CN111399374B - Linear output regulation tracking control method and system based on RBF neural network - Google Patents

Linear output regulation tracking control method and system based on RBF neural network Download PDF

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CN111399374B
CN111399374B CN202010125824.7A CN202010125824A CN111399374B CN 111399374 B CN111399374 B CN 111399374B CN 202010125824 A CN202010125824 A CN 202010125824A CN 111399374 B CN111399374 B CN 111399374B
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高会军
孙维超
王新
于兴虎
林伟阳
曲东升
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Abstract

The invention relates to a linear output regulation tracking control method and system based on a Radial Basis Function (RBF) neural network, belongs to the field of trajectory tracking control, and solves the problem that an external source system is difficult to construct or cannot be constructed due to the fact that a reference signal to be tracked is complex. The method specifically comprises the following steps: firstly, establishing an RBF neural network according to a tracking task target; secondly, training an RBF neural network by using a reference signal to be tracked; and thirdly, constructing an external source system by using the trained RBF neural network and designing a controller to realize the track tracking control of the linear system. The method or the system provided by the invention is particularly suitable for the tracking control task of the linear system with complex reference signals.

Description

Linear output regulation tracking control method and system based on RBF neural network
Technical Field
The invention relates to the field of trajectory tracking control, in particular to a linear output regulation tracking control method and system based on an RBF neural network.
Background
The trajectory tracking problem is an important problem in control systems, and in linear systems, linear output regulation is a common method for solving the tracking control problem. When solving the tracking control problem of linear systems using a linear output regulation framework, it is common practice to design an auxiliary system, called an exogenous system, based on a given reference signal. The reference signal to be tracked can be linearly represented by the state of the exogenous system. However, the construction of the exogenous system requires an artificial design based on the reference signal. For some complex reference signals, this approach undoubtedly increases the design difficulty and workload of the designer. Therefore, there is a need to develop a simple, efficient and more versatile linear output regulation tracking control method.
Disclosure of Invention
The invention aims to solve the problem that an external source system is difficult to construct or cannot be constructed due to the fact that a reference signal is complex, and provides a linear output regulation tracking control method and system based on an RBF neural network.
In order to achieve the purpose, the invention provides the following scheme:
a linear output regulation tracking control method based on an RBF neural network comprises the following steps:
establishing an RBF neural network according to the target of the tracking task;
training the RBF neural network by using a reference signal to be tracked to obtain a trained RBF neural network;
constructing an external source system of a reference signal to be tracked by utilizing the trained RBF neural network;
and constructing a tracking controller of the reference signal to be tracked according to the output regulation theory and the exogenous system.
Optionally, the establishing an RBF neural network according to the target of the tracking task specifically includes:
determining the number of nodes of an input layer, a hidden layer and an output layer according to the target of a tracking task, and further establishing a basic RBF neural network;
setting initial parameters of the basic RBF neural network, and determining a final RBF neural network; the initial parameters comprise an initial weight vector, a center vector, a Gaussian function vector, a coordinate vector of a central point of the Gaussian function and the width of the Gaussian function.
Optionally, the training of the RBF neural network by using the reference signal to be tracked to obtain a trained RBF neural network specifically includes:
training the RBF neural network by using the reference signal to be tracked to enable the RBF neural network to approach the reference signal to be tracked, and further obtaining the trained RBF neural network; wherein, the updating algorithm of the weight vector of the RBF neural network is a gradient descent method.
Optionally, the constructing an external source system of a reference signal to be tracked by using the trained RBF neural network specifically includes:
and constructing an external source system of the reference signal to be tracked by utilizing the Gaussian basis function vector of the trained RBF neural network.
Optionally, the tracking controller of the reference signal to be tracked is:
u(t)＝-Kx(t)+LΦ(t)；
wherein u (t) is a tracking controller of a reference signal to be tracked, x (t) is a state vector of the system, K is a feedback gain, L is a feedforward gain, and phi (t) is a Gaussian basis function vector of the trained RBF neural network.
A linear output regulation tracking control system based on an RBF neural network, comprising:
the RBF neural network establishing module is used for establishing an RBF neural network according to the target of the tracking task;
the RBF neural network training module is used for training the RBF neural network by using a reference signal to be tracked to obtain a trained RBF neural network;
the external source system construction module is used for constructing an external source system of a reference signal to be tracked by utilizing the trained RBF neural network;
and the tracking controller constructing module is used for constructing a tracking controller of the reference signal to be tracked according to the output regulation theory and the external source system.
Optionally, the RBF neural network establishing module specifically includes:
the basic RBF neural network establishing unit is used for determining the number of nodes of an input layer, a hidden layer and an output layer according to the target of the tracking task so as to establish a basic RBF neural network;
an RBF neural network establishing unit, which is used for setting the initial parameters of the basic RBF neural network and determining the final RBF neural network; the initial parameters comprise an initial weight vector, a center vector, a Gaussian function vector, a coordinate vector of a central point of the Gaussian function and the width of the Gaussian function.
Optionally, the RBF neural network training module specifically includes:
the RBF neural network training unit is used for training the RBF neural network by using the reference signal to be tracked, so that the RBF neural network approaches the reference signal to be tracked, and the trained RBF neural network is obtained; wherein, the updating algorithm of the weight vector of the RBF neural network is a gradient descent method.
Optionally, the exogenous system configuration module specifically includes:
and the external source system constructing unit is used for constructing the external source system of the reference signal to be tracked by utilizing the Gaussian basis function vector of the trained RBF neural network.
Optionally, a tracking controller of a reference signal to be tracked in the tracking controller constructing module is:
u(t)＝-Kx(t)+LΦ(t)；
wherein u (t) is a tracking controller of a reference signal to be tracked, x (t) is a state vector of the system, K is a feedback gain, L is a feedforward gain, and phi (t) is a Gaussian basis function vector of the trained RBF neural network.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a linear output regulation tracking control method and a system based on an RBF neural network, which aim at the problem of trajectory tracking control of a linear system and are used for training the RBF neural network to approach a reference signal to be tracked with certain precision. After training is finished, an external source system is constructed by using the obtained RBF neural network, and a tracking controller is solved based on a linear output regulation theory, so that the system tracks a reference signal.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a linear output regulation tracking control method based on RBF neural network according to the present invention;
FIG. 2 is a control block diagram of the linear output regulation tracking control method based on RBF neural network of the present invention;
FIG. 3 is a diagram showing the variation and convergence of each weight of the network with the training duration in the process of training the RBF neural network to approach the reference signal according to the present invention;
FIG. 4 is a diagram illustrating the output of a trained RBF neural network approaching a reference signal to be tracked according to the present invention;
FIG. 5 is a graph of the approximation error of the output of the trained RBF neural network and the reference signal to be tracked in accordance with the present invention;
FIG. 6 is a diagram of the output of a linear system according to the present invention tracking a reference signal trace to be tracked;
FIG. 7 is a diagram illustrating changes in various states of a linear system in accordance with the present invention;
FIG. 8 is a tracking error plot of the output of the linear system tracking the track of the reference signal to be tracked in accordance with the present invention;
fig. 9 is a block diagram of a linear output regulation tracking control system based on an RBF neural network according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to solve the problem that an external source system is difficult to construct or cannot be constructed due to the fact that a reference signal is complex, and provides a linear output regulation tracking control method and system based on an RBF neural network.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the method for linear output regulation tracking control based on RBF neural network provided by this embodiment includes the following steps:
step 101: and establishing the RBF neural network according to the target of the tracking task.
The method specifically comprises the following steps:
step 1011: and selecting the number of nodes of a proper input layer, a proper hidden layer and a proper output layer according to the target of the tracking task to establish a basic RBF neural network.
Considering the tracking control problem of a linear system, the system model is as follows:
Figure BDA0002394354950000051
y(t)＝Cx(t)
where x (t) is the state vector of the system, y (t) is the output vector of the system, and u (t) is the control input. The matrices A, B, C represent the state transition matrix, input matrix, and output matrix of the system, respectively. Preferably, it may be a matrix
Figure BDA0002394354950000052
C＝[1 0]。
The reference signal to be tracked is r (t), and may be r (t) sin (pi · t) + cos (2 pi · t), and the tracking error may be defined as:
e(t)＝y(t)-r(t)
the tracking task aims at designing the tracking controller u (t) so that the output y (t) of the system tracks the reference signal r (t) to be tracked.
In this embodiment, the number of nodes of the input layer, the hidden layer, and the output layer is selected to be 2, 5, and 1, respectively, according to experience, so as to obtain the basic RBF neural network. If the tracking effect is not ideal, the number of nodes can be increased or decreased appropriately.
The number of neural network nodes is chosen as an open problem, where testing refers to choosing a number to try based on experience.
Step 1012: setting initial parameters of the basic RBF neural network, and determining a final RBF neural network; the initial parameters comprise parameters such as initial weight vectors, central vectors, Gaussian function widths and the like.
The specific form of the RBF neural network is as follows:
Figure BDA0002394354950000053
Figure BDA0002394354950000061
wherein p (t) ═ p1(t)...pn(t)]TAs input to the RBF neural network, ynet(t) is the output of the RBF neural network; the weight vector of the RBF neural network is WT＝[w1 ... wm]，Φ(t)＝[φ1(t)...φm(t)]TIs a Gaussian basis function vector, phij(t) is the output of the jth node of the hidden layer; b ═ b1 ... bm]Is the width of the Gaussian base function, c ═ c1 ... cm]Is a coordinate vector of the center point of the Gaussian basis function and cj＝[c1j ... cnj]T(ii) a i 1, 2.. n denotes the number of input layer nodes of the RBF neural network, and j 1, 2.. m denotes the number of hidden layer nodes. In this embodiment, an RBF neural network with two input layers, a single output layer, and an implicit layer node number of 5 is selected, that is, n is 2, and m is 5.
Step 102: and training the RBF neural network by using the reference signal to be tracked to obtain the trained RBF neural network. Wherein, the signal to be tracked is the tracking target of the tracking task.
And training the RBF neural network by using the reference signal to be tracked to enable the RBF neural network to approach the reference signal to be tracked until the approaching precision of the RBF neural network meets the requirement.
According to the universal approximation theorem, the reference signal r (t) to be tracked can be obtained by approximation of RBF neural network, that is
r(t)＝WTΦ(t)+ε
Where ε represents the approximation error. Under certain precision requirement, r (t) ═ y can be approximately considerednet(t)＝WTΦ(t)。
The training process of the RBF neural network comprises the following steps:
taking a reference signal r (t) to be tracked as an input of an RBF neural network, wherein the output of the RBF neural network is ynet(t) of (d). The goal of the training is to make the error et(t)＝ynet(t) -r (t) tends to 0, i.e. ynetWhere Φ (t) is used to construct the exogenous system. And in the training process, a weight vector W of the RBF neural network is updated by adopting a gradient descent method.
wj＝wj+Δwj；Δwj＝-η·et·φj。
The RBF neural network is used for approaching the reference signal to be tracked, and after the training is finished, the output y of the RBF neural networknet(t) is approximately equal to the reference signal to track r (t).
Step 103: and constructing an external source system of the reference signal to be tracked by utilizing the trained RBF neural network.
And constructing an external source system by using the Gaussian basis function vector phi (t) of the trained RBF neural network.
Figure BDA0002394354950000071
r(t)＝-(-WT)Φ(t)
Wherein the content of the first and second substances,
Figure BDA0002394354950000072
denotes the derivative (derivative with respect to time) of Φ (t), e (t) denotes a matrix, the elements of which vary with time t,
Figure BDA0002394354950000073
alpha represents each element of E (t), and is used for replacing the more complex expression to facilitate writing. c represents the elements of the coordinate vector of the center point of the gaussian function.
Suppose alphaj(t) is bounded, i.e. | αj(t)|≤αmax，αmaxIs a constant. Inputs p (t) to the trained RBF neural network and their derivatives
Figure BDA0002394354950000074
Sampling over a period of time (i.e. to the reference signal to be tracked r (t) and its derivative to
Figure BDA0002394354950000075
Sampling) to obtain a matrix value E (k) at each sampling time k, where k is 1,2, and L (E (k), i.e., E (t), which is obtained at different times t, E (1) is obtained when t is 1 second, E (2) is obtained when t is 2 seconds, and L is the number of sampling points. In the present embodiment, L is 1000. Order to
Figure BDA0002394354950000076
A constant matrix E is obtained.
Step 104: and constructing a tracking controller of the reference signal to be tracked according to the output regulation theory and the exogenous system.
Specifically, an external source system of a reference signal to be tracked is constructed by utilizing a trained RBF neural network, and a feedback-feedforward controller, namely a tracking controller of the reference signal to be tracked is designed according to an output regulation theory, so that the track tracking control of a linear system is realized.
According to the controlled system and the external source system, an augmentation system is formed:
Figure BDA0002394354950000081
Figure BDA0002394354950000082
e(t)＝Cx(t)-WTΦ(t)
wherein, E is a constant matrix obtained by calculating E (t) in step 103.
To realize tracking control of the trajectory, z (t) X (t) -X Φ (t), v (t) U (t) -U Φ (t) are defined, wherein X, U is a matrix of appropriate dimensions, and the following matrix equation is satisfied:
XE＝AX+BU
0＝CX+F
wherein F is a constant matrix, and F ═ WT。
Taking the derivative of z (t) yields:
Figure BDA0002394354950000083
e(t)＝Cz(t)
the control law v (t) ═ -kz (t) is designed so that the following performance indicator function is minimal:
Figure BDA0002394354950000084
wherein Q is QT≥0，R＝RT＞0。
According to the optimal control theory, the solution to this problem can be obtained by solving the following algebraic ricatt equation:
ATP+PA+Q-PBR-1BTP＝0
wherein, feedback control gain K ═ R-1BTP。
The actual control law is as follows:
u(t)＝v(t)+UΦ(t)＝-Kz(t)+UΦ(t)＝-Kx(t)+(KX+U)Φ(t)
thus, a tracking controller is available:
u(t)＝-Kx(t)+LΦ(t)
where K is the feedback gain and L is the feedforward gain. For the tracking problem of a closed loop system, the feedback gain K stabilizes the A-BK. Feed forward gain:
L＝U+KX
wherein matrices X and U are solutions of the following matrix equations:
XE＝AX+BU
0＝CX+F
if the linear output adjustment problem has a solution, one can get:
Figure BDA0002394354950000091
Figure BDA0002394354950000092
therefore, the tracking error of the system converges asymptotically.
The control block diagram of this embodiment is shown in fig. 2, the RBF neural network is trained to approach a reference signal to be tracked, and after the training is completed, a gaussian basis function vector Φ (t) of the trained RBF neural network is used as the state of an external source system, and a tracking controller u (t) is designed according to an output regulation theory, so as to realize the tracking control of the system.
The simulation related parameters and initial values are as follows:
fig. 3-5 are simulation results of training a selected RBF neural network to approximate a reference signal. Fig. 6-7 show the simulation effect of the tracking controller designed by using the trained RBF neural network to construct an exogenous system. According to the simulation result, the following results are obtained: the controller designed by the linear output regulation tracking control method based on the RBF neural network does not need to manually construct an external auxiliary system, and can simply and effectively realize the tracking control task of the linear system.
In this embodiment, the present invention is described with reference to a specific implementation manner, wherein an initial value of the network weight is W ═ 00000]TInitial value of coordinate vector of central point of Gaussian base function
Figure BDA0002394354950000093
Initial value of Gaussian function width b ═ 11111]The learning rate of the gradient descent method was 0.05.
Parameters of performance index function
Figure BDA0002394354950000094
R is 1, and the system initial value x0＝[0 0]T。
In order to achieve the above object, the present invention further provides a linear output regulation tracking control system based on an RBF neural network, as shown in fig. 9, including:
an RBF neural network establishing module 201, configured to establish an RBF neural network according to a target of a tracking task.
And an RBF neural network training module 202, configured to train the RBF neural network by using the reference signal to be tracked, so as to obtain a trained RBF neural network.
And the external source system constructing module 203 is used for constructing an external source system of the reference signal to be tracked by utilizing the trained RBF neural network.
And a tracking controller constructing module 204, configured to construct a tracking controller of the reference signal to be tracked according to the output regulation theory and the exogenous system.
The RBF neural network establishing module 201 specifically includes:
and the basic RBF neural network establishing unit is used for determining the number of nodes of the input layer, the hidden layer and the output layer according to the target of the tracking task so as to establish the basic RBF neural network.
An RBF neural network establishing unit, which is used for setting the initial parameters of the basic RBF neural network and determining the final RBF neural network; the initial parameters comprise an initial weight vector, a center vector, a Gaussian function vector, a coordinate vector of a central point of the Gaussian function and the width of the Gaussian function.
The RBF neural network training module 202 specifically includes:
the RBF neural network training unit is used for training the RBF neural network by using the reference signal to be tracked, so that the RBF neural network approaches the reference signal to be tracked, and the trained RBF neural network is obtained; wherein, the updating algorithm of the weight vector of the RBF neural network is a gradient descent method.
The exogenous system configuration module 203 specifically includes:
and the external source system constructing unit is used for constructing the external source system of the reference signal to be tracked by utilizing the Gaussian basis function vector of the trained RBF neural network.
The tracking controller of the reference signal to be tracked in the tracking controller constructing module 204 is:
u(t)＝-Kx(t)+LΦ(t)；
wherein u (t) is a tracking controller of a reference signal to be tracked, x (t) is a state vector of the system, K is a feedback gain, L is a feedforward gain, and phi (t) is a Gaussian basis function vector of the trained RBF neural network.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (6)

1. A linear output regulation tracking control method based on an RBF neural network is characterized by comprising the following steps:
establishing an RBF neural network according to the target of the tracking task;
training the RBF neural network by using a reference signal to be tracked to obtain a trained RBF neural network;
constructing an external source system of a reference signal to be tracked by utilizing the trained RBF neural network;
constructing a tracking controller of a reference signal to be tracked according to an output regulation theory and the exogenous system;
the training of the RBF neural network by using the reference signal to be tracked to obtain the trained RBF neural network specifically includes:
training the RBF neural network by using a reference signal to be tracked, and enabling the RBF neural network to approach the reference signal to be tracked until the approaching precision of the RBF neural network meets the requirement;
according to the universal approximation theorem, the reference signal r (t) to be tracked is obtained by approximation of the RBF neural network, namely
r(t)＝WTΦ(t)+ε
Where e represents an approximation error, and phi (t) ═ phi1(t)…φm(t)]TIs a gaussian basis function vector; under certain precision requirement, consider r (t) ═ ynet(t)＝WTΦ(t)；
The training process of the RBF neural network comprises the following steps:
taking the reference signal r (t) to be tracked as the input of the RBF neural network, wherein the output of the RBF neural network is ynet(t); the goal of the training is to make the error et(t)＝ynet(t) -r (t) goes to 0, where Φ (t) is used to construct the exogenous system; updating a weight vector W of the RBF neural network by adopting a gradient descent method in the training process; wT＝[w1...wm]；
wj＝wj+Δwj；Δwj＝-ηet·φj；
The RBF neural network is used for approaching the reference signal to be tracked, and after training is finished, the output y isnet(t) is approximately equal to the reference signal to track r (t);
the step of constructing the tracking controller of the reference signal to be tracked according to the output regulation theory and the exogenous system specifically comprises the following steps:
constructing an external source system of the reference signal to be tracked by using the trained RBF neural network, and designing a tracking controller of the reference signal to be tracked according to an output regulation theory so as to realize the track tracking control of a linear system;
according to the controlled system and the external source system, an augmentation system is formed:
Figure FDA0002762258370000021
Figure FDA0002762258370000022
e(t)＝Cx(t)-WTΦ(t)
wherein E is a constant matrix, x (t) is a state vector of the augmented system, u (t) is a control input of the augmented system, and the matrix A, B, C represents a state transition matrix, an input matrix, and an output matrix of the augmented system, respectively;
to realize tracking control of the trajectory, z (t) X (t) -X Φ (t), v (t) U (t) -U Φ (t) are defined, wherein X, U is a matrix of appropriate dimensions, and the following matrix equation is satisfied:
XE＝AX+BU
0＝CX+F
wherein F is a constant matrix, and F ═ WT；
Derivative z (t) to obtain:
Figure FDA0002762258370000023
e(t)＝Cz(t)
the control law v (t) ═ -kz (t) is designed so that the following performance indicator function is minimal:
Figure FDA0002762258370000031
wherein Q is QT≥0，R＝RT＞0；
According to the optimal control theory, the solution to this problem is obtained by solving the algebraic ricatt equation:
ATP+PA+Q-PBR-1BTP＝0
wherein, feedback control gain K ═ R-1BTP；
The actual control law is as follows:
u(t)＝v(t)+UΦ(t)＝-Kz(t)+UΦ(t)＝-Kx(t)+(KX+U)Φ(t)
thus, a tracking controller is available:
u(t)＝-Kx(t)+LΦ(t)
wherein K is feedback gain and L is feedforward gain; for the tracking problem of a closed loop system, the feedback gain K enables A-BK to be stable; the feed forward gain is as follows:
L＝U+KX
wherein the matrices X and U are solutions of the following matrix equations:
XE＝AX+BU
0＝CX+F
if the linear output adjustment problem has a solution, we get:
Figure FDA0002762258370000032
Figure FDA0002762258370000033
therefore, the tracking error of the system converges asymptotically.
2. The method as claimed in claim 1, wherein the establishing of the RBF neural network according to the target of the tracking task specifically includes:
determining the number of nodes of an input layer, a hidden layer and an output layer according to the target of a tracking task, and further establishing a basic RBF neural network;
setting initial parameters of the basic RBF neural network, and determining a final RBF neural network; the initial parameters comprise an initial weight vector, a center vector, a Gaussian function vector, a coordinate vector of a central point of the Gaussian function and the width of the Gaussian function.
3. The RBF neural network-based linear output regulation tracking control method as claimed in claim 1, wherein said constructing an exogenous system of reference signals to be tracked by using said trained RBF neural network specifically comprises:
and constructing an external source system of the reference signal to be tracked by utilizing the Gaussian basis function vector of the trained RBF neural network.
4. A linear output regulation tracking control system based on an RBF neural network, comprising:
the RBF neural network establishing module is used for establishing an RBF neural network according to the target of the tracking task;
the RBF neural network training module is used for training the RBF neural network by using a reference signal to be tracked to obtain a trained RBF neural network;
the external source system construction module is used for constructing an external source system of a reference signal to be tracked by utilizing the trained RBF neural network;
the tracking controller constructing module is used for constructing a tracking controller of a reference signal to be tracked according to an output regulation theory and the external source system;
the training of the RBF neural network by using the reference signal to be tracked to obtain the trained RBF neural network specifically includes:
training the RBF neural network by using a reference signal to be tracked, and enabling the RBF neural network to approach the reference signal to be tracked until the approaching precision of the RBF neural network meets the requirement;
according to the universal approximation theorem, the reference signal r (t) to be tracked is obtained by approximation of the RBF neural network, namely
r(t)＝WTΦ(t)+ε
Where e represents an approximation error, and phi (t) ═ phi1(t)…φm(t)]TIs a gaussian basis function vector; under certain precision requirement, consider r (t) ═ ynet(t)＝WTΦ(t)；
The training process of the RBF neural network comprises the following steps:
taking the reference signal r (t) to be tracked as the input of the RBF neural network, wherein the output of the RBF neural network is ynet(t); the goal of the training is to make the error et(t)＝ynet(t) -r (t) goes to 0, where Φ (t) is used to construct the exogenous system; updating a weight vector W of the RBF neural network by adopting a gradient descent method in the training process; wT＝[w1...wm]；
wj＝wj+Δwj；Δwj＝-ηet·φj；
The RBF neural network is used for approaching the reference signal to be tracked, and after training is finished, the output y isnet(t) is approximately equal to the reference signal to track r (t);
the step of constructing the tracking controller of the reference signal to be tracked according to the output regulation theory and the exogenous system specifically comprises the following steps:
constructing an external source system of the reference signal to be tracked by using the trained RBF neural network, and designing a tracking controller of the reference signal to be tracked according to an output regulation theory so as to realize the track tracking control of a linear system;
according to the controlled system and the external source system, an augmentation system is formed:
Figure FDA0002762258370000051
Figure FDA0002762258370000052
e(t)＝Cx(t)-WTΦ(t)
wherein E is a constant matrix, x (t) is a state vector of the augmented system, u (t) is a control input of the augmented system, and the matrix A, B, C represents a state transition matrix, an input matrix, and an output matrix of the augmented system, respectively;
to realize tracking control of the trajectory, z (t) X (t) -X Φ (t), v (t) U (t) -U Φ (t) are defined, wherein X, U is a matrix of appropriate dimensions, and the following matrix equation is satisfied:
XE＝AX+BU
0＝CX+F
wherein F is a constant matrix, and F ═ WT；
Derivative z (t) to obtain:
Figure FDA0002762258370000061
e(t)＝Cz(t)
the control law v (t) ═ -kz (t) is designed so that the following performance indicator function is minimal:
Figure FDA0002762258370000062
wherein Q is QT≥0，R＝RT＞0；
According to the optimal control theory, the solution to this problem is obtained by solving the algebraic ricatt equation:
ATP+PA+Q-PBR-1BTP＝0
wherein, feedback control gain K ═ R-1BTP；
The actual control law is as follows:
u(t)＝v(t)+UΦ(t)＝-Kz(t)+UΦ(t)＝-Kx(t)+(KX+U)Φ(t)
thus, a tracking controller is available:
u(t)＝-Kx(t)+LΦ(t)
wherein K is feedback gain and L is feedforward gain; for the tracking problem of a closed loop system, the feedback gain K enables A-BK to be stable; the feed forward gain is as follows:
L＝U+KX
wherein the matrices X and U are solutions of the following matrix equations:
XE＝AX+BU
0＝CX+F
if the linear output adjustment problem has a solution, we get:
Figure FDA0002762258370000071
Figure FDA0002762258370000072
therefore, the tracking error of the system converges asymptotically.
5. The system according to claim 4, wherein the RBF neural network building block specifically comprises:
the basic RBF neural network establishing unit is used for determining the number of nodes of an input layer, a hidden layer and an output layer according to the target of the tracking task so as to establish a basic RBF neural network;
an RBF neural network establishing unit, which is used for setting the initial parameters of the basic RBF neural network and determining the final RBF neural network; the initial parameters comprise an initial weight vector, a center vector, a Gaussian function vector, a coordinate vector of a central point of the Gaussian function and the width of the Gaussian function.
6. The RBF neural network-based linear output regulation tracking control system as claimed in claim 4, wherein said exogenous system configuration module specifically comprises:
and the external source system constructing unit is used for constructing the external source system of the reference signal to be tracked by utilizing the Gaussian basis function vector of the trained RBF neural network.
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