CN109597308A - Pilotless automobile model predictive controller design method based on kinetic model - Google Patents
Pilotless automobile model predictive controller design method based on kinetic model Download PDFInfo
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- 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
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
Abstract
The pilotless automobile model predictive controller design method based on kinetic model that the invention discloses a kind of: new vehicle kinetic model is established；Design the pilotless automobile model predictive controller based on new vehicle kinetic model；1. predicting using in the new vehicle kinetic model that present operating point linearizes output state of the system in prediction time domain；2. being exported using obtained system prediction and given reference output constructing optimization problem；3. solving optimization problem is applied to the one-component of U (k) as the optimum control amount at current time in system.The present invention increases car speed as control amount, while introducing error compensation item to make up model accuracy, linearisation and discretization bring accumulated error during prediction, so that automatic driving vehicle be made to have better trajectory track effect.
Description
Technical field
The invention belongs to pilotless automobile controller design fields, and more specifically, it relates to one kind to be based on dynamics
The pilotless automobile model predictive controller design method of model.
Background technique
In the past few years, as the most important a part of artificial intelligence, while global positioning system is benefited from
(GPS), the development of radar system and machine vision, the unmanned extensive concern for obtaining various circles of society.It is unmanned can be with
It is divided into four part shown in FIG. 1: global path planning, environment sensing, local paths planning and trajectory track.By Lateral Controller
Trajectory track controller with longitudinal controller composition is unpiloted important component.
Originally, scholars complete trajectory track task using proportional-integral-differential (PID) controller.But due to
Automobile is multi-input multi-output system, and the limitation of ambient enviroment and vehicle itself physical structure can bring a variety of constraints, PID
The control effect of controller is unsatisfactory.Then, model predictive controller (MPC) is used for nothing by its advantage protruded
The trajectory track of people's driving vehicle.
MPC is a kind of effective ways for handling multiple constraint and Multivariable.It uses control pair in current sample time
The model of elephant carrys out the state of forecasting system each sampling instant in prediction time domain.On the basis of predicted state, calculating makes pre-
The smallest control sequence of error between survey state and reference state, and the control sequence needs to meet all constraint condition.
Finally it is applied to the one-component of sequence as the optimal input at current time in system.It is pre- used in prediction process
It is most important for the quality of control effect to survey model.Currently, there is a kind of highly effective auto model not yet to describe vehicle
Characteristic, and existing kinetic model is only using front wheel slip angle as control amount, prevents longitudinally controlled and crosswise joint from having
Combine to machine.New type power model proposed by the present invention increases car speed work compared with existing kinetic model
For control amount, vehicle can be made to change speed according to the demand of crosswise joint.The characteristic of auto model and the actual characteristic of vehicle
Between error it is inevitable, the linearisation of this external model and discretization also bring along state error.Therefore, invention increases
Error compensation item carrys out the accumulated error during compensation prediction.The above method not only has specific theory significance, but also has
Very strong practical application value and realistic meaning.
Summary of the invention
Purpose of the invention is to overcome the shortcomings in the prior art, provides a kind of nobody based on kinetic model and drives
Car model Design of Predictive method is sailed, increases car speed as control amount, while introducing error compensation item to make up
Model accuracy, linearisation and discretization bring accumulated error during prediction, so that it is more preferable to have automatic driving vehicle
Trajectory track effect.
The purpose of the present invention is what is be achieved through the following technical solutions.
Pilotless automobile model predictive controller design method based on kinetic model of the invention, including following step
It is rapid:
Step 1: establishing new vehicle kinetic model
Using the side force of tire and tractive force model proposed by Pacejka, longitudinal force, turning torque, Hui Zhengli are described
Numerical relation between square, the moment of resistance, side drift angle and slip rate；Tire force is expressed as form:
Wherein, FlFor longitudinal force of tire, ClFor the longitudinal rigidity of tire, s indicates slip rate, FcFor side force of tire, CcFor
The lateral rigidity of tire, α indicate side drift angle；
Ignore automobile in the movement of vertical direction, the structure and stress of automobile are described with single track model, according to newton second
Law obtains the stress balance equation on following three directions:
Wherein, m indicates the quality of automobile, and x is abscissa of the centre of gravity of vehicle under vehicle-mounted coordinate system, and y is that centre of gravity of vehicle exists
Ordinate under vehicle-mounted coordinate system,For the course angle of automobile,For longitudinal velocity of the automobile under vehicle-mounted coordinate system,For automobile
Lateral velocity under vehicle-mounted coordinate system,For the first derivative of course angle, the i.e. angular speed of automobile in the vertical direction,For
Longitudinal acceleration of the automobile under vehicle-mounted coordinate system,For transverse acceleration of the automobile under vehicle-mounted coordinate system,It is automobile perpendicular
The upward angular acceleration of histogram, FxfThe power for being front-wheel suffered by x-axis direction, FxrThe power for being rear-wheel suffered by x-axis direction, FyfFor
Front-wheel power suffered by y-axis direction, δ represent the front wheel slip angle of automobile, FyrFor rear-wheel power suffered by y-axis direction, I is automobile
Rotary inertia, a are the distance between centre of gravity of vehicle and front axle, and b is the distance between centre of gravity of vehicle and rear axle；
Fxf、Fxr、FyfAnd FyrIt is calculated by following formula using the longitudinal force and lateral force of tire:
Wherein, FlfFor the longitudinal force that front-wheel is subject to, FcfFor the lateral force that front-wheel is subject to, FlrFor the longitudinal force that rear-wheel is subject to,
FcrThe lateral force being subject to for rear-wheel；These types of power is calculated by formula (1), and wherein slip rate s and side drift angle α utilizes speed
It is obtained with wheel speed calculation；
Simultaneous formula (1), (2), (3), and new vehicle power is obtained after linearisation and Euler sliding-model control
Learn model:
Wherein, k indicates current sample time, " k+n ", n=1, adopting for n-th after 2,3 ... expression current sample times
The sample moment,Indicate the system mode at current time, Y is automobile under inertial coodinate system
Ordinate, X is abscissa of the automobile under inertial coodinate system, and the transposition of superscript " T " representing matrix, ξ (k+1) is next to adopt
The system mode at sample moment, u (k)=[v, δ]TIt being inputted for the control at current time, v indicates car speed,
It is exported for the system at current time, AkFor the state-transition matrix of system, BkFor the input matrix of system, C is the output square of system
Battle array；
Step 2: pilotless automobile model predictive controller of the design based on new vehicle kinetic model
1. utilizing in the new vehicle kinetic model that present operating point linearizes to system in prediction time domain
Output state is predicted:
Y (k)=Ψkξ(k|k)+ΘkU(k)+Γkγ(k) (5)
Wherein,Output for system in the following Np sampling instant, Np expression prediction time domain,
" k+n | k ", n=0,1 ..., NpIndicate the variable for+n sampling instants of kth predicted in k-th of sampling instant, ξe(k)=f
(ξ(k),u(k))-Akξ(k)-BkU (k) is the caused state error of linearisation, NcIndicate control time domain, ξ (k+1)=f (ξ
(k), u (k)) it is discrete non-linear vehicle dynamic model；
2. utilizing the system prediction output and given reference output building optimization problem obtained by formula (5):
Wherein, J (ξ (k), U (k)) is cost function；
3. solving optimization problem, optimal solution U (k) meets the needs of various physical constraints, comfort level and control precision, by U
(k) one-component u (k | k) is applied in system as the optimum control amount at current time.
Side drift angle α and slip rate s are obtained by the following formula in the first step::
Wherein, vc=vy cosδ-vxSin δ is the side velocity of tire, vxFor automobile along x-axis side under vehicle-mounted coordinate system
To speed, vyFor speed of the automobile under vehicle-mounted coordinate system along the y-axis direction, vl=vy sinδ+vxCos δ is the longitudinal direction of tire
Speed, r are the radius of tire, and w is the angular speed of tire.
The optimization problem constructed in second step specifically:
Meet: ξ (k+1)=Akξ(k)+Bku(k)
η (k)=C ξ (k)
U (k-1 | k)=u (k-1)
αmin≤α(k+i|k)≤αmax, i=0 ..., Np
Δ u (k+i | k)=u (k+i | k)-u (k+i-1 | k), i=0 ..., Np
Δumin≤Δu(k+i|k)≤Δumax, i=0 ..., Nc-1
Δ u (k+i | k)=0, i=Nc,…,Np
Wherein, ηrReference to provide exports, " | | * | |2" representing matrix Euclid norm, Q be output error power
Weight matrix, R are the weight matrix of controlling increment.Side drift angle α is limited in αminAnd αmaxBetween, in order to meet pilotless automobile
Requirement for stability and comfort, controlling increment Δ u are strictly limited in Δ uminWith Δ umaxBetween.In addition, in the time
SectionIt is interior, it is assumed that control amount u is a definite value.
Compared with prior art, the beneficial effects brought by the technical solution of the present invention are as follows:
(1) the control input invention increases speed as model, allows pilotless automobile according to the reality of road
Border situation and the demand of crosswise joint change the speed of vehicle, therefore can achieve preferably control effect.
(2) invention increases error compensation items, to compensate the linearisation and discretization of model during status predication
Caused accumulated error so prediction result is more accurate, and then can achieve more accurate trajectory track effect.
Detailed description of the invention
Fig. 1 is unpiloted hierarchical diagram；
Fig. 2 is longitudinal force of tire and lateral force schematic diagram under Different Ground coefficient of friction；
Fig. 3 is the single track illustraton of model of automobile；
Fig. 4 is the simulation result diagram at 18km/h；
Fig. 5 is the simulation result diagram at 45km/h；
Fig. 6 is the simulation result diagram at 72km/h.
Specific embodiment
In order to keep the objectives, technical solutions, and advantages of the present invention clearer, below from new vehicle kinetic model
Foundation, the design principle of model predictive controller and method for solving etc. are described further, following specific design methods
To explain the present invention, but it is not limited to the present invention.
Pilotless automobile model predictive controller design method based on kinetic model of the invention, including following step
It is rapid:
Step 1: establishing new vehicle kinetic model
In addition to gravity and air drag, all important power that automobile is subject to nearly all are acted directly on tire.Because
The complexity of tire force and non-linear selects a suitable tire model for establishing accurate vehicle dynamic model to pass
It is important.The present invention is used by the Pacejka side force of tire proposed and tractive force model.The model is by combining multiple triangle letters
To be fitted experimental data, it can be described between longitudinal force, turning torque, aligning torque, the moment of resistance, side drift angle and slip rate number
Numerical relation.If from longitudinal force shown in Fig. 2 and lateral force as the situation of change of slip rate and side drift angle can be seen that
Slip rate and side drift angle are defined in a certain range, and the relationship between longitudinal force and lateral force and slip rate and side drift angle can be with
It is approximately linear relationship.In fact, most of vehicle has good anti-lock braking system (ABS), so slip rate can be kept
In preferable operating point.Therefore, tire force can be expressed as form:
Wherein, FlFor longitudinal force of tire, ClFor the longitudinal rigidity of tire, s indicates slip rate, FcFor side force of tire, CcFor
The lateral rigidity of tire, α indicate side drift angle.
Ignore automobile in the movement of vertical direction, the structure and stress of automobile can be described with single track model shown in Fig. 3.It should
Model can characterize most kinetic characteristics relevant to stability of automobile.According to Newton's second law, it is available with
Stress balance equation on lower three directions:
Wherein, m indicates the quality of automobile, and x is abscissa of the centre of gravity of vehicle under vehicle-mounted coordinate system, and y is that centre of gravity of vehicle exists
Ordinate under vehicle-mounted coordinate system,For the course angle of automobile,For longitudinal velocity of the automobile under vehicle-mounted coordinate system,For vapour
Lateral velocity of the vehicle under vehicle-mounted coordinate system,For the first derivative of course angle, the i.e. angular speed of automobile in the vertical direction,
For longitudinal acceleration of the automobile under vehicle-mounted coordinate system,For transverse acceleration of the automobile under vehicle-mounted coordinate system,Exist for automobile
Angular acceleration on vertical direction, FxfThe power for being front-wheel suffered by x-axis direction, FxrThe power for being rear-wheel suffered by x-axis direction, Fyf
For front-wheel power suffered by y-axis direction, δ represents the front wheel slip angle of automobile, FyrFor rear-wheel power suffered by y-axis direction, I is automobile
Rotary inertia, a be the distance between centre of gravity of vehicle and front axle, b be the distance between centre of gravity of vehicle and rear axle.
Fxf、Fxr、FyfAnd FyrIt can be calculated by following formula using the longitudinal force and lateral force of tire:
Wherein, FlfFor the longitudinal force that front-wheel is subject to, FcfFor the lateral force that front-wheel is subject to, FlrFor the longitudinal force that rear-wheel is subject to,
FcrThe lateral force being subject to for rear-wheel.These types of power can be calculated by formula (1), and wherein slip rate s and side drift angle α are available
Speed and wheel speed calculation obtain:
Wherein, vc=vy cosδ-vxSin δ is the side velocity of tire, vxFor automobile along x-axis side under vehicle-mounted coordinate system
To speed, vyFor speed of the automobile under vehicle-mounted coordinate system along the y-axis direction, vl=vy sinδ+vxCos δ is the longitudinal direction of tire
Speed, r are the radius of tire, and w is the angular speed of tire.
Simultaneous formula (1), formula (2) and formula (3), non-linear dynamic model can be reduced to:
Wherein,For the state variable of system,Indicate that the derivative of state variable, Y are automobile used
Property coordinate system under ordinate, X be abscissa of the automobile under inertial coodinate system, superscript " T " indicate vector transposition, u=
[v,δ]TFor the input of model, v indicates the speed of vehicle,For the output of model.
By non-linear dynamic model (4) after present operating point linearisation, linear kinetic model can be obtained:
Wherein, Representative functionIn t moment pairPartial differential, BkFor the input matrix of system,C is the output matrix of system.
Using Euler discretization method by the available Discrete Linear kinetic simulation of linear kinetic model (5) discretization
Type, i.e. new vehicle kinetic model:
Wherein, k indicates current sample time, " k+n ", n=1, adopting for n-th after 2,3 ... expression current sample times
The sample moment,Indicate the system mode at current time, Y is automobile under inertial coodinate system
Ordinate, X is abscissa of the automobile under inertial coodinate system, and the transposition of superscript " T " representing matrix, ξ (k+1) is next to adopt
The system mode at sample moment, u (k)=[v, δ]TIt being inputted for the control at current time, v indicates car speed,
It is exported for the system at current time, AkFor the state-transition matrix of system, Ak=I+TAt, I is the unit matrix of suitable dimension, T
For the sampling period of system, BkFor the input matrix of system, Bk=TBt, C is the output matrix of system.
Step 2: pilotless automobile model predictive controller of the design based on new vehicle kinetic model
1. utilizing in the new vehicle kinetic model that present operating point linearizes to system in prediction time domain
Output state is predicted:
Y (k)=Ψkξ(k|k)+ΘkU(k)+Γkγ(k) (7)
Wherein,It is system in the following NpThe output of a sampling instant, NpIndicate prediction time domain,
" k+n | k ", n=0,1 ..., NpIndicate the variable for+n sampling instants of kth predicted in k-th of sampling instant,
ξe(k)=f (ξ (k), u (k))-Akξ(k)-BkU (k) is the caused state error of linearisation, NcWhen indicating control
Domain, ξ (k+1)=f (ξ (k), u (k)) are discrete non-linear vehicle dynamic model.
2. being using what is obtained by formula (7) after considering various physical constraints, comfort level and controlling the requirement of precision
System prediction output and given reference output building optimization problem:
Wherein, J (ξ (k), U (k)) is cost function.
Optimization problem specifically:
Meet: ξ (k+1)=Akξ(k)+Bku(k)
η (k)=C ξ (k)
U (k-1 | k)=u (k-1)
αmin≤α(k+i|k)≤αmax, i=0 ..., Np
Δ u (k+i | k)=u (k+i | k)-u (k+i-1 | k), i=0 ..., Np
Δumin≤Δu(k+i|k)≤Δumax, i=0 ..., Nc-1
Δ u (k+i | k)=0, i=Nc,…,Np
Wherein, ηrReference to provide exports, " | | * | |2" representing matrix Euclid norm, Q be output error power
Weight matrix, R are the weight matrix of controlling increment.Side drift angle α is limited in αminAnd αmaxBetween, in order to meet pilotless automobile
Requirement for stability and comfort, controlling increment Δ u are strictly limited in Δ uminWith Δ umaxBetween.In addition, in the time
SectionIt is interior, it is assumed that control amount u is a definite value.
3. optimization problem (9) can be converted into the form of standard quadratic programming, a variety of solvers can be used quick later
It solves, optimal solution U (k) need to meet the needs of various physical constraints, comfort level and control precision.Solution U (k)=[u of problem (9)
(k|k),u(k+1|k),…,u(k+Nc- 1 | k)] it is in the sequence for controlling the control amount at each moment in time domain, model prediction control
The one-component u of U (k) (k | k) is only applied in system by device processed as the optimum control amount at current time, it may be assumed that
U (k)=u (k | k) (10)
Fig. 4,5 and 6 respectively show the simulation result at tri- kinds of 18km/h, 45km/h and 72km/h.Use original
The controller of dynamic model and new type power model is named as controller A and controller B respectively.
Can be seen that controller B from the simulation result in the case of three kinds reduces car speed in corner, in protruding crook
Car speed is improved, so control effect will be far better than controller A.Fig. 4 (e), 5 (e) and 6 (e) illustrate three kinds of situations
It down include the tracking error of error compensation item and the controller B not comprising error compensation item.As can be seen that error compensation item can be with
Substantially reduce tracking error, plays important function in improving tracking precision.
In addition, slip rate and side drift angle need to be limited in a certain range to ensure in formula (1) to wheel in the present invention
Tire power does the reasonability of linearization process, and the ABS that tyre skidding rate s can be carried by automobile guarantees that slip rate α then needs to lead to
The range of Planar Mechanisms control amount guarantees, so needing when solving optimization problem (9) the variation model in view of side drift angle α
It encloses.The purpose of the present invention is improve the speed of controller solution to meet the needs of automatic driving vehicle is for rapidity, this hair
Bright proposed new vehicle kinetic model and error compensation item are equally applicable to Nonlinear Model Predictive Control device.
Although function and the course of work of the invention are described above in conjunction with attached drawing, the invention is not limited to
Above-mentioned concrete function and the course of work, the above mentioned embodiment is only schematical, rather than restrictive, ability
The those of ordinary skill in domain under the inspiration of the present invention, is not departing from present inventive concept and scope of the claimed protection situation
Under, many forms can be also made, all of these belong to the protection of the present invention.
Claims (3)
1. a kind of pilotless automobile model predictive controller design method based on kinetic model, which is characterized in that including
Following steps:
Step 1: establishing new vehicle kinetic model
Using the side force of tire and tractive force model proposed by Pacejka, longitudinal force, turning torque, aligning torque, resistance are described
Numerical relation between torque, side drift angle and slip rate；Tire force is expressed as form:
Wherein, FlFor longitudinal force of tire, ClFor the longitudinal rigidity of tire, s indicates slip rate, FcFor side force of tire, CcFor tire
Lateral rigidity, α indicate side drift angle；
Ignore automobile in the movement of vertical direction, the structure and stress of automobile are described with single track model, according to Newton's second law,
Obtain the stress balance equation on following three directions:
Wherein, m indicates the quality of automobile, and x is abscissa of the centre of gravity of vehicle under vehicle-mounted coordinate system, and y is centre of gravity of vehicle vehicle-mounted
Ordinate under coordinate system,For the course angle of automobile,For longitudinal velocity of the automobile under vehicle-mounted coordinate system,Exist for automobile
Lateral velocity under vehicle-mounted coordinate system,For the first derivative of course angle, the i.e. angular speed of automobile in the vertical direction,For vapour
Longitudinal acceleration of the vehicle under vehicle-mounted coordinate system,For transverse acceleration of the automobile under vehicle-mounted coordinate system,It is automobile vertical
Angular acceleration on direction, FxfThe power for being front-wheel suffered by x-axis direction, FxrThe power for being rear-wheel suffered by x-axis direction, FyfIt is preceding
The power suffered by y-axis direction is taken turns, δ represents the front wheel slip angle of automobile, FyrFor rear-wheel power suffered by y-axis direction, I is turning for automobile
Dynamic inertia, a are the distance between centre of gravity of vehicle and front axle, and b is the distance between centre of gravity of vehicle and rear axle；
Fxf、Fxr、FyfAnd FyrIt is calculated by following formula using the longitudinal force and lateral force of tire:
Wherein, FlfFor the longitudinal force that front-wheel is subject to, FcfFor the lateral force that front-wheel is subject to, FlrFor the longitudinal force that rear-wheel is subject to, FcrFor
The lateral force that rear-wheel is subject to；These types of power is calculated by formula (1), and wherein slip rate s and side drift angle α utilizes speed and wheel
Speed is calculated；
Simultaneous formula (1), (2), (3), and new vehicle kinetic simulation is obtained after linearisation and Euler sliding-model control
Type:
Wherein, k indicate current sample time, " k+n ", n=1,2,3 ... indicate current sample times after n-th of sampling when
It carves,Indicate the system mode at current time, Y is that automobile is vertical under inertial coodinate system
Coordinate, X are abscissa of the automobile under inertial coodinate system, the transposition of superscript " T " representing matrix, when ξ (k+1) is next sampling
The system mode at quarter, u (k)=[v, δ]TIt being inputted for the control at current time, v indicates car speed,To work as
The system at preceding moment exports, AkFor the state-transition matrix of system, BkFor the input matrix of system, C is the output matrix of system；
Step 2: pilotless automobile model predictive controller of the design based on new vehicle kinetic model
1. utilizing the output in the new vehicle kinetic model that present operating point linearizes to system in prediction time domain
State is predicted:
Y (k)=Ψkξ(k|k)+ΘkU(k)+Γkγ(k) (5)
Wherein,It is system in the following NpThe output of a sampling instant, NpIndicate prediction time domain, " k+n |
K ", n=0,1 ..., NpIndicate the variable for+n sampling instants of kth predicted in k-th of sampling instant,
ξe(k)=f (ξ (k), u (k))-Akξ(k)-BkU (k) is the caused state error of linearisation, NcIndicate control time domain, ξ
(k+1)=f (ξ (k), u (k)) is discrete non-linear vehicle dynamic model；
2. utilizing the system prediction output and given reference output building optimization problem obtained by formula (5):
Wherein, J (ξ (k), U (k)) is cost function；
3. solving optimization problem, optimal solution U (k) meets the needs of various physical constraints, comfort level and control precision, by U's (k)
One-component u (k | k) is applied in system as the optimum control amount at current time.
2. the pilotless automobile model predictive controller design method according to claim 1 based on kinetic model,
It is characterized in that, side drift angle α and slip rate s are obtained by the following formula in the first step::
Wherein, vc=vycosδ-vxSin δ is the side velocity of tire, vxFor speed of the automobile under vehicle-mounted coordinate system along the x-axis direction
Degree, vyFor speed of the automobile under vehicle-mounted coordinate system along the y-axis direction, vl=vysinδ+vxCos δ is the longitudinal velocity of tire, and r is
The radius of tire, w are the angular speed of tire.
3. the pilotless automobile model predictive controller design method according to claim 1 based on kinetic model,
It is characterized in that, the optimization problem constructed in second step specifically:
Meet: ξ (k+1)=Akξ(k)+Bku(k)
η (k)=C ξ (k)
U (k-1 | k)=u (k-1)
αmin≤α(k+i|k)≤αmax, i=0 ..., Np
Δ u (k+i | k)=u (k+i | k)-u (k+i-1 | k), i=0 ..., Np
Δumin≤Δu(k+i|k)≤Δumax, i=0 ..., Nc-1
Δ u (k+i | k)=0, i=Nc,…,Np
Wherein, ηrReference to provide exports, " | | * | |2" representing matrix Euclid norm, Q be output error weight square
Battle array, R are the weight matrix of controlling increment.Side drift angle α is limited in αminAnd αmaxBetween, in order to meet pilotless automobile for
The requirement of stability and comfort, controlling increment Δ u are strictly limited in Δ uminWith Δ umaxBetween.In addition, in the periodIt is interior, it is assumed that control amount u is a definite value.
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