CN112947089A - Self-adaptive neural network tracking control method with preset tracking precision - Google Patents

Self-adaptive neural network tracking control method with preset tracking precision Download PDF

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CN112947089A
CN112947089A CN202110288886.4A CN202110288886A CN112947089A CN 112947089 A CN112947089 A CN 112947089A CN 202110288886 A CN202110288886 A CN 202110288886A CN 112947089 A CN112947089 A CN 112947089A
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李靖
张朝辉
杨晓利
吴水艳
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Xidian University
Xianyang Normal University
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Abstract

The invention belongs to the technical field of switching systems, and discloses a preset tracking precision self-adaptive neural network tracking control method and system. In order to approximate an unknown nonlinear function and an unknown periodic time-varying parameter, a radial basis function neural network and Fourier series expansion are respectively introduced, and an approximation error upper bound is processed for the first time. Two bilateral smooth switching functions are introduced, and a public Lyapunov function meeting all subsystems is constructed. A new self-adaptive neural network control scheme is constructed by utilizing a back-stepping method and a public Lyapunov function theory. The invention realizes the convergence of the tracking error to the neighborhood of the preset zero point, and ensures the preset performance of the tracking error and the final bounded result of the semi-global consistency of all signals of a closed-loop system. The invention combines the practical problem, establishes the model and solves the model to obtain the result, and provides a new idea and a solution for the cross research of mathematics and engineering problems.

Description

Self-adaptive neural network tracking control method with preset tracking precision
Technical Field
The invention belongs to the technical field of switching systems, and particularly relates to a preset tracking precision self-adaptive neural network tracking control method and system.
Background
At present: the switching system is a very important type in a hybrid system, and is composed of a set of continuous or discrete dynamic subsystems and a set of switching rules (switching laws or switching signals) for determining how to switch between the subsystems, and the whole switching system switches between the subsystems according to the set of switching rules. The switching system organically combines a discrete event dynamic system and a continuous variable dynamic system, and can effectively describe a system which has parameters or structural mutation, adopts a multi-controller switching mechanism for a single object, has large uncertainty in a model, is difficult to identify on line and cannot be stabilized by a smooth continuous controller. The switching system provides a new idea and method for solving the control problem of the complex system, so that the switching system has very important significance in theoretical research and practical application. Research on the control problem of switching systems has been carried out with many efforts in recent years, and has been put into practical use, such as network control systems, automobile control systems, robot control systems, aircraft control systems, and the like. In practical application, uncertain factors such as function uncertainty, external interference uncertainty, internal parameter uncertainty, uncertainty of parameters not considered in modeling and the like always exist in a system. The switching system considers the uncertain factors, so that the accuracy of model establishment can be increased, but compared with the condition of only considering the deterministic switching system, the research of the uncertain switching nonlinear system is more complex and has practical significance.
At present, in the research of system uncertainty, most approximation algorithms only consider the case of processing function uncertainty, but rarely consider the case of unknown periodic disturbance in the actual system. For an uncertain nonlinear system with periodic disturbance, a proper approximation algorithm needs to be designed to solve a more complex practical problem. In addition, in most studies of tracking control problems, the main objective of the designed control algorithm is to make the output signal track the upper reference track. Although these algorithms achieve the goal of convergence of the tracking error to zero, the size of their convergence field depends on the choice of control parameters and cannot be directly determined. The practical problem that the tracking error convergence domain has a requirement or the ideal tracking performance is to be realized needs to redesign the control algorithm meeting the preset tracking precision so as to achieve the control target. The prior art has the following defects: 1) for the uncertain switching nonlinear system, the condition that a system function is unknown and is subjected to periodic disturbance is not considered, and a corresponding approximation algorithm needs to be deeply researched; 2) the approaching performance cannot be intuitively displayed. In most approximation algorithms, the upper bound of the approximation error is ignored as an unknown constant, and the corresponding approximation performance cannot be obtained through the tracking error. 3) Aiming at an uncertain switching nonlinear system with periodic parameters, an approximation algorithm needs to be improved and approximation errors need to be processed with certain difficulty, and meanwhile, the technical difficulty of ensuring that tracking errors are converged into a preset small neighborhood of an original point is high.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) for the uncertain switching nonlinear system, the condition that the system function is unknown and is subjected to periodic disturbance is not considered, and how to design a corresponding approximation algorithm needs to be studied deeply.
(2) The approaching performance cannot be intuitively displayed. In most approximation algorithms, the upper bound of the approximation error is ignored as an unknown constant, and the corresponding approximation performance cannot be obtained through the tracking error.
(3) Aiming at an uncertain switching nonlinear system with periodic parameters, an approximation algorithm needs to be improved and approximation errors need to be processed with certain difficulty, and meanwhile, the technical difficulty of ensuring that tracking errors are converged into a preset small neighborhood of an original point is high.
The difficulty in solving the above problems and defects is: due to the existence of system uncertainty and periodic time-varying parameters and the realization of a tracking target with known tracking accuracy, it is very difficult and challenging to consider an adaptive neural network control strategy with a suitable approximation algorithm.
The significance of solving the problems and the defects is as follows: the method has great significance for realizing the tracking target with known tracking precision and plays a great role in the development of science and technology. The problems of missile tracking, spacecraft motion trajectory control, mobile phone positioning tracking, robot motion trajectory and the like are the research that a controlled system can track an upper target trajectory in practical application. Due to the complexity of the geographical location and the environment, in practical applications, these controlled systems are often disturbed, and the general disturbance situation is considered, and the periodic disturbance causes the failure of the designed controller and the degradation of the stability of the system. Therefore, if the periodic time-varying disturbance can be quickly processed and the target of preset tracking performance can be realized under the existing conditions, the method is very important, so that the effectiveness of an approximation algorithm, the accuracy of a designed controller and the convergence of a tracking error can be ensured, the robustness of a system can be met, the method is also a key point of research, the practical problem is designed, the method has strong applicability and has certain support for research in a plurality of practical application research fields.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a preset tracking precision self-adaptive neural network tracking control method and system.
The invention is realized by a controller of a nonlinear parametric switching system, the kinetic equation of which is
Figure BDA0002981607000000031
The controller is
Figure BDA0002981607000000032
Wherein
Figure BDA0002981607000000033
Is a system state vector; y is the system output signal; u is a control input;
Figure BDA0002981607000000034
a switching signal representing a system; for any of j 1,2, a, m and l 1,2, a, n,
Figure BDA0002981607000000035
is an unknown smooth nonlinear function and satisfies
Figure BDA0002981607000000036
θj(t) is an unknown time-varying parameter of known periodicity.
The invention also aims to provide a preset tracking precision self-adaptive neural network tracking control method by utilizing the controller of the nonlinear parameterized switching system, which applies the controller u of the nonlinear parameterized switching system on a controlled system and combines an introduced special switching function
Figure BDA0002981607000000037
Selecting Lyapunov functions
Figure BDA0002981607000000038
Through the knowledge of the Lyapunov stability theory, the related mathematical theory and the algebraic graph theory, the method can prove that
Figure BDA0002981607000000039
And | z when t → ∞ time1(t)|≤∈。
Further, the preset tracking precision adaptive neural network tracking control method includes:
the system output signal and the reference signal are used as the input of a switching function with known tracking precision;
processing an unknown periodic time-varying parameterized function in the system by using two approximation algorithms;
combining a back-stepping method and a self-adaptive control algorithm, processing unknown constant parameters, and considering an approximation error upper-bound estimation value;
and designing a corresponding controller to be applied to a controlled system.
Further, the system output signal and the reference signal as inputs to a switching function with known tracking accuracy comprises:
1) based on the introduction of special handover functions
Figure BDA0002981607000000041
Constructing a Lyapunov function:
Figure BDA0002981607000000042
2) the derivative of the designed Lyapunov function is subjected to a switching function with unknown periodic time-varying parameters due to uncertainty of the system
Figure BDA0002981607000000043
According to Young's inequality, the unknown function is divided into two parts, namely an unknown switching function Lambda1And a periodic time varying function Θ1(t) using an approximation algorithm fourier series and an unknown function of the neural network processing system, respectively:
Figure BDA0002981607000000044
Figure BDA0002981607000000045
wherein the content of the first and second substances,
Figure BDA0002981607000000046
respectively approximating the upper bound of errors by a neural network and a Fourier series algorithm;
3) designing a corresponding virtual controller according to a back stepping method on the basis of the step 2);
4) to deal with unknown weights a in the approximation algorithm1,W1 *Redesigning the Lyapunov function:
Figure BDA0002981607000000047
wherein
Figure BDA0002981607000000048
Is a positive definite diagonal matrix; based on the self-adaptive back-stepping control technology,
Figure BDA0002981607000000049
is an approximation algorithm weight a1,W1 *Designing a corresponding adaptive control law:
Figure BDA00029816070000000410
5) substituting the virtual controller designed in 3) and the adaptive law designed in 4) into a first subsystem of the controlled system, and simplifying derivative functions of the Lyapunov function.
Further, the processing of the unknown periodic time-varying parameterized function in the system by using two approximation algorithms includes: aiming at the first m-1 subsystems of a controlled system, designing a corresponding Lyapunov function:
Figure BDA0002981607000000051
and repeating the design process, and respectively designing a virtual controller for the m-1 subsystems:
Figure BDA0002981607000000052
and parameter adaptation law:
Figure BDA0002981607000000053
and then substituting the designed virtual controller and the designed adaptive law into a subsystem corresponding to the controlled system, and simplifying the derivative function of the Lyapunov function.
Further, the combining the inverse method and the adaptive control algorithm, processing the unknown constant parameter, and considering the approximation error upper bound estimation value includes: on the basis of the first m-1 step, aiming at the whole m-order system, a public Lyapunov function meeting all subsystems is designed, and the estimation error of the upper bound of the approximation error is taken into account for the first time:
Figure BDA0002981607000000054
wherein
Figure BDA0002981607000000055
Upper bound for radial basis function neural network and Fourier series approximation error, respectively
Figure BDA0002981607000000056
The estimation error of (2). Based on the self-adaptive backstepping method, repeating the design process of the previous m-1 steps, and designing an actual controller:
Figure BDA0002981607000000057
and parameter adaptation law:
Figure BDA0002981607000000058
defining state error variables
Figure BDA0002981607000000059
Wherein alpha isj-1Is a virtual controller. The controller u is applied to a controlled system
Figure BDA0002981607000000061
Selecting Lyapunov functions
Figure BDA0002981607000000062
Substituting the designed parameter self-adaptation law into the method can prove that the method has the advantages of good stability, relevant mathematical theory and algebraic graph theory
Figure BDA0002981607000000063
And | z when t → ∞ time1(t)|≤∈。
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
the system output signal and the reference signal are used as the input of a switching function with known tracking precision;
processing an unknown periodic time-varying parameterized function in the system by using two approximation algorithms;
combining a back-stepping method and a self-adaptive control algorithm, processing unknown constant parameters, and considering an approximation error upper-bound estimation value;
and designing a corresponding controller to be applied to a controlled system.
Another objective of the present invention is to provide a switching circuit system information data processing terminal, which is used for implementing the preset tracking accuracy adaptive neural network tracking control method.
Another object of the present invention is to provide a preset tracking accuracy adaptive neural network tracking control system for implementing the preset tracking accuracy adaptive neural network tracking control method, the preset tracking accuracy adaptive neural network tracking control system comprising:
the signal input module is used for realizing that a system output signal and a reference signal are used as the input of a switching function with known tracking precision;
the function processing module is used for processing an unknown periodic time-varying parameterized function in the system by utilizing two approximation algorithms;
the unknown constant parameter processing module is used for processing the unknown constant parameters by combining a back-stepping method and a self-adaptive control algorithm and considering an approximation error upper-bound estimation value;
and the controller design module is used for designing a corresponding controller to be applied to the controlled system.
By combining all the technical schemes, the invention has the advantages and positive effects that: compared with the situation that the tracking error convergence domain is determined by continuously adjusting the control parameters, the method avoids the parameter adjustment process which inevitably wastes much time and a large amount of resources, and realizes the tracking performance that the tracking error converges to the preset small neighborhood of the zero point; the complex problem that the control target cannot be realized due to the fact that the complex problem contains an unknown time-varying function is converted into the problem that the complex problem only contains unknown constant-value parameters and is easy to control; and an approximation algorithm is improved, and approximation performance of approximation error upper bound display is processed for the first time. The method can realize that the tracking error converges to the preset small neighborhood of the origin, so that the error signal track fluctuates in the preset small neighborhood of the origin and the boundedness of all signals of the closed-loop system is proved.
The method improves the approximation algorithm to approximate unknown functions and periodic time-varying parameters based on the radial basis neural network and the Fourier series approximation method, solves the problem of unknown upper bound of approximation errors for the first time by designing the self-adaptive law, is more favorable for showing approximation performance, and provides criteria for improving the approximation accuracy of the approximation algorithm.
The invention combines the public Lyapunov function constructed by special switching function and applies the self-adaptive backstepping method, thereby ensuring that the output signal tracks the upper reference signal and ensuring that the tracking error converges to the small neighborhood of the preset zero point. The invention has practical significance for ensuring that the tracking error can only be converged into the neighborhood of an unknown zero point, and the size of the tracking error depends on the tracking performance of the selected control parameter, avoiding the parameter adjustment process of wasting time and energy, and realizing the tracking target of the tracking error converged into the small neighborhood of any given zero point.
The invention provides a self-adaptive neural network control scheme to process approximation errors, further improve approximation performance of an approximation algorithm and ensure that tracking errors of a switching nonlinear system with periodic time-varying parameters are finally converged into a small neighborhood of a preset zero point. Meanwhile, a new idea is provided for the accurate tracking control of the actual system.
Drawings
Fig. 1 is a flowchart of a preset tracking accuracy adaptive neural network tracking control method according to an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of an adaptive neural network tracking control system with preset tracking accuracy according to an embodiment of the present invention;
in fig. 2: 1. a signal input module; 2. a function processing module; 3. an unknown constant parameter processing module; 4. and a controller design module.
Fig. 3 is a flowchart of an implementation of the preset tracking accuracy adaptive neural network tracking control method according to the embodiment of the present invention.
Fig. 4 is a state diagram of an output signal and a reference signal provided by an embodiment of the present invention.
Fig. 5 is a tracking error trajectory diagram provided by an embodiment of the present invention.
Fig. 6 is a control input trace diagram provided by an embodiment of the invention.
Fig. 7 is a diagram of a switching signal according to an embodiment of the present invention.
Fig. 8 is a 2-norm trajectory diagram of the neural network approximation weight estimation provided by the embodiment of the present invention.
Fig. 9 is a 2-norm trajectory diagram of fourier series approximation weight estimation according to an embodiment of the present invention.
FIG. 10 is a trajectory diagram of the upper error bound estimation of the radial basis function neural network and the Fourier series approximation provided by the embodiment of the invention.
Fig. 11 is a circuit switching diagram according to an embodiment of the present invention.
Fig. 12 is a state diagram of an output signal and a reference signal provided by an embodiment of the present invention.
Fig. 13 is a tracking error trajectory diagram provided by an embodiment of the present invention.
Fig. 14 is a diagram of a switching signal according to an embodiment of the present invention.
Fig. 15 is a 2-norm trajectory diagram of the neural network approximation weight estimation provided by the embodiment of the present invention.
Fig. 16 is a 2-norm trajectory diagram of fourier series approximation weight estimation according to an embodiment of the present invention.
FIG. 17 is a trajectory diagram of the upper error bound estimation of the radial basis function neural network and the Fourier series approximation provided by the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a preset tracking precision adaptive neural network tracking control method and a preset tracking precision adaptive neural network tracking control system, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the preset tracking accuracy adaptive neural network tracking control method provided by the present invention includes the following steps:
s101: the system output signal and the reference signal are used as the input of a switching function with known tracking precision;
s102: processing an unknown periodic time-varying parameterized function in the system by using two approximation algorithms;
s103: combining a back-stepping method and a self-adaptive control algorithm, processing unknown constant parameters, and considering an approximation error upper-bound estimation value;
s104: and designing a corresponding controller to be applied to a controlled system.
A person skilled in the art of the preset tracking accuracy adaptive neural network tracking control method provided by the present invention may also use other steps to implement, and the preset tracking accuracy adaptive neural network tracking control method provided by the present invention in fig. 1 is only a specific embodiment.
As shown in fig. 2, the preset tracking accuracy adaptive neural network tracking control system provided by the present invention includes:
the signal input module 1 is used for realizing that a system output signal and a reference signal are used as input of a switching function with known tracking precision;
the function processing module 2 is used for processing an unknown periodic time-varying parameterized function in the system by utilizing two approximation algorithms;
the unknown constant parameter processing module 3 is used for processing the unknown constant parameters by combining a back-stepping method and a self-adaptive control algorithm and considering an approximation error upper-bound estimation value;
and the controller design module 4 is used for designing a corresponding controller to be applied to the controlled system.
The technical solution of the present invention is further described with reference to the following specific examples.
The self-adaptive neural network control scheme provided by the embodiment of the invention is mainly implemented by 3 steps:
the method comprises the following steps:
1) special switching function based on the above introduction
Figure BDA0002981607000000101
Constructing a Lyapunov function:
Figure BDA0002981607000000102
2) the derivative of the designed Lyapunov function is subjected to a switching function with unknown periodic time-varying parameters due to uncertainty of the system
Figure BDA0002981607000000103
According to Young's inequality, the unknown function is divided into two parts, namely an unknown switching function Lambda1And a periodic time varying function Θ1(t) using approximation algorithms (fourier series and unknown function of neural network processing system:
Figure BDA0002981607000000104
Figure BDA0002981607000000105
wherein the content of the first and second substances,
Figure BDA0002981607000000106
the upper bound of the approximation error of the neural network and the Fourier series algorithm are respectively.
3) And (2) designing a corresponding virtual controller according to a back-stepping method.
4) To deal with unknown weights a in the approximation algorithm1 T,W1 *TRedesigning the Lyapunov function:
Figure BDA0002981607000000107
wherein
Figure BDA0002981607000000108
Is a positive definite diagonal matrix. Based on the self-adaptive backstepping control technology, corresponding design is carried out for estimating the weight of the approximation algorithmAdaptive control law of (2):
Figure BDA0002981607000000109
5) substituting the virtual controller designed in 3) and the adaptive law designed in 4) into a first subsystem of the controlled system, and simplifying derivative functions of the Lyapunov function.
Step two:
aiming at the first m-1 subsystems of a controlled system, designing a corresponding Lyapunov function:
Figure BDA00029816070000001010
and repeating the design process of the first step, and designing the virtual controllers for the m-1 subsystems respectively:
Figure BDA00029816070000001011
and parameter adaptation law:
Figure BDA0002981607000000111
and substituting the designed virtual controller and the designed adaptive law into a subsystem corresponding to the controlled system, and simplifying the derivative function of the Lyapunov function.
Step three: on the basis of the first m-1 step, aiming at the whole m-order system, a public Lyapunov function meeting all subsystems is designed, and the estimation error which approaches the upper bound of the error is considered for the first time:
Figure BDA0002981607000000112
wherein
Figure BDA0002981607000000113
Upper bound for radial basis function neural network and Fourier series approximation error, respectively
Figure BDA0002981607000000114
Is estimated byAnd (4) error. Based on the self-adaptive backstepping method, repeating the design process of the previous m-1 steps, and designing an actual controller:
Figure BDA0002981607000000115
and parameter (approximation weight and approximation error upper bound) adaptive law:
Figure BDA0002981607000000116
defining state error variables
Figure BDA0002981607000000117
Wherein alpha isj-1Is a virtual controller. The controller u is applied to a controlled system
Figure BDA0002981607000000118
Selecting Lyapunov functions
Figure BDA0002981607000000119
Substituting the designed parameter self-adaptation law into the method can prove that the method has the advantages of good stability, relevant mathematical theory and algebraic graph theory
Figure BDA00029816070000001110
And | z when t → ∞ time1(t) is less than or equal to E. Illustrating that the tracking error asymptotically converges to a predetermined range and that all signals of the closed loop system are bounded.
The above theory proves that: by constructing a common Lyapunov function which meets all subsystems and designing a controller and a self-adaptation law, the process of continuously adjusting parameters by realizing ideal tracking performance is avoided, and the aim of converging the tracking error to a small neighborhood of a preset zero point is fulfilled.
The technical effects of the present invention will be described in detail with reference to simulations.
Simulation 1, with a second order nonlinear switching system:
Figure BDA0002981607000000121
numerical simulations were performed for the examples. 1) The simulation conditions are as follows: reference track is ydSin (3t) + cos (t), and the period time-varying parameter is set to θ1(t)＝sin(t),θ2(t) sin (2t) and a system function of
Figure BDA0002981607000000122
f1,2＝x1cos(x1) And are and
Figure BDA0002981607000000123
f2,2＝x2. The initial conditions and parameter values in the simulation are shown in table 1.
TABLE 1 simulation realization conditions and parameter values
Figure BDA0002981607000000124
Wherein 1.5 is a 5-dimensional column vector ([1.5,1.5,1.5, 1.5)]T) And diag {10} is an identity matrix with all 10 diagonal elements.
2) And (3) simulation results: as shown in fig. 4, the output signal can track the upper reference track after 0.3 seconds. For better exhibition of tracking performance, the tracking error trajectory is presented in fig. 5. As shown in fig. 5, the tracking error is stabilized in the range of the preset precision e of the origin being 0.02, and the validity of the algorithm proposed by the present invention is well verified by the simulation result. Fig. 6 and 7 show traces of the controller and the switching signal, respectively, which achieve simulation results. Fig. 8 and 9 respectively show a trajectory diagram of a neural network and a fourier series approximation weight estimation 2-norm, which is mainly because the approximation weight is a vector, and if the trajectory of each weight estimation is given, the whole trajectory of the weight value cannot be clearly shown, so that the trajectory diagram of the weight estimation norm is given. The trajectory graph of the approximation error is shown in fig. 10, and the performance of the approximation algorithm can be visually seen according to the trajectory of the error upper-bound estimation value, which is an index for judging the performance of the approximation algorithm. In addition, it can be seen from the simulation diagram that the tracking error converges to the neighborhood of the preset zero point and all signals (output signal, approximation algorithm weight estimation and approximation error) of the whole closed-loop system are bounded, and the algorithm provided by the invention is effective.
Simulation 2, the algorithm proposed by the present invention is applied to a switching circuit system with a practical physical background, and the internal principle thereof is shown in fig. 11. 1) Simulation conditions are as follows: system function of f11＝f12＝(1/L)x2-x2And f21＝-(1/C1)x1-(R/L)x2,f22＝-(1/C2)x1-(R/L)x2(ii) a The reference trajectory is: y isd(t) ═ sin (4t) + cos (t). The initial conditions and parameters in the simulation are shown in table 2:
TABLE 2 simulation implementation conditions and parameter values
Figure BDA0002981607000000131
Figure BDA0002981607000000141
2) The simulation results are shown in fig. 12-17, respectively. Fig. 12 illustrates that the output signal can track the upper reference track. The corresponding trace plot of the tracking error is shown in fig. 13, and the tracking error converges to a small neighborhood of the predetermined zero point. Fig. 12 and fig. 13 illustrate a system of the specific practical background of the algorithm proposed by the present invention, which is still effective, and the application range of the algorithm is popularized. Fig. 14 shows a system switching signal trace for achieving simulation results. As shown in fig. 15, fig. 16 and fig. 17, the trajectories of the 2-norm approximation weight value estimation and the approximation error upper bound estimation value are respectively stable around a bounded value, which illustrates the signal's bounding property.
In conclusion, the algorithm provided by the invention is effective, not only is the approaching performance intuitively shown, but also the process of continuously adjusting parameters to realize ideal tracking performance is avoided, and the purpose that the tracking error converges to the target in the small neighborhood of the preset zero point and all signals of the whole closed-loop system are bounded is realized.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. A controller of a nonlinear parameterized switching system is characterized in that a kinetic equation of the nonlinear parameterized switching system is
Figure FDA0002981606990000011
The controller is
Figure FDA0002981606990000012
Wherein
Figure FDA0002981606990000013
Is a system state vector; y is the system output signal;
Figure FDA0002981606990000014
a switching signal representing a system; for any given j 1,2, a, m,
Figure FDA0002981606990000015
is an unknown smooth nonlinear function and satisfies
Figure FDA0002981606990000016
θj(t) is an unknown time-varying parameter of known periodicity.
2. A tracking control method of adaptive neural network with preset tracking accuracy using the controller of nonlinear parameterized switching system as in claim 1, characterized in that the controller u of nonlinear parameterized switching system is applied to the controlled system in combination with the introduction of special switching functions
Figure FDA0002981606990000017
Selecting Lyapunov functions
Figure FDA0002981606990000018
Through the knowledge of the Lyapunov stability theory, the related mathematical theory and the algebraic graph theory, the method can prove that
Figure FDA0002981606990000019
And | z when t → ∞ time1(t)|≤∈。
3. The adaptive neural network tracking control method with preset tracking accuracy as claimed in claim 2, wherein said system output signal and reference signal as inputs to a switching function with known tracking accuracy comprises:
1) based on the introduction of special handover functions
Figure FDA00029816069900000110
Constructing a Lyapunov function:
Figure FDA00029816069900000111
2) the derivative of the designed Lyapunov function is subjected to a switching function with unknown periodic time-varying parameters due to uncertainty of the system
Figure FDA00029816069900000112
According to Young's inequality, the unknown function is divided into two parts, namely an unknown switching function Lambda1And a periodic time varying function Θ1(t) using an approximation algorithm fourier series and an unknown function of the neural network processing system, respectively:
FSE：
Figure FDA0002981606990000021
NN：Λ1＝W1 *TS(Z1)+μ1,
Figure FDA0002981606990000022
wherein the content of the first and second substances,
Figure FDA0002981606990000023
respectively approximating the upper bound of errors by a neural network and a Fourier series algorithm;
3) designing a corresponding virtual controller according to a back stepping method on the basis of the step 2);
4) to deal with unknown weights a in the approximation algorithm1,W1 *Redesigning the Lyapunov function:
Figure FDA0002981606990000024
wherein
Figure FDA0002981606990000025
Is a positive definite diagonal matrix;based on the self-adaptive back-stepping control technology,
Figure FDA0002981606990000026
is an approximation algorithm weight a1,W1 *Designing a corresponding adaptive control law:
Figure FDA0002981606990000027
5) substituting the virtual controller designed in 3) and the adaptive law designed in 4) into a first subsystem of the controlled system, and simplifying derivative functions of the Lyapunov function.
4. The adaptive neural network tracking control method with preset tracking accuracy as claimed in claim 2, wherein said processing the unknown periodic time-varying parameterized function in the system by using two approximation algorithms comprises: aiming at the first m-1 subsystems of a controlled system, designing a corresponding Lyapunov function:
Figure FDA0002981606990000028
and repeating the design process, and respectively designing a virtual controller for the m-1 subsystems:
Figure FDA0002981606990000029
and parameter adaptation law:
Figure FDA00029816069900000210
and then substituting the designed virtual controller and the designed adaptive law into a subsystem corresponding to the controlled system, and simplifying the derivative function of the Lyapunov function.
5. The adaptive neural network tracking control method with preset tracking accuracy as claimed in claim 3, wherein the combination of the back-stepping method and the adaptive control algorithmThe method, which processes the unknown constant parameter and considers the approximation error upper bound estimation value, comprises the following steps: on the basis of the first m-1 step, aiming at the whole m-order system, a public Lyapunov function meeting all subsystems is designed, and the estimation error of the upper bound of the approximation error is taken into account for the first time:
Figure FDA0002981606990000031
wherein
Figure FDA0002981606990000032
Upper bound for radial basis function neural network and Fourier series approximation error, respectively
Figure FDA0002981606990000033
Based on the self-adaptive back-stepping method, repeating the design process of the previous m-1 steps, and designing an actual controller:
Figure FDA0002981606990000034
and parameter adaptation law:
Figure FDA0002981606990000035
defining state error variables
Figure FDA0002981606990000036
Wherein alpha isj-1The controller u is applied to a controlled system to be a virtual controller
Figure FDA0002981606990000037
Selecting Lyapunov functions
Figure FDA0002981606990000038
Substituting the designed parameter self-adaptation law into the method can prove that the method has the advantages of good stability, relevant mathematical theory and algebraic graph theory
Figure FDA0002981606990000039
And | z when t → ∞ time1(t)|≤∈。
6. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:
the system output signal and the reference signal are used as the input of a switching function with known tracking precision;
processing an unknown periodic time-varying parameterized function in the system by using two approximation algorithms;
combining a back-stepping method and a self-adaptive control algorithm, processing unknown constant parameters, and considering an approximation error upper-bound estimation value;
and designing a corresponding controller to be applied to a controlled system.
7. A switching circuit system information data processing terminal, which is characterized in that the switching circuit system information data processing terminal is used for realizing the preset tracking precision adaptive neural network tracking control method as claimed in any one of claims 2 to 6.
8. A preset tracking precision adaptive neural network tracking control system for implementing the preset tracking precision adaptive neural network tracking control method according to any one of claims 2 to 5, wherein the preset tracking precision adaptive neural network tracking control system comprises:
the signal input module is used for realizing that a system output signal and a reference signal are used as the input of a switching function with known tracking precision;
the function processing module is used for processing an unknown periodic time-varying parameterized function in the system by utilizing two approximation algorithms;
the unknown constant parameter processing module is used for processing the unknown constant parameters by combining a back-stepping method and a self-adaptive control algorithm and considering an approximation error upper-bound estimation value;
and the controller design module is used for designing a corresponding controller to be applied to the controlled system.
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