameters through the radial basis function neural network model to construct the radial basis function neural network PID controller:
the controller uses an incremental PID control theory, and the control error is as follows:
e(t)＝V d (t)-V(t)(9)
wherein, V d (t) is the tracking target vehicle speed at the time t, V (t) is the actual tracking vehicle speed at the time t, and e (t) is the tracking error at the time t;
the input of the controller and the control algorithm are as follows:
Figure BDA0001908158700000051
Figure BDA0001908158700000052
wherein e (t) is the tracking error at the time t, e (t-1) is the tracking error at the time t-1, e (t-2) is the tracking error at the time t-2, xc (1) is a first input parameter of the PID controller, xc (2) is a second input parameter of the PID controller, xc (3) is the third input parameter of the PID controller, A (t) is the output of the PID controller at time t, A (t-1) is the output of the PID controller at time t-1, Δ A (t) is the increment of A (t) at time t, K p (t) is the proportional coefficient at time t of the PID controller, K i (t) is the integral coefficient of PID controller at time t, K d (t) is a differential coefficient of the PID controller at the moment t, and the performance index of the parameter regulation of the PID controller is set as follows:
Figure BDA0001908158700000061
wherein, V d (t) is the tracking target vehicle speed at the time t, and V (t) is the actual tracking vehicle speed at the time t;
to make J at t time C (t) minimum, adjusting the gain parameter of the PID using a gradient descent method
Figure BDA0001908158700000062
In the formula,. DELTA.K P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of the PID at the time t, η p0 is the initial value of the proportional coefficient learning rate of the PID controller, η i0 is the initial value of the integral coefficient learning rate of the PID controller, η d0 is the initial value of the differential coefficient learning rate of the PID controller;
Figure BDA0001908158700000063
wherein x is 1 The input vector for the radial basis function neural network is X = (X) 1 ,x 2 ,x 3 ) T The first element of (a), i.e. x 1 ＝A(t-1)，b j (j =1,2, \ 8230; m) is the base width of the hidden layer node of the jth neuron, w j (j =1,2, \8230; m) is the weight of the connection of the ith hidden layer neuron to the output layer, h j (j =1,2, \ 8230; m) is the radial basis of the hidden layer node of the jth neuron, c j,1 (i =1,2, \8230; n) is the 1 st central value of the jth neuron hidden layer node;
the output of the PID controller at time t is:
A(t)＝A(t-1)+(K P0 +ΔK P (t))xc(1)+(K i0 +ΔK i (t))xc(2)+(K d0 +ΔK d (t))xc(3)
wherein, K P0 Is the initial value of the proportionality coefficient, K, of the PID controller i0 Is the initial value of the integral coefficient, K, of the PID controller d0 Is the initial value of the differential coefficient, Δ K, of the PID controller P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of the PID at the time t, xc (1) is the first input parameter of the PID controller, xc (2) is the second input parameter of the PID controller, and xc (3) is the third input parameter of the PID controller
A (t) is introduced to simplify the control of the speed, and when A (t) is a positive value, it is regarded as the opening A of the throttle valve T When A (t) is a negative value, the absolute value of A (t) is regarded as the position A of the brake pedal B ；
Preferably, in step 3, the particle swarm optimization algorithm is used for off-line optimization to:
initializing particle position and speed information, setting the population scale to be N, the total iteration number to be L, and the dimension of the particle position information to be D, namely D parameters to be optimized, namely the particle positions:
Figure BDA0001908158700000071
wherein the content of the first and second substances,
Figure BDA0001908158700000072
the initial value of the scaling factor of the PID controller representing the h-th particle of the kth iteration,
Figure BDA0001908158700000073
maximum value of (1) is P 1,MAX ，
Figure BDA0001908158700000074
Minimum value of (1) is P 1,MIN ，
Figure BDA0001908158700000075
The initial value of the integral coefficient of the PID controller representing the h-th particle of the kth iteration,
Figure BDA0001908158700000076
maximum value of (1) is P 2,MAX ，
Figure BDA0001908158700000077
Minimum value of (A) is P 2,MAX ，
Figure BDA0001908158700000078
The initial value of the differential coefficient of the PID controller representing the h particle of the kth iteration,
Figure BDA0001908158700000079
maximum value of (1) is P 3,MAX ，
Figure BDA00019081587000000710
Minimum value of (A) is P 3,MIN ,ηp0 h K Initial value of the learning rate of the scale factor of the PID controller representing the h-th particle of the Kth iteration, η p0 h K Maximum value of (1) is P 4,MAX ，ηp0 h K Minimum value of (A) is P 4,MIN ，ηi0 h K Initial value of the learning rate of the integral coefficients of the PID controller representing the h-th particle of the Kth iteration, η i0 h K Maximum value of (1) is P 5,MAX ，ηi0 h K Minimum value of (A) is P 5,MIN ，ηd0 h K Represents the PID of the h particle of the Kth iterationInitial value of learning rate of differential coefficient of controller, setting η d0 h K Maximum value of (1) is P 6,MAX ，ηd0 h K Minimum value of (A) is P 6,MIN ；c0 h K Initial value of the central value of the neural network representing the h particle of the Kth iteration, set c0 h K Maximum value of (1) is P 7,MAX ，c0 h K Minimum value of (A) is P 7,MIN ，b0 h K Initial value of neural network base width value representing h particle of Kth iteration, setting b0 h K Maximum value of (1) is P 8,MAX ，b0 h K Minimum value of (A) is P 8,MIN ，w0 h K Initial value, w0, of neural network weight value representing the h particle of the Kth iteration h K Maximum value of (A) is P 9,MAX ,w0 h K Minimum value of (A) is P 9,MIN ；
The upper limit of the particle position is:
P MAX ＝[P 1,MAX ,P 2,MAX ,P 3,MAX ,P 4,MAX ,P 5,MAX ,P 6,MAX ,P 7,MAX ,P 8,MAX ,P 9,MAX ]
the lower limit of the particle position is: p MIN ＝[P 1,MIN ,P 2,MIN ,P 3,MIN ,P 4,MIN ,P 5,MIN ,P 6,MIN ,P 7,MIN ,P 8,MIN ,P 9,MIN ]
Setting the maximum value of the particle velocity to V MAX Minimum particle velocity of V MIN Velocity of particle V ∈ [ V ] MIN ,V MAX ]；
The objective function, i.e. the fitness function, is set as:
Figure BDA00019081587000000711
where t is the simulation time of the control system, V d (t) is the tracking target vehicle speed at the time t, V (t) is the actual tracking vehicle speed at the time t, and e (t) is the tracking error at the time t;
the particle flight speed update formula is as follows:
V h,d K+1 ＝WV h,d K +c 1 rand 1 (P h,d K -X h,d K )+c 2 rand 2 (P g,d K -X h,d K ) (17)
the particle position update formula is:
X h,d K+1 ＝X h,d K +V h,d K+1 ,K∈[1,L],h∈[1,N],d∈[1,D]
where K is the current iteration number of the algorithm, V h,d K+1 D-dimensional component, V, representing the flight velocity vector of the K +1 th iteration particle h h,d K D-dimension component, X, representing the flight velocity vector of the K-th iteration particle h h,d K+1 D-dimensional component, X, representing the K +1 th iteration particle h position vector h,d K Representing the d-dimensional component, P, of the K-th iteration particle h-position vector h,d K The d-dimension component, P, representing the individual extremum of the K-th iteration particle h g,d K D-dimensional component representing extremum of K-th iteration group, c 1 Is a first acceleration factor, c 2 Is the second acceleration factor, rand 1 Are distributed in [0,1 ]]First random value in between, rand 2 Is distributed in [0,1 ]]A second random value in between, W being the inertial weight;
the parameters after particle swarm optimization in the step 3 are as follows:
d parameters of the control system after L times of iterative optimization are respectively as follows:
*Kp0，*Ki0，*Kd0，*ηp0，*ηi0，*ηd0，*c0，*b0，*w0；
wherein K P0 Is the initial value of the proportional coefficient of the optimized PID controller i0 Is the initial value of the proportional coefficient of the optimized PID controller d0 Is the initial value of the proportional coefficient of the optimized PID controller; * η p0 is an initial value of a proportional coefficient learning rate of the optimized PID controller,. Eta.i 0 is an initial value of an integral coefficient learning rate of the optimized PID controller,. Eta.d 0 is optimized PID controlAn initial value of a differential coefficient learning rate of the controller; * c0 is an initial value of a central value of the optimized neural network, b0 is an initial value of a base width value of the optimized neural network, and w0 is an initial value of a weight value of the optimized neural network; initializing a matrix with the dimension of the central vector c of the neural network being 3 × 6 to make the 18 values equal to each other as × c0, a matrix with the dimension of the central vector b of the neural network being 1 × 6 to make the 6 values equal to each other as × b0, a matrix with the dimension of the central vector w of the neural network being 1 × 6 to make the 6 values equal to each other as × w0;
preferably, the feedback error of the speed in step 6 is V (τ) -V R (τ)，V d (τ)-V(τ)；
The parameters of the radial basis function neural network in the step 6 are as follows: a center vector c, a base width vector b, and a weight vector w.
The parameters of the PID controller in the step 6 are as follows: proportional coefficient K of PID controller p Integral coefficient K of PID controller i Differential coefficient K of PID controller d ；
In step 6, the simulation time τ is increased by a time step: τ = τ + Δτ, Δ τ being the time step;
τ∈[0,T MAX ]τ is the simulation time, T MAX To simulate the maximum time.
The technology is that a radial basis function neural network PID controller model and a vehicle dynamics model are established to form a forward simulation model, the speed of the global light automobile under the test cycle condition is used as the tracking target speed, and the target speed and the forward simulation model form a closed loop feedback loop. And (3) performing offline optimization on the particle swarm optimization algorithm to intelligently select initial parameters of the PID controller of the radial basis function neural network. And (3) giving the initial value of the optimized selection to a PID controller of the radial basis function neural network, and then realizing the self-adaptive online real-time adjustment of the parameters under the working condition of a new European driving cycle.
The invention has the advantages that: the RBF-PID controller based on particle swarm optimization can ensure that the model does not need to randomly initialize parameters, and the model intelligently selects optimized parameters, thereby realizing safe and stable speed tracking control.
Drawings
FIG. 1: a system frame diagram for vehicle tracking control;
FIG. 2: a controller model map of a vehicle tracking control system;
FIG. 3: a dynamic model of a vehicle of the vehicle tracking control system;
FIG. 4: the speed variation relation with time under the test cycle working condition of the global light automobile;
FIG. 5: a structural topology of the radial basis function neural network;
FIG. 6: optimizing parameters and the optimal value of the fitness value after the particle swarm optimization algorithm is optimized in an off-line mode;
FIG. 7: the change relationship of the speed under the new European driving cycle working condition along with the time;
FIG. 8: simulation example of velocity tracking: when the target speed is the speed under the new European driving cycle working condition, tracking effect graphs of the three controllers are shown;
FIG. 9: simulation example of velocity tracking: tracking speed and speed errors under three controls;
FIG. 10: performance index of speed error.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
Embodiments of the present invention will be described below with reference to fig. 1 to 10. The implementation mode of the invention comprises the following specific steps:
step 1: constructing an automobile dynamics model through an engine model, a transmission system model, a vehicle model and a brake model;
the engine model in step 1 is:
Figure BDA0001908158700000091
wherein, T e (t) effective torque of engine at time t，N e (t) is the rotational speed of the crankshaft at time t, A T (T) is the opening of the throttle valve at time T, T i (t) impeller torque requested for crankshaft shift at time t, I e Is the rotational inertia of the engine crankshaft;
in the step 1, the transmission system model is as follows:
Figure BDA0001908158700000101
wherein N is e (T) is the speed of rotation of the crankshaft at time T, K (T) is the capacity factor at time T, T i (T) impeller torque requested for crankshaft shift at time T, T q (t) is the torque of the output shaft of the torque converter at time t, R TQ (t) is the torque factor at time t, R TR (t) is the transmission ratio of the transmission at time t, which corresponds to values of 2.39,1.45,1,0.67, T in gears 1-4, respectively o (t) is the output shaft torque of the automatic transmission at time t, η t Is the efficiency of the automatic transmission, N m (t) is the input shaft rotational speed of the automatic transmission at time t, N o (t) is the rotational speed of the output shaft of the automatic transmission at time t, N w (t) is the speed of rotation of the wheel at time t, R fd Is the main reducer transmission ratio, K (t) and R TQ (t) is determined by the following expression:
Figure BDA0001908158700000102
where f2 is the capacity coefficient, f3 is the torque conversion coefficient, N m (t) the input shaft rotation speed of the automatic transmission at time t, N e (t) the rotational speed of the crankshaft at time t;
the vehicle model in step 1 is:
Figure BDA0001908158700000103
wherein, I v Is the moment of inertia of the rotor and,
Figure BDA0001908158700000105
is the derivative of the rotational speed of the wheel at time t, R fd Is the main reducer transmission ratio, T o (T) is the output shaft torque of the automatic transmission at time T, T load (t) is the torque of the load at time t, V (t) is the actual tracking vehicle speed at time t, r is the radius of the wheel, N w (t) is the speed of rotation of the wheel at time t, R load,0 Is the coefficient of friction resistance, R load,2 Is the aerodynamic drag coefficient, T u (t) torque of braking at time t;
in the step 1, the brake model is as follows:
Figure BDA0001908158700000104
wherein r is the radius of the wheel, A B (T) position of the brake pedal at time T, T u (t) a braking torque at time t;
step 2: establishing a radial basis function neural network model, calculating parameters of the radial basis function neural network model through a gradient descent method, and adaptively adjusting the parameters through the radial basis function neural network model by the PID controller to construct a radial basis function neural network PID controller;
the step 2 of establishing the radial basis function neural network model comprises the following steps:
the input vector of the radial basis function neural network is:
X＝(x 1 ,x 2 ,x 3 ) T
wherein x is 1 Is the output A (t-1), x of the PID controller at time t-1 2 Is the actual tracking vehicle speed V (t), x at time t 3 Actual tracking vehicle speed V (t-1) at time (t-1);
the number of nodes of the input layer of the radial basis function neural network is 3;
the number of nodes of the hidden layer of the radial basis function neural network is 6;
the output of the radial basis function neural network is a model output V at the time t R (t), the number of nodes of the output layer of the radial basis function neural network is 1;
in the radial basis function neural network structure, X = [ X ] 1 ,x 2 ,…,x n ] T As input vector, x, of the radial basis function neural network i (i =1,2, \8230; (n) is the ith input quantity of X, and the number of nodes of the input layer of the radial basis function neural network is n =3,h = [ h = [ (/) 1 ,h 2 ,…,h m ] T Hiding layer node radial basis vectors, h, for a radial basis function neural network j (j =1,2, \8230; m) is a radial basis of the node of the hidden layer of the jth neuron, the number of the nodes of the hidden layer of the radial basis neural network is m =6, and a radial basis function is a Gaussian function:
Figure BDA0001908158700000111
wherein, X = [ X ] 1 ,x 2 ,…,x n ] T Is the input vector, x, of the radial basis function neural network i (i =1,2, \8230; n) is the ith input quantity of X, c j ＝[c j,1 ,c j,2 ,…,c j,n ] T Is the central vector of the node of the hidden layer of the jth neuron, c j,i (i =1,2, \8230n) is the i-th central value of the j-th neuron hidden layer node, b = [ b = 1 ,b 2 ,…,b m ] T A base width vector of nodes of the hidden layer, b j (j =1,2, \8230; m) is the base width of the hidden layer node of the jth neuron, w = [ w = ] 1 ,w 2 ,…,w m ] T Is a weight vector, w, for the connection of the hidden layer to the output layer j (j =1,2, \8230; m) is the weight of the connection of the ith hidden layer neuron to the output layer, V R (t) is the output of the neural network, the number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
the output of the radial basis function neural network at the time t is V R (t), the output of the automobile dynamic model is the actual tracking vehicle speed V (t) at the time t in the step 1, and the performance index function of the radial basis function neural network is as follows:
Figure BDA0001908158700000112
the radial basis function neural network adopts supervised learning, and in order to minimize the value of J (t) at the time t, a gradient descent method is adopted to continuously update the central vector c of the hidden layer node j ＝[c j,1 ,c j,2 ,…,c j,n ] T And a base width vector b = [ b ] of hidden layer node 1 ,b 2 ,…,b m ] T And weight vector w = [ w ] for hidden layer to output layer connection 1 ,w 2 ,…,w m ] T The number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
in the step 2, the parameters of the radial basis function neural network model calculated by the gradient descent method are as follows:
Figure BDA0001908158700000121
the number of nodes of the input layer of the radial basis function neural network is n =3, the number of nodes of the hidden layer of the radial basis function neural network is m =6, beta is the learning rate of the neural network, alpha is a momentum factor, beta, alpha is an element (0, 1), c is j,i (t) is the ith central value of the jth neuron hidden layer node at the time t, c j,i (t-1) is the ith central value of the jth neuron hidden layer node at time t-1, c j,i (t-2) is the ith central value, Δ c, of the jth neuron hidden layer node at time t-2 j,i (t) an increment of an ith central value of a jth neuron hidden layer node at time t;
X＝[x 1 ,x 2 ,…,x n ] T is the input vector of the radial basis function neural network, c j ＝[c j,1 ,c j,2 ,…,c j,n ] T Is the central vector of the node of the hidden layer of the jth neuron, b j (j =1,2, \ 8230; m) is the base width of the hidden layer node of the jth neuron, w j (j =1,2, \8230; m) is the weight of the connection of the ith hidden layer neuron to the output layer, Δ c j (t) is the increment of the weight of the jth neuron hidden layer node at time t，V R (t) is the output of the radial basis function neural network at the time t, and V (t) is the actual tracking vehicle speed at the time t in the step 1;
b j (t) base width of the jth neuron hidden layer node at time t, b j (t-1) is the base width of the hidden layer node of the jth neuron at the time t-1, b j (t-2) base width of the hidden layer node of the jth neuron at time t-2, Δ b j (t) is the increment of the base width of the jth neuron hidden layer node at the time t, h j (j =1,2, \8230; m) is the radial basis of the hidden layer node of the jth neuron;
w j (t) is the weight of the hidden layer node of the jth neuron at time t, w j (t-1) is the weight of the hidden layer node of the jth neuron at time t-1, w j (t-2) is the weight of the hidden layer node of the jth neuron at time t-2, Δ w j (t) is the increment of the weight of the jth neuron hidden layer node at time t;
in the step 2, the PID controller adaptively adjusts parameters through the radial basis function neural network model to construct the radial basis function neural network PID controller:
the controller uses an increment PID control theory, and the control error is as follows:
e(t)＝V d (t)-V(t)(9)
wherein, V d (t) is the tracking target vehicle speed at the time t, V (t) is the actual tracking vehicle speed at the time t, and e (t) is the tracking error at the time t;
the input of the controller and the control algorithm are as follows:
Figure BDA0001908158700000131
Figure BDA0001908158700000132
wherein e (t) is the tracking error at the time t, e (t-1) is the tracking error at the time t-1, e (t-2) is the tracking error at the time t-2, xc (1) is the first input parameter of the PID controller, and xc (2) is the PID controlA second input parameter of the controller, xc (3) is a third input parameter of the PID controller, A (t) is an output of the PID controller at time t, A (t-1) is an output of the PID controller at time t-1, Δ A (t) is an increment of A (t) at time t, K p (t) is the proportional coefficient at time t of the PID controller, K i (t) is the integral coefficient of PID controller at time t, K d (t) is a differential coefficient of the PID controller at the moment t, and the performance index of the parameter regulation of the PID controller is set as follows:
Figure BDA0001908158700000133
wherein, V d (t) is the tracking target vehicle speed at the time t, and V (t) is the actual tracking vehicle speed at the time t;
to make J at t time C (t) minimum, adjusting the gain parameter of the PID using a gradient descent method
Figure BDA0001908158700000134
In the formula,. DELTA.K P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of the PID at time t, η p0 is the initial value of the learning rate of the proportional coefficient of the PID controller, η i0 is the initial value of the learning rate of the integral coefficient of the PID controller, η d0 is the initial value of the learning rate of the differential coefficient of the PID controller;
Figure BDA0001908158700000135
wherein x is 1 The input vector for the radial basis function neural network is X = (X) 1 ,x 2 ,x 3 ) T The first element of (1), i.e. x 1 ＝A(t-1)，b j (j =1,2, \8230m) is the base width of the hidden layer node of the jth neuron, w j (j =1,2, \8230m) is the weight of the i-th hidden layer neuron to output layer connection, h j (j =1,2, \8230m) is the j-th nerveRadial basis of meta-hidden layer nodes, c j,1 (i =1,2, \8230; n) is the 1 st central value of the jth neuron hidden layer node;
the output of the PID controller at time t is:
A(t)＝A(t-1)+(K P0 +ΔK P (t))xc(1)+(K i0 +ΔK i (t))xc(2)+(K d0 +ΔK d (t))xc(3)
wherein, K P0 Is the initial value of the proportionality coefficient, K, of the PID controller i0 Is the initial value of the integral coefficient of the PID controller, K d0 Is the initial value of the differential coefficient, Δ K, of the PID controller P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of the PID at the time t, xc (1) is the first input parameter of the PID controller, xc (2) is the second input parameter of the PID controller, and xc (3) is the third input parameter of the PID controller
A (t) is introduced to simplify the control of the speed, and when A (t) is a positive value, it is regarded as the opening A of the throttle valve T When A (t) is a negative value, the absolute value of A (t) is regarded as the position A of the brake pedal B ；
And step 3: performing offline optimization through a particle swarm optimization algorithm to obtain parameters after particle swarm optimization;
in step 3, the off-line optimization through the particle swarm optimization algorithm is as follows:
initializing particle position and speed information, setting the population size to be N =10, setting the total iteration number to be L =30, setting the dimension of the particle position information to be D =9, namely the D =9 parameter to be optimized, namely the particle position is:
Figure BDA0001908158700000141
wherein the content of the first and second substances,
Figure BDA0001908158700000142
the initial value of the scaling factor of the PID controller representing the h-th particle of the kth iteration,
Figure BDA0001908158700000143
maximum value of (1) is P 1,MAX ＝160，
Figure BDA0001908158700000144
Minimum value of (A) is P 1,MIN ＝0.01，
Figure BDA0001908158700000145
The initial value of the integral coefficient of the PID controller representing the h-th particle of the kth iteration,
Figure BDA0001908158700000146
maximum value of (1) is P 2,MAX ＝160，
Figure BDA0001908158700000147
Minimum value of (A) is P 2,MAX ＝0.01，
Figure BDA0001908158700000148
The initial value of the differential coefficient of the PID controller representing the h particle of the kth iteration,
Figure BDA0001908158700000149
maximum value of (1) is P 3,MAX ＝160，
Figure BDA00019081587000001410
Minimum value of (A) is P 3,MIN ＝0.01,ηp0 h K Initial value of the learning rate of the scale factor, η p0, of the PID controller representing the h-th particle of the Kth iteration h K Maximum value of (1) is P 4,MAX ＝1，ηp0 h K Minimum value of (A) is P 4,MIN ＝0.01，ηi0 h K Initial value of the learning rate of the integral coefficients of the PID controller representing the h-th particle of the Kth iteration, η i0 h K Maximum value of (1) is P 5,MAX ＝1，ηi0 h K Minimum value of (A) is P 5,MIN ＝0.01，ηd0 h K Setting η d0 as an initial value of a learning rate of a differential coefficient of a PID controller for expressing the h-th particle of the Kth iteration h K Maximum value of (1) is P 6,MAX ＝1，ηd0 h K Minimum value of (A) is P 6,MIN ＝0.01；c0 h K Initial value of the central value of the neural network representing the h particle of the Kth iteration, set c0 h K Maximum value of (1) is P 7,MAX ＝40，c0 h K Minimum value of (A) is P 7,MIN ＝0.01，b0 h K Initial value of neural network base width value representing h particle of Kth iteration, setting b0 h K Maximum value of (1) is P 8,MAX ＝40，b0 h K Minimum value of (A) is P 8,MIN ＝0.01，w0 h K Initial value, w0, of neural network weight value representing the h particle of the Kth iteration h K Maximum value of (1) is P 9,MAX ＝40,w0 h K Minimum value of (A) is P 9,MIN ＝0.01；
The upper limit of the particle position is:
P MAX ＝[P 1,MAX ,P 2,MAX ,P 3,MAX ,P 4,MAX ,P 5,MAX ,P 6,MAX ,P 7,MAX ,P 8,MAX ,P 9,MAX ]
the lower limit of the particle position is: p MIN ＝[P 1,MIN ,P 2,MIN ,P 3,MIN ,P 4,MIN ,P 5,MIN ,P 6,MIN ,P 7,MIN ,P 8,MIN ,P 9,MIN ]
Setting the maximum value of the particle velocity to V MAX =0.5, minimum particle velocity V MIN =0.5, particle velocity V ∈ [ V ] MIN ,V MAX ]；
The objective function, i.e. the fitness function, is set as:
Figure BDA0001908158700000151
where t is the simulation time of the control system, V d (t) is the tracking target vehicle speed at the time t, V (t) is the actual tracking vehicle speed at the time t, and e (t) is the tracking error at the time t;
the particle flight speed update formula is as follows:
V h,d K+1 ＝WV h,d K +c 1 rand 1 (P h,d K -X h,d K )+c 2 rand 2 (P g,d K -X h,d K ) (17)
the particle position update formula is:
X h,d K+1 ＝X h,d K +V h,d K+1 ,K∈[1,L],h∈[1,N],d∈[1,D]
where K is the current iteration number of the algorithm, V h,d K+1 Represents the d-dimensional component, V, of the K +1 th iterative particle h flight velocity vector h,d K D-dimension component, X, representing the flight velocity vector of the K-th iteration particle h h,d K+1 D-dimensional component, X, representing the K +1 th iteration particle h position vector h,d K The d-dimensional component, P, representing the position vector of the K-th iteration particle h h,d K The d-dimension component, P, representing the individual extremum of the K-th iteration particle h g,d K D-dimensional component representing extremum of K-th iteration group, c 1 Is a first acceleration factor, c 2 Is a second acceleration factor, c 1 ＝c 2 ＝2，rand 1 Are distributed in [0,1 ]]First random value in between, rand 2 Is distributed in [0,1 ]]A second random value in between, W being the inertial weight;
the parameters after particle swarm optimization in the step 3 are as follows:
d =9 parameters of the control system after L =30 iterative optimizations are Kp0=1.078, respectively
*Ki0＝160，*Kd0＝0.01，*ηp0＝0.01，*ηi0＝1，*ηd0＝1，*c0＝0.01，*b0＝40，*w0＝0.01；
Wherein K P0 =1.078 is the initial value of the proportionality coefficient of the PID controller after optimization,. K i0 =160 is the initial value of the proportionality coefficient of the PID controller after optimization, # K d0 =0.01 is the initial value of the proportionality coefficient of the optimized PID controller; * η p0=0.01 is an initial value of the proportional coefficient learning rate of the optimized PID controllerη i0=1 is an initial value of an integral coefficient learning rate of the optimized PID controller, and η d0=0.01 is an initial value of a differential coefficient learning rate of the optimized PID controller; * c0=0.01 is an initial value of a central value of the optimized neural network, b0=40 is an initial value of a base width value of the optimized neural network, and w0=0.01 is an initial value of a weight value of the optimized neural network; the dimension of the central vector c of the neural network is a matrix of 3 × 6, the 18 values are initialized to be equal to c0, the dimension of the central vector b of the neural network is a matrix of 1 × 6, the 6 values are initialized to be equal to b0, the dimension of the central vector w of the neural network is a matrix of 1 × 6, and the 6 values are initialized to be equal to w0;
and 4, step 4: initializing and assigning the parameters after particle swarm optimization to a radial basis function (PID) controller;
and 5: obtaining initial throttle opening or initial brake pedal position through an initialized radial basis function neural network PID controller, inputting the initial throttle opening or the initial brake pedal position into an automobile dynamic model to calculate actual tracking vehicle speed V (tau), wherein tau belongs to 0 MAX ]τ is the simulation time, T MAX To simulate a maximum time, and T MAX ＝1180s；
Step 6: actually tracking a vehicle speed V (tau) and inputting A (tau-1) of a tau-1 moment output by a PID controller into a neural network, adjusting parameters of a radial basis neural network and the PID controller according to a feedback error of the speed, increasing a time step by a simulation time tau, transferring to a step 5, and executing in a circulating way until the simulation time tau reaches a simulation maximum time T MAX 。
The feedback error of the speed in the step 6 is V (tau) -V R (τ)，V d (τ)-V(τ)；
The parameters of the radial basis function neural network in the step 6 are as follows: a center vector c, a base width vector b, and a weight vector w.
PID in step 6 the parameters of the controller are: proportional coefficient K of PID controller p Integral coefficient K of PID controller i Differential coefficient K of PID controller d ；
In step 6, the simulation time τ is increased by a time step: τ = τ + Δτ, Δ τ being the time step, and Δ τ =0.04s;
τ∈[0,T MAX ]τ is the simulation time, T MAX To simulate the maximum time.
RBF-PID is radial basis function neural network and PID, PSO-RBF-PID is radial basis function neural network and PID based on particle swarm.
As shown in fig. 1, a framework of the control system includes a longitudinal dynamics model and a controller model based on a radial basis function neural network and a PID optimized by particle swarm, the controller model optimizes initial parameters offline by adopting a particle swarm optimization, the radial basis function neural network and the PID are combined to adjust parameters in an online adaptive manner, the whole process is controlled intelligently, manual parameter adjustment is not needed, and higher control precision is realized. The dynamic model is used as a controlled object and is based on the input accelerator opening degree A T Position A of the brake pedal B And outputting the actual speed V of the tracked vehicle, the error e of the speed of the target vehicle and the speed of the tracked vehicle and the speed V of the tracked vehicle, and dynamically adjusting the opening of a throttle valve and the position of a brake pedal on line as two inputs of a control model to form closed-loop control.
As shown in fig. 3, the overall framework of vehicle dynamics includes an engine model, a transmission system model, a vehicle model, and a brake model. The transmission system model comprises a hydraulic torque converter model, a transmission model and a logic gear shifting model.
As shown in FIG. 5, the network structure topology is a feedforward neural network, which has simple structure, fast learning speed, capability of processing overfitting and capability of parallel computing and processing nonlinear systems.
As shown in fig. 7, a new european driving cycle NEDC is selected as a target speed for tracking, and online speed tracking control is realized by a controller, wherein the working conditions of the new european driving cycle include multiple scenes such as urban roads and suburban roads, and the range span of speed change is large and is between 0 and 120 km/h.
As shown in FIGS. 8 and 9, after the loop execution is finished, the tracking effect and the speed tracking error of the three controllers are respectively within the speed error range of [ -1.1770m/s and 1.8316m/s ] of the PID controller, the speed error range of the RBF-PID controller is [ -0.8380m/s and 0.6862m/s ] and the speed error range of the PSO-RBF-PID controller is [ -0.1559m/s and 0.2112m/s ].
Selecting the maximum speed error e max Mean value e v And variance e m The three are used as performance indexes of precision.
Figure BDA0001908158700000171
It can be seen from fig. 10 that the maximum speed error e of the three controllers max Sequentially 1.8316m/s,0.6862m/s and 0.2112m/s; mean value e v Sequentially is 0.2321,0.0559 and 0.0186; variance e m 0.3249,0.0320 and 0.0029 in sequence.
Local precision: maximum speed error e of three controllers max Are sequentially reduced, so the local precision of the PID-RBF controller based on particle swarm optimization is superior to that of the other two controllers.
Global precision: mean value e of PID controller v Much larger than those of the other two controllers, lower global control precision, and e of the PSO-RBF-PID controller v The value is smaller than that of the RBF-PID controller, so the overall precision of the RBF-PID controller based on particle swarm optimization is better than that of the other two controllers.
Stability: variance e of RBF-PID controller based on particle swarm optimization m The value of (c) is the smallest and therefore the most stable control, the next most so for the RBF-PID controller, the least stable PID controller.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made or substituted in a similar manner to the embodiments described herein by those skilled in the art without departing from the spirit of the invention or exceeding the scope thereof as defined in the appended claims.

Claims (1)

1. A particle swarm optimized radial basis function neural network vehicle speed tracking method is characterized by comprising the following steps:
step 1: constructing an automobile dynamics model through an engine model, a transmission system model, a vehicle model and a brake model;
step 2: establishing a radial basis function neural network model, calculating parameters of the radial basis function neural network model through a gradient descent method, and adaptively adjusting the parameters through the radial basis function neural network model by the PID controller to construct a radial basis function neural network PID controller;
and step 3: performing offline optimization through a particle swarm optimization algorithm to obtain parameters after particle swarm optimization;
and 4, step 4: initializing and assigning the parameters after particle swarm optimization to a radial basis function (PID) controller;
and 5: obtaining initial throttle opening or initial brake pedal position through an initialized radial basis function neural network PID controller, inputting the initial throttle opening or the initial brake pedal position into an automobile dynamic model to calculate actual tracking vehicle speed V (tau), wherein tau belongs to 0 MAX ]τ is the simulation time, T MAX The simulation maximum time;
step 6: inputting the actual tracking vehicle speed V (tau) and the A (tau-1) of the tau-1 moment output by the PID controller into the neural network, adjusting the parameters of the radial basis function neural network and the PID controller according to the feedback error of the speed, increasing the time step length of the simulation time tau, transferring to the step 5, and executing in a circulating way until the simulation time tau reaches the maximum simulation time T MAX ；
The engine model in step 1 is:
Figure FDA0003906134610000011
wherein, T e (t) effective torque of the engine at time t, N e (t) is the rotational speed of the crankshaft at time t, A T (T) is the opening of the throttle valve at time T, T i (t) impeller torque requested for crankshaft shift at time t, I e Is the rotational inertia of the engine crankshaft;
the transmission system model in the step 1 is as follows:
Figure FDA0003906134610000012
wherein N is e (T) is the speed of rotation of the crankshaft at time T, K (T) is the capacity factor at time T, T i (T) impeller torque requested for crankshaft shift at time T, T q (t) is the torque of the output shaft of the torque converter at time t, R TQ (t) is the torque factor at time t, R TR (T) is the transmission ratio of the variator at time T, T o (t) is the output shaft torque of the automatic transmission at time t, η t Is the efficiency of the automatic transmission, N m (t) is the input shaft rotational speed of the automatic transmission at time t, N o (t) is the rotational speed of the output shaft of the automatic transmission at time t, N w (t) is the speed of rotation of the wheel at time t, R fd Is the main reducer transmission ratio, K (t) and R TQ (t) is determined by the following expression:
Figure FDA0003906134610000021
where f2 is the capacity coefficient, f3 is the torque conversion coefficient, N m (t) the input shaft rotation speed of the automatic transmission at time t, N e (t) the rotational speed of the crankshaft at time t;
the vehicle model in step 1 is:
Figure FDA0003906134610000022
wherein, I v Is the moment of inertia of the rotor and,
Figure FDA0003906134610000024
is the derivative of the rotational speed of the wheel at time t, R fd Is the main reducer transmission ratio, T o (T) is the output shaft torque of the automatic transmission at time T, T load (t) istorque of the load at time t, V (t) an actual tracking vehicle speed at time t, r a radius of the wheel, N w (t) is the speed of rotation of the wheel at time t, R load，0 Is the coefficient of friction resistance, R load，2 Is the aerodynamic drag coefficient, T u (t) torque of braking at time t;
in the step 1, the brake model is as follows:
Figure FDA0003906134610000023
wherein r is the radius of the wheel, A B (T) position of the brake pedal at time T, T u (t) is the braking torque at time t;
the step 2 of establishing the radial basis function neural network model comprises the following steps:
the input vector of the radial basis function neural network is:
X＝(x 1 ，x 2 ，x 3 ) T
wherein x is 1 Is the output A (t-1), x of the PID controller at time t-1 2 Is the actual tracking vehicle speed V (t), x at time t 3 Actual tracking vehicle speed V (t-1) at time (t-1);
the number of nodes of the input layer of the radial basis function neural network is 3;
the number of nodes of the hidden layer of the radial basis function neural network is 6;
the output of the radial basis function neural network is a model output V at the time t R (t), the number of nodes of the output layer of the radial basis function neural network is 1;
in the radial basis function neural network structure, X = [ X ] 1 ，x 2 ，…，x n ] T As input vector, x, of the radial basis function neural network i I =1,2, \8230nis the ith input quantity of X, and the number of nodes of the input layer of the radial basis function neural network is n =3,h = [ h = [ ] 1 ，h 2 ，…，h m ] T Hiding layer node radial basis vectors, h, for a radial basis function neural network j J =1,2, \ 8230and m is the radial basis of the hidden layer node of the jth neuron, and the neural network hiding of the radial basisThe number of nodes of a layer is m =6, and the radial basis function is a gaussian function:
Figure FDA0003906134610000031
wherein, X = [ X ] 1 ，x 2 ，…，x n ] T Is the input vector, x, of the radial basis function neural network i I =1,2, \ 8230n is the ith input quantity of X, c j ＝[c j，1 ，c j，2 ，…，c j，n ] T Is the central vector of the node of the hidden layer of the jth neuron, c j，i I =1,2, \8230nis the i-th central value of the j-th neuron hidden layer node, b = [ b ] 1 ，b 2 ，…，b m ] T A base width vector of nodes of the hidden layer, b j J =1,2, \8230mis the base width of the hidden layer node of the jth neuron, w = [ w 1 ，w 2 ，…，w m ] T Is a weight vector, w, for the connection of the hidden layer to the output layer i J =1,2, \8230, m is a weight value connected from the neuron of the ith hidden layer to the output layer, VR (t) is the output of the neural network, the number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
the output of the radial basis function neural network at the time t is V R (t), the output of the automobile dynamic model is the actual tracking speed V (t) at the time t, and the performance index function of the radial basis function neural network is as follows:
Figure FDA0003906134610000032
the radial basis function neural network adopts supervised learning, and in order to minimize the value of J (t) at the time t, a gradient descent method is adopted to continuously update the central vector c of the hidden layer node j ＝[c j，1 ，c j，2 ，…，c j，n ] T Base width vector b = [ b ] of hidden layer node 1 ，b 2 ，…，b m ] T And weight vector w = [ w ] for hidden layer to output layer connection 1 ，w 2 ，…，w m ] T The number of nodes of the input layer of the radial basis function neural network is n =3, and the number of nodes of the hidden layer of the radial basis function neural network is m =6;
in the step 2, the parameters of the radial basis function neural network model calculated by the gradient descent method are as follows:
Figure FDA0003906134610000033
the number of nodes of the input layer of the radial basis function neural network is n =3, the number of nodes of the hidden layer of the radial basis function neural network is m =6, beta is the learning rate of the neural network, alpha is a momentum factor, beta, alpha is an element (0, 1), c is j，i (t) is the ith central value of the jth neuron hidden layer node at the time t, c j，i (t-1) is the ith central value of the jth neuron hidden layer node at time t-1, c j，i (t-2) is the ith central value, Δ c, of the jth neuron hidden layer node at time t-2 j，i (t) an increment of an ith central value of a jth neuron hidden layer node at time t;
X＝[x 1 ，x 2 ，…，x n ] T is the input vector of the radial basis function neural network, c j ＝[c j，1 ，c j，2 ，…，c j，n ] T Is the central vector of the node of the hidden layer of the jth neuron, b j J =1,2, \8230wherem is the base width of the hidden layer node of the jth neuron j J =1,2, \ 8230that m is the weight value of the connection from the j hidden layer neuron to the output layer, Δ c j (t) is the increment of the weight of the jth neuron hidden layer node at time t, V R (t) is the output of the radial basis function neural network at the time t, and V (t) is the actual tracking vehicle speed at the time t in the step 1;
b j (t) base width of the jth neuron hidden layer node at time t, b j (t-1) is the base width of the hidden layer node of the jth neuron at the time t-1, b j (t-2) the jth neuron concealment at time t-2Base width of layer node, Δ b j (t) is the increment of the base width of the jth neuron hidden layer node at the time t, h j J =1,2, \ 8230, m is the radial basis of the hidden layer node of the jth neuron;
w j (t) is the weight of the hidden layer node of the jth neuron at time t, w j (t-1) is the weight of the hidden layer node of the jth neuron at time t-1, w j (t-2) is the weight of the hidden layer node of the jth neuron at time t-2, Δ w j (t) is the increment of the weight of the jth neuron hidden layer node at time t;
in the step 2, the PID controller adaptively adjusts parameters through the radial basis function neural network model to construct a radial basis function neural network PID controller:
the controller uses an increment PID control theory, and the control error is as follows:
e(t)＝V d (t)-V(t)(9)
wherein, V d (t) is the tracking target vehicle speed at the time t, V (t) is the actual tracking vehicle speed at the time t, and e (t) is the tracking error at the time t;
the input of the controller and the control algorithm are:
Figure FDA0003906134610000041
Figure FDA0003906134610000042
wherein e (t) is the tracking error at time t, e (t-1) is the tracking error at time t-1, e (t-2) is the tracking error at time t-2, xc (1) is the first input parameter of the PID controller, xc (2) is the second input parameter of the PID controller, xc (3) is the third input parameter of the PID controller, A (t) is the output of the PID controller at time t, A (t-1) is the output of the PID controller at time t-1, Δ A (t) is the increment of A (t) at time t, K p (t) is the proportional coefficient at time t of the PID controller, K i (t) is the integral coefficient of PID controller at time t, K d (t) is a PID controllerAnd (3) setting the performance indexes of parameter adjustment of the PID controller as the following according to the differential coefficient at the time t:
Figure FDA0003906134610000051
wherein, V d (t) is the tracking target vehicle speed at the time t, and V (t) is the actual tracking vehicle speed at the time t;
to make J at t time C (t) minimum, adjusting the gain parameter of the PID using a gradient descent method
Figure FDA0003906134610000052
In the formula,. DELTA.K P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of PID at time t, η P0 Is an initial value, η, of the learning rate of the proportional coefficients of the PID controller i0 Is an initial value, η, of the learning rate of the integral coefficient of the PID controller d0 Is an initial value of the learning rate of the differential coefficient of the PID controller;
Figure FDA0003906134610000053
wherein x is 1 The input vector for the radial basis function neural network is X = (X) 1 ，x 2 ，x 3 ) T The first element of (1), i.e. x 1 ＝A(t-1)，b j J =1,2, \ 8230that m is the base width of the hidden layer node of the jth neuron, w j J =1,2, \ 8230that m is the weight value of the connection from the j hidden layer neuron to the output layer, h j J =1,2, \ 8230m is the radial basis of the hidden layer node of the j-th neuron, c j，1 J =1,2, \ 8230, m is the 1 st central value of the hidden layer node of the jth neuron;
the output of the PID controller at time t is:
A(t)＝A(t-1)+(K P0 +ΔK P (t))xc(1)+(K i0 +ΔK i (t))xc(2)+(K d0 +ΔK d (t))xc(3)
wherein, K P0 Is the initial value of the proportionality coefficient, K, of the PID controller i0 Is the initial value of the integral coefficient of the PID controller, K d0 Is the initial value of the differential coefficient, Δ K, of the PID controller P (t) is the increment of the proportionality coefficient of PID at time t, Δ K i (t) is the increment of the integral coefficient of PID at time t, Δ K d (t) is the increment of the differential coefficient of the PID at the time t, xc (1) is a first input parameter of the PID controller, xc (2) is a second input parameter of the PID controller, and xc (3) is a third input parameter of the PID controller;
a (t) is introduced to simplify the control of the speed, and when A (t) is a positive value, it is regarded as the opening A of the throttle valve T When A (t) is a negative value, the absolute value of A (t) is regarded as the position A of the brake pedal B ；
In the step 3, the off-line optimization is realized through a particle swarm optimization algorithm as follows:
initializing particle position and speed information, setting the population scale to be N, the total iteration number to be L, and the dimension of the particle position information to be D, namely D parameters to be optimized, namely the particle position:
Figure FDA0003906134610000061
wherein the content of the first and second substances,
Figure FDA0003906134610000062
the initial value of the scaling factor of the PID controller representing the h-th particle of the kth iteration,
Figure FDA0003906134610000063
maximum value of (1) is P 1，MAX ，
Figure FDA0003906134610000064
Minimum value of (A) is P 1，MIN ，
Figure FDA0003906134610000065
The initial value of the integration coefficient of the PID controller representing the h-th particle of the kth iteration,
Figure FDA0003906134610000066
maximum value of (1) is P 2，MAX ，
Figure FDA0003906134610000067
Minimum value of (1) is P 2，MAX ，
Figure FDA0003906134610000068
The initial value of the differential coefficient of the PID controller representing the h-th particle of the kth iteration,
Figure FDA0003906134610000069
maximum value of (1) is P 3，MAX ，
Figure FDA00039061346100000610
Minimum value of (A) is P 3，MIN ，ηp0 h K Initial value of the learning rate of the scale factor, η p0, of the PID controller representing the h-th particle of the Kth iteration h K Maximum value of (1) is P 4，MAX ，ηp0 h K Minimum value of (1) is P 4，MIN ，ηi0 h K Initial value of the learning rate of the integral coefficients of the PID controller representing the h-th particle of the Kth iteration, η i0 h K Maximum value of (1) is P 5，MAX ，ηi0 h K Minimum value of (A) is P 5，MIN ，ηd0 h K Setting η d0 as an initial value of a learning rate of a differential coefficient of a PID controller for expressing the h-th particle of the Kth iteration h K Maximum value of (1) is P 6，MAX ，ηd0 h K Minimum value of (A) is P 6，MIN ；c0 h K Initial value of the central value of the neural network representing the h particle of the Kth iteration, set c0 h K Maximum value of (1) is P 7，MAX ，c0 h K Minimum value of (A) is P 7，MIN ，b0 h K Setting b0 as the initial value of the neural network base width value of the h particle of the Kth iteration h K Maximum value of (1) is P 8，MAX ，b0 h K Minimum value of (A) is P 8，MIN ，w0 h K Initial value, w0, of neural network weight value representing the h particle of the Kth iteration h K Maximum value of (1) is P 9，MAX ，w0 h K Minimum value of (A) is P 9，MIN ；
The upper limit of the particle position is:
P MAX ＝[P 1，MAX ，P 2，MAX ，P 3，MAX ，P 4，MAX ，P 5，MAX ，P 6，MAX ，P 7，MAX ，P 8，MAX ，P 9，MAX ]
the lower limit of the particle position is: p MIN ＝[P 1，MIN ，P 2，MIN ，P 3，MIN ，P 4，MIN ，P 5，MIN ，P 6，MIN ，P 7，MIN ，P 8，MIN ，P 9，MIN ]
Setting the maximum value of the particle velocity to V MAX Minimum particle velocity of V MIN Velocity of particle V ∈ [ V ] MIN ，V MAX ]；
The objective function, i.e. the fitness function, is set as:
Figure FDA00039061346100000611
wherein t is the simulation time of the control system, and e (t) is the tracking error at the moment t;
the particle flight speed update formula is as follows:
V h，d K+1 ＝WV h，d K +c 1 rand 1 (P h，d K -X h，d K )+c 2 rand 2 (P g，d K -X h，d K ) (17)
the particle position update formula is:
X h，d K+1 ＝X h，d K +V h，d K+1 ，K∈[1，L]，h∈[1，N]，d∈[1，D]
where K is the current iteration number of the algorithm, V h，d K+1 Represents the d-dimensional component, V, of the K +1 th iterative particle h flight velocity vector h，d K D-dimensional component, X, representing the K-th iterative particle h-flight velocity vector h，d K+1 D-dimensional component, X, representing the K +1 th iteration particle h position vector h，d K Representing the d-dimensional component, P, of the K-th iteration particle h-position vector h，d K The d-dimension component, P, representing the individual extremum of the K-th iteration particle h g，d K D-dimensional component representing extremum of K-th iteration group, c 1 Is a first acceleration factor, c 2 Is the second acceleration factor, rand 1 Are distributed in [0,1 ]]First random value in between, rand 2 Is distributed in [0,1 ]]W is the inertial weight;
the parameters after particle swarm optimization in the step 3 are as follows:
d parameters of the control system after L times of iterative optimization are respectively as follows:
*K P0 ，*K i0 ，*K d0 ，*ηp0，*ηi0，*ηd0，*c0，*b0，*w0；
wherein K p0 Is the initial value of the proportional coefficient of the optimized PID controller i0 Is the initial value of the proportional coefficient of the optimized PID controller d0 Is the initial value of the proportional coefficient of the optimized PID controller; * η p0 is an initial value of a proportional coefficient learning rate of the optimized PID controller, η i0 is an initial value of an integral coefficient learning rate of the optimized PID controller, and η d0 is an initial value of a differential coefficient learning rate of the optimized PID controller; * c0 is an initial value of a central value of the optimized neural network, b0 is an initial value of a base width value of the optimized neural network, and w0 is an initial value of a weight value of the optimized neural network; the central vector c of the neural network has a 3 x 6 dimensional matrix, and the 18 values are initialized to be equal and are all x c0, and the neural networkThe dimension of the central vector b of (a) is 1 × 6, the 6 values are initialized to be equal to b0, the dimension of the central vector w of the neural network is 1 × 6, and the 6 values are initialized to be equal to w0;
the feedback error of the speed in the step 6 is V (tau) -V R (τ)，V d (τ)-V(τ)；
The parameters of the radial basis function neural network in the step 6 are as follows: a center vector c, a base width vector b, and a weight vector w;
the parameters of the PID controller in the step 6 are as follows: proportional coefficient K of PID controller p Integral coefficient K of PID controller i Differential coefficient K of PID controller d ；
In step 6, the simulation time τ is increased by a time step: τ = τ + Δ τ, Δ τ being the time step;
τ∈[0，T MAX ]τ is the simulation time, T MAX To simulate the maximum time.
CN201811541341.4A 2018-12-17 2018-12-17 Particle swarm optimization radial basis function neural network vehicle speed tracking method Active CN109376493B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201811541341.4A CN109376493B (en) 2018-12-17 2018-12-17 Particle swarm optimization radial basis function neural network vehicle speed tracking method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201811541341.4A CN109376493B (en) 2018-12-17 2018-12-17 Particle swarm optimization radial basis function neural network vehicle speed tracking method

Publications (2)

Publication Number Publication Date
CN109376493A CN109376493A (en) 2019-02-22
CN109376493B true CN109376493B (en) 2023-02-03

Family

ID=65374094

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201811541341.4A Active CN109376493B (en) 2018-12-17 2018-12-17 Particle swarm optimization radial basis function neural network vehicle speed tracking method

Country Status (1)

Country Link
CN (1) CN109376493B (en)

Families Citing this family (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111027235B (en) * 2020-01-07 2022-08-30 湖南工业大学 Heavy-duty train sliding mode tracking control method with input saturation
CN111290263B (en) * 2020-03-23 2022-10-11 东南大学 Improved PID (proportion integration differentiation) optimization control algorithm based on RBFNN (radial basis function network) and BAS (basic automatic component analysis)
CN111862157B (en) * 2020-07-20 2023-10-10 重庆大学 Multi-vehicle target tracking method integrating machine vision and millimeter wave radar
CN114056386B (en) * 2020-07-30 2023-08-08 比亚迪股份有限公司 Vehicle speed control method and device, storage medium and vehicle
CN111950204B (en) * 2020-08-13 2022-04-19 一汽解放汽车有限公司 Hinge structure optimization method and device, computer equipment and storage medium
CN112564557B (en) * 2020-12-14 2023-02-24 华侨大学 Control method, device and equipment of permanent magnet synchronous motor and storage medium
CN112644344A (en) * 2020-12-29 2021-04-13 武汉格罗夫氢能汽车有限公司 BP neural network-based power distribution optimization system and optimization method
CN112947055B (en) * 2021-03-04 2022-09-09 北京交通大学 Method for tracking and controlling displacement speed of magnetic suspension train based on echo state network
CN112947056B (en) * 2021-03-04 2022-10-14 北京交通大学 Magnetic-levitation train displacement speed tracking control method based on IGWO-BP-PID
CN113085858A (en) * 2021-04-27 2021-07-09 湖北文理学院 Vehicle speed tracking control method, device, equipment and storage medium
CN113756973B (en) * 2021-08-27 2023-05-12 东风商用车有限公司 Self-adaptive control method for minimum torque of automobile engine
CN114118365B (en) * 2021-11-08 2022-09-06 北京理工大学 Cross-medium aircraft rapid water inlet approximate optimization method based on radial basis network
CN115009278B (en) * 2022-08-08 2022-11-29 潍柴动力股份有限公司 Cruise control method, device, equipment and storage medium
CN116418261B (en) * 2023-02-22 2024-05-03 深圳市一本自动化有限公司 Motor PID control method based on radial basis function neural network

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102109821A (en) * 2010-12-30 2011-06-29 中国科学院自动化研究所 System and method for controlling adaptive cruise of vehicles
CN105136469A (en) * 2015-07-23 2015-12-09 江苏大学 Unmanned vehicle speed control method based on PSO and RBF neutral network
CN106128208A (en) * 2016-08-19 2016-11-16 武汉理工大学 A kind of research automobile driving simulator of rotatable passenger cabin
CN107255923A (en) * 2017-06-14 2017-10-17 哈尔滨工程大学 Drive lacking unmanned boat Track In Track control method based on the RBF ICA CMAC neutral nets recognized
CN107729706A (en) * 2017-11-29 2018-02-23 湖南科技大学 A kind of kinetic model construction method of Nonlinear Mechanical Systems
CN108227491A (en) * 2017-12-28 2018-06-29 重庆邮电大学 A kind of intelligent vehicle Trajectory Tracking Control method based on sliding formwork neural network
CN108646763A (en) * 2018-07-18 2018-10-12 扬州大学 A kind of autonomous driving trace tracking and controlling method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070294017A1 (en) * 2006-06-20 2007-12-20 Eaton Corporation Method for estimating clutch engagement parameters in a strategy for clutch management in a vehicle powertrain

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102109821A (en) * 2010-12-30 2011-06-29 中国科学院自动化研究所 System and method for controlling adaptive cruise of vehicles
CN105136469A (en) * 2015-07-23 2015-12-09 江苏大学 Unmanned vehicle speed control method based on PSO and RBF neutral network
CN106128208A (en) * 2016-08-19 2016-11-16 武汉理工大学 A kind of research automobile driving simulator of rotatable passenger cabin
CN107255923A (en) * 2017-06-14 2017-10-17 哈尔滨工程大学 Drive lacking unmanned boat Track In Track control method based on the RBF ICA CMAC neutral nets recognized
CN107729706A (en) * 2017-11-29 2018-02-23 湖南科技大学 A kind of kinetic model construction method of Nonlinear Mechanical Systems
CN108227491A (en) * 2017-12-28 2018-06-29 重庆邮电大学 A kind of intelligent vehicle Trajectory Tracking Control method based on sliding formwork neural network
CN108646763A (en) * 2018-07-18 2018-10-12 扬州大学 A kind of autonomous driving trace tracking and controlling method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于三自由度直升机模型的粒子群优化神经网络控制算法研究;王显博;《中国优秀硕士学位论文全文数据库》;20170315(第03期);第20-36页 *

Also Published As

Publication number Publication date
CN109376493A (en) 2019-02-22

Similar Documents

Publication Publication Date Title
CN109376493B (en) Particle swarm optimization radial basis function neural network vehicle speed tracking method
CN106154831B (en) A kind of intelligent automobile longitudinal direction neural network sliding mode control method based on learning method
CN112148001B (en) Intelligent fleet longitudinal following control method based on fuzzy model predictive control
CN101598109B (en) Intelligent control method for windmill generator yaw system
CN111267831A (en) Hybrid vehicle intelligent time-domain-variable model prediction energy management method
CN110949366B (en) Terminal sliding mode control method of RBF neural network applying intelligent vehicle longitudinal speed control
CN111608868B (en) Maximum power tracking adaptive robust control system and method for wind power generation system
CN101441441B (en) Design method of intelligent swing-proof control system of crane
CN103235620A (en) Greenhouse environment intelligent control method based on global variable prediction model
CN103324085A (en) Optimal control method based on supervised reinforcement learning
CN107919813A (en) Ultrasound electric machine rotating speed control based on fuzzy neural network
CN110347155A (en) A kind of intelligent vehicle automatic Pilot control method and system
CN110594317B (en) Starting control strategy based on double-clutch type automatic transmission
CN110989597A (en) Adaptive path tracking method of integrated fuzzy neural network
Yuan et al. Neural network based self-learning control strategy for electronic throttle valve
CN112874504B (en) Control method of extensible entropy weight combined controller
CN113253779A (en) Heat pump temperature control system based on particle swarm fuzzy PID algorithm
CN109910863B (en) Control method based on special transmission for plug-in hybrid electric vehicle
CN110162910A (en) A kind of hill start optimization method based on technology of Internet of things
CN110758413A (en) Train speed self-adaptive control method based on system parameter identification
CN113093526A (en) Overshoot-free PID controller parameter setting method based on reinforcement learning
CN108549213A (en) A kind of speed ratio control method based on RBF neural PID
CN104527637B (en) Method for controlling hybrid power vehicle and system
CN113741199B (en) Whole vehicle economical speed planning method based on intelligent network connection information
CN113232651B (en) Fuel automobile ecological self-adaptive cruise control method based on ADHDP

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant