CN111352344A - Data-driven self-adaptive predictor of dynamic completely unknown system - Google Patents

Data-driven self-adaptive predictor of dynamic completely unknown system Download PDF

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CN111352344A
CN111352344A CN202010131320.6A CN202010131320A CN111352344A CN 111352344 A CN111352344 A CN 111352344A CN 202010131320 A CN202010131320 A CN 202010131320A CN 111352344 A CN111352344 A CN 111352344A
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彭周华
阮明昊
刘陆
王丹
李铁山
王浩亮
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Dalian Maritime University
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Abstract

The embodiment of the invention discloses a data-driven self-adaptive predictor of a dynamic completely unknown system, which is characterized by comprising the following steps: the system comprises a controller module, an extended state observer module, a stacker module and a robustness predictor module; the controller module is capable of obtaining control input parameters as input values to the system based on state parameters in the system, control input gain parameters in the robustness predictor module, output parameters in the extended state observer, desired state parameters of the system, and control parameter estimation scalar parameters. The invention can realize rapid system parameter b alignment in short time0、θ1And
Figure DDA0002395847330000011
accurate and stable identification is carried out, and meanwhile, the derivative of the system state parameter can be eliminated
Figure DDA0002395847330000012
Of (a) such thatThe design method is more beneficial to practical engineering application.

Description

Data-driven self-adaptive predictor of dynamic completely unknown system
Technical Field
The invention relates to the technical field of nonlinear system control, in particular to a data-driven self-adaptive predictor of a dynamic completely unknown system.
Background
As industrial production progresses, production devices and processes become more complex, and it is difficult to know the dynamic characteristics of the system exactly, but these production processes generate and store a large amount of data information, and nonlinear system control becomes a research hotspot in academia and industry. There are many methods for nonlinear system control research, such as adaptive control, optimal control, robust control, and intelligent control. The adaptive control can automatically adjust the parameters of the controller according to the internal disturbance and the external uncertainty of the nonlinear system, so that the input parameters of the controlled system can track and converge to the reference parameters, and the adaptive capacity of the required control strategy and control parameters can be gradually formed in a changing environment.
The current adaptive control methods include nonlinear adaptive control based on feedback linearization, nonlinear adaptive control based on backstepping method and nonlinear adaptive control based on neural network. Wherein the neural network based control design comprises: the method comprises the following steps of prediction control based on a neural network, model reference control based on the neural network and internal model control based on the neural network. The neural network control algorithm is an important method for solving the problem of nonlinear control and has a good control effect. The nonlinear adaptive control based on the neural network has wide application in the fields of ship control, unmanned aerial vehicle control and the like.
However, in the field of nonlinear system control, the following disadvantages still exist in the existing control technology for a completely unknown system aiming at dynamics:
first, in the existing predictor control method for a dynamic completely unknown system, although unknown parameters can be identified, it can be ensured that the observed values of the identified parameters converge within a certain interval of the actual values, but the parameters of the nonlinear system cannot be accurately identified, so that the requirements of precision industrial production are difficult to achieve.
Second, in the existing self-learning method for a dynamic completely unknown system, although parameter identification can be performed, the derivative of the known complex nonlinear system state is required
Figure BDA0002395847310000011
The method is limited in practical application.
Third, disturbance is often accompanied in the existing parameter identification method for a dynamic completely unknown system, and although the existing method can better suppress disturbance, specific parameters of a known system model are required.
Fourthly, in the existing control method for the completely unknown dynamic system, the suppression of disturbance and the identification of parameters cannot be realized at the same time, and a good control effect cannot be achieved.
Disclosure of Invention
Based on the above, in order to solve the defects in the prior art, the invention particularly provides a data-driven self-adaptive predictor of a dynamic completely unknown system, the invention combines a self-adaptive control method with predictor design, and provides a data-driven self-adaptive predictor structural design of the dynamic completely unknown system with quick response, high benefit and strong environmental adaptability, which can realize the rapid response of a nonlinear system parameter b in a short time0、θ1And
Figure BDA0002395847310000021
the method can accurately and stably identify and simultaneously eliminate the derivative of the state parameter of the nonlinear system
Figure BDA0002395847310000022
The design method is more beneficial to practical engineering application due to the dependence of the design method.
A data-driven adaptive predictor for a dynamic totally unknown system, comprising: the system comprises a controller module, an extended state observer module, a stacker module and a robustness predictor module;
wherein the controller module is capable of controlling the input gain parameter based on the state parameter x in the dynamic completely unknown system and the control input gain parameter in the robustness predictor module
Figure BDA0002395847310000023
Output parameters in extended state observer
Figure BDA0002395847310000024
Expected state parameter r and control parameter estimation scalar parameter of dynamic completely unknown system
Figure BDA0002395847310000025
Acquiring a control input parameter u as an input value of the system, wherein the input end of the controller module is respectively connected with the output ends of the system, the robustness predictor module and the extended state observer module, and the output end of the controller module is respectively connected with the input ends of the system, the stacker module, the extended state observer module and the robustness predictor module; the input end of the extended state observer module is connected with the output ends of the system and the robustness predictor module respectively, and the output end of the extended state observer module is connected with the input end of the controller module; the input end of the stacker module is respectively connected with the output ends of the system and the input controller module, and the output end of the stacker module is connected with the input end of the robustness predictor module; the input end of the robustness predictor module is respectively connected with the output ends of the system and the stacker module, and the output end of the robustness predictor module is respectively connected with the input ends of the controller module and the extended state observer module;
the state equation corresponding to the dynamic completely unknown system is as follows:
Figure BDA0002395847310000026
wherein the content of the first and second substances,
Figure BDA00023958473100000313
as derivatives of system state parameters, Y1To control the output parameter, θ1To identify control output parameter scalars, b0To identify the control input gain, ω is the system disturbance parameter and the row parameter variable matrix is Y ═ Y1,u]The column parameter constant matrix is.
Figure BDA0002395847310000032
Optionally, in one embodiment, the corresponding calculation equation of the control input parameter u is:
Figure BDA0002395847310000033
wherein ω iscScalar of a parameter referenced by the controller module, and ωcAnd a control parameter omega0The mathematical relationship is
Figure BDA0002395847310000034
Optionally, in one embodiment, the data-driven adaptive predictor further includes a first comparator, where the first comparator is capable of obtaining a state tracking error parameter of the system, that is, a difference between an actual state and an expected state of the system; the corresponding calculation formula is xdX-r, wherein xdRepresenting the state tracking error parameters of the system.
Optionally, in one embodiment, the output parameters in the extended state observer module
Figure BDA0002395847310000035
Corresponding calculation equation is
Figure BDA0002395847310000036
Wherein k is1∈R，k3∈R，k3∈ R are parameters referenced by a given extended state observer, where each referenced parameter is associated with a labelQuantity parameter omega0Are respectively [ k ] as1,k2,k3]＝[2ω0,ω0 2,0]；
Optionally, in one embodiment, the data-driven adaptive predictor further includes a second comparator, where the second comparator is capable of obtaining a state observation error of the system, that is, a difference between an observed state of the system and an actual state, and a corresponding calculation formula is
Figure BDA0002395847310000037
Wherein xmIndicating the state observation error of the system.
Optionally, in one embodiment, the stacker module is capable of outputting tkStored data Y (k) of time,
Figure BDA0002395847310000038
And YT(k) The robustness predictor module is used as an input signal of the robustness predictor module; corresponding calculation equation is
Figure BDA0002395847310000039
Wherein, the stack memory P1For storing historical data of the parameter matrix Y, and a stack memory for storing derivatives of state parameters of the system
Figure BDA00023958473100000310
(ii) historical storage data; k is any integer greater than 0.
Optionally, in one embodiment, the stacker module further includes a differential tracker TD, an input end of the differential tracker inputs the system state parameter x, and an output end of the differential tracker inputs the system state derivative
Figure BDA00023958473100000311
Corresponding calculation equation is
Figure BDA00023958473100000312
Where α and β are the parameters referenced by a given differential tracker.
Optionally, in one embodiment, the robustness predictor module can estimate the derivative of the parameter matrix estimate
Figure BDA0002395847310000041
And obtaining the parameter estimation value
Figure BDA0002395847310000042
As input signals for a robustness predictor module and a controller module; corresponding calculation equation is
Figure BDA0002395847310000043
Wherein the content of the first and second substances,
Figure BDA0002395847310000044
is an estimate of a system state parameter x, mu1，μ2，μ3Are parameter scalars referenced by a given robustness predictor module.
Optionally, in one embodiment, the data-driven adaptive predictor further includes a third comparator, where the third comparator is capable of obtaining a state estimation error of the system, that is, a difference between an estimated state and an actual state, and a corresponding calculation formula is
Figure BDA0002395847310000045
Wherein xeRepresenting the state estimation error of the system.
The embodiment of the invention has the following beneficial effects:
firstly, the method can ensure that the method can quickly identify the related parameters in a short time and the identification result is accurate and stable through the historical data drive of the system state derivative;
second, the present invention eliminates the pair-pairing by establishing a differential tracker TD to differentiate the known nonlinear system state xNonlinear system state derivative
Figure BDA0002395847310000046
(iii) dependence of (c);
thirdly, in the control of a dynamic completely unknown system, the predictor is combined with a self-adaptive rate method, so that the suppression of disturbance and the identification of parameters can be realized simultaneously;
fourthly, the estimated state is adopted for feedback, and the interference of the measurement noise on the nonlinear system is eliminated, so that the design method of the controller is beneficial to practical engineering application.
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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 used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Wherein:
FIG. 1 is a diagram illustrating an exemplary architecture of the data-driven adaptive predictor;
FIG. 2 shows the system identification parameter b according to one embodiment0The observation effect graph of (1);
FIG. 3 is a diagram illustrating the system identification parameter θ in one embodiment1The observation effect graph of (1);
FIG. 4 shows the system identification parameters in one embodiment
Figure BDA0002395847310000051
The observation effect map of (1).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and 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.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. It will be understood that, as used herein, the terms "first," "second," and the like may be used herein to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present application. The first and second elements are both elements, but they are not the same element.
In this embodiment, a data-driven adaptive predictor for a dynamic completely unknown system is proposed, as shown in fig. 1-2, and includes: the system comprises a controller module, an extended state observer module, a stacker module and a robustness predictor module;
wherein the controller module is capable of controlling the input gain parameter based on the state parameter x in the dynamic completely unknown system and the control input gain parameter in the robustness predictor module
Figure BDA0002395847310000052
Output parameters in extended state observer
Figure BDA0002395847310000053
Desired state parameter r, control parameter estimation scalar parameter of system
Figure BDA0002395847310000054
Acquiring a control input parameter u as an input value of a system, wherein the input end of the controller module is respectively connected with the output ends of the system, the robustness predictor module and the extended state observer module, and the output end of the controller module is respectively connected with the input ends of the system, the stacker module, the extended state observer module and the robustness predictor module; the expanded state viewThe input end of the detector module is respectively connected with the output ends of the system and the robustness predictor module, and the output end of the extended state observer module is connected with the input end of the controller module; the input end of the stacker module is respectively connected with the output ends of the system and the input controller module, and the output end of the stacker module is connected with the input end of the robustness predictor module; the input end of the robustness predictor module is respectively connected with the output ends of the system and the stacker module, and the output end of the robustness predictor module is respectively connected with the input ends of the controller module and the extended state observer module;
the corresponding state equation of the system is as follows:
Figure BDA0002395847310000061
wherein the content of the first and second substances,
Figure BDA0002395847310000062
as derivatives of system state parameters, Y1To control the output parameter, θ1To identify control output parameter scalars, b0To identify the control input gain, ω is the system disturbance parameter and the row parameter variable matrix is Y ═ Y1,u]The column parameter constant matrix is
Figure BDA0002395847310000063
In some specific embodiments, the corresponding calculation equation of the control input parameter u is:
Figure BDA0002395847310000064
wherein ω iscScalar of a parameter referenced by the controller module, and ωcAnd a control parameter omega0The mathematical relationship is
Figure BDA0002395847310000065
In some specific embodiments, the data-driven adaptive predictor further comprises a first comparator capable of obtaining a seriesTracking error parameters of the system state, namely the difference between the actual state and the expected state of the system; the corresponding calculation formula is xdX-r, wherein xdRepresenting the state tracking error parameters of the system.
In some specific embodiments, the output parameters in the extended state observer module
Figure BDA00023958473100000612
Corresponding calculation equation is
Figure BDA0002395847310000066
Wherein k is1∈R，k3∈R，k3∈ R are parameters referenced by a given extended state observer, where each referenced parameter is associated with a scalar parameter ω0Are respectively [ k ] as1,k2,k3]＝[2ω0,ω0 2,0]；
In some specific embodiments, the data-driven adaptive predictor further includes a second comparator, the second comparator is capable of obtaining a state observation error of the system, i.e. a difference between an observed state of the system and an actual state, and the corresponding calculation formula is
Figure BDA0002395847310000067
Wherein xmIndicating the state observation error of the system.
In some embodiments, the stacker module is capable of outputting tkStored data Y (k) of time,
Figure BDA0002395847310000068
And YT(k) The robustness predictor module is used as an input signal of the robustness predictor module; corresponding calculation equation is
Figure BDA0002395847310000069
Wherein, the stack memory P1For storing historical data of the parameter matrix Y, stack memory forStoring state derivatives of non-linear systems
Figure BDA00023958473100000610
(ii) historical storage data; k is any integer greater than 0.
In some specific embodiments, the stacker module further comprises a differential tracker TD, an input end of the differential tracker inputs the system state parameter x, and an output end of the differential tracker inputs the system state derivative
Figure BDA00023958473100000611
Corresponding calculation equation is
Figure BDA0002395847310000071
Wherein x iszFor the integration of the system state parameter x, α and β are the parameters referenced by a given differential tracker.
In some embodiments, the robustness estimator module can estimate the derivative of the parameter matrix estimate
Figure BDA0002395847310000072
And obtaining the parameter estimation value
Figure BDA0002395847310000073
As input signals of the current robustness predictor module and the controller module; corresponding calculation equation is
Figure BDA0002395847310000074
Wherein the content of the first and second substances,
Figure BDA0002395847310000075
is an estimate of a system state parameter x, mu1，μ2，μ3Are parameter scalars referenced by a given robustness predictor module.
In some specific embodiments, the data-driven adaptive predictor further comprisesA third comparator capable of obtaining a state estimation error of the system, i.e. a difference value between the estimated state and the actual state of the system, wherein the corresponding calculation formula is
Figure BDA0002395847310000076
Wherein xeRepresenting the state estimation error of the system.
Based on the scheme, the scheme is subjected to simulation design: the system state equation is as follows:
Figure BDA0002395847310000077
when the simulation time T is less than the set time T, the set time T is 30, each identification parameter theta1＝-1，b0＝1，
Figure BDA0002395847310000078
When the simulation time T is more than or equal to the set time T equal to 30, each identification parameter theta1＝-1.2，b0＝0.8，x＝0.3；
The controller module relates to design parameters as follows:
Figure BDA0002395847310000079
wherein parameters are quoted for control input: omegac＝20；
The extended state observer module involves design parameters that are:
Figure BDA00023958473100000710
the parameters introduced are as follows: k is a radical of1＝2ω0＝100，k2＝ω0 2＝2500，k3＝0；
The robustness predictor module relates to design parameters as follows:
Figure BDA00023958473100000711
the parameters introduced are as follows: mu.s1＝20，μ2＝100，μ3＝500；
FIG. 2 shows a complex nonlinear system identification parameter b as described herein0FIG. 3 is a graph of the complex nonlinear system identification parameter θ1Has θ is known as1Is for a given parameter theta1The prediction identification is carried out; FIG. 4 is a diagram of complex nonlinear system identification parameters
Figure BDA0002395847310000081
As can be seen from the observed effect graph of (c),
Figure BDA0002395847310000082
is for a given parameter
Figure BDA0002395847310000083
The prediction of (1) is identified.
According to simulation results, in a short time, the data-driven self-adaptive predictor structure design method for the dynamic completely unknown system can ensure that the effect of identifying system parameters can be rapidly and stably achieved by a method of combining predictor design and self-adaptive rate under the condition that the dynamic performance of a complex nonlinear system is unknown. In summary, the data-driven adaptive predictor design method for the dynamic completely unknown system provided by the invention is obviously superior to the existing parameter identification method under the same dynamic unknown system environment.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (9)

1. A data-driven adaptive predictor for a dynamic totally unknown system, comprising: the system comprises a controller module, an extended state observer module, a stacker module and a robustness predictor module;
wherein the controller module is capable of controlling the gain parameter based on a state parameter x in the system, a control input gain parameter in the robustness predictor module
Figure FDA0002395847300000016
Output parameters in extended state observer
Figure FDA0002395847300000018
Desired state parameter r, control parameter estimation scalar parameter of system
Figure FDA0002395847300000017
Acquiring a control input parameter u as an input value of a system, wherein the input end of the controller module is respectively connected with the output ends of the system, the robustness predictor module and the extended state observer module, and the output end of the controller module is respectively connected with the input ends of the system, the stacker module, the extended state observer module and the robustness predictor module; the input end of the extended state observer module is connected with the output ends of the system and the robustness predictor module respectively, and the output end of the extended state observer module is connected with the input end of the controller module; the input end of the stacker module is respectively connected with the output ends of the system and the input controller module, and the output end of the stacker module is connected with the input end of the robustness predictor module; the input end of the robustness predictor module is respectively connected with the output ends of the system and the stacker module, and the output end of the robustness predictor module is respectively connected with the input ends of the controller module and the extended state observer module;
the corresponding state equation of the system is as follows:
Figure FDA0002395847300000011
wherein the content of the first and second substances,
Figure FDA0002395847300000012
as derivatives of system state parameters, Y1To control the output parameter, θ1To identify control output parameter scalars, b0To identify the control input gain, ω is the system disturbance parameter and the row parameter variable matrix is Y ═ Y1,u]The column parameter constant matrix is
Figure FDA0002395847300000013
2. The data driven adaptive predictor of claim 1,
the corresponding calculation equation of the control input parameter u is:
Figure FDA0002395847300000014
wherein ω iscScalar of a parameter referenced by the controller module, and ωcAnd a control parameter omega0Has the mathematical relationship of
Figure FDA0002395847300000015
3. The data driven adaptive predictor of claim 2,
the data-driven adaptive pre-estimator further comprises a first comparator, wherein the first comparator can acquire a state tracking error parameter of a system, namely a difference value between an actual state and an expected state of the system; the corresponding calculation formula is xdX-r, wherein xdRepresenting the state tracking error parameters of the system.
4. The data driven adaptive predictor of claim 1,
output parameters in the extended state observer module
Figure FDA0002395847300000021
Corresponding calculation equation is
Figure FDA0002395847300000022
Wherein k is1∈R，k3∈R，k3∈ R are parameters referenced by a given extended state observer, where each referenced parameter is associated with a scalar parameter ω0Are respectively in the mathematical relationship of
Figure FDA0002395847300000023
5. The data driven adaptive predictor of claim 4,
the data-driven self-adaptive pre-estimator further comprises a second comparator, wherein the second comparator can obtain a state observation error of a system, namely a difference value between an observation state and an actual state of the system, and a corresponding calculation formula is
Figure FDA0002395847300000024
Wherein xmIndicating the state observation error of the system.
6. The data driven adaptive predictor of claim 1,
the stacker module is capable of outputting tkStored data Y (k) of time,
Figure FDA0002395847300000025
And YT(k) The robustness predictor module is used as an input signal of the robustness predictor module; corresponding calculation equation is
Figure FDA0002395847300000026
Wherein, the stack memory P1For storing historical data of the parameter matrix Y, and a stack memory for storing derivatives of state parameters of the system
Figure FDA0002395847300000027
(ii) historical storage data; k is any integer greater than 0.
7. The data driven adaptive predictor of claim 6,
the stacker module further comprises a differential tracker TD, wherein the input end of the differential tracker is input with a system state parameter x, and the output end of the differential tracker is input with a system state derivative
Figure FDA0002395847300000028
Corresponding calculation equation is
Figure FDA0002395847300000029
Where α and β are the parameters referenced by a given differential tracker.
8. The data driven adaptive predictor of claim 1,
the robustness predictor module can estimate the derivative of the parameter matrix
Figure FDA00023958473000000210
And obtaining the parameter estimation value
Figure FDA00023958473000000211
As input signals for a robustness predictor module and a controller module; corresponding calculation equation is
Figure FDA00023958473000000212
Wherein the content of the first and second substances,
Figure FDA0002395847300000031
is an estimate of a system state parameter x, mu1，μ2，μ3Are parameter scalars referenced by a given robustness predictor module.
9. The data driven adaptive predictor of claim 8,
the data-driven adaptive pre-estimator further comprises a third comparator, and the third comparator can acquire a state estimation error of the nonlinear system, namely a difference value between an estimated state and an actual state.
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