CN113110055B - Self-adaptive event trigger output feedback control method and system of time-lag switching system - Google Patents

Self-adaptive event trigger output feedback control method and system of time-lag switching system Download PDF

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CN113110055B
CN113110055B CN202110425443.5A CN202110425443A CN113110055B CN 113110055 B CN113110055 B CN 113110055B CN 202110425443 A CN202110425443 A CN 202110425443A CN 113110055 B CN113110055 B CN 113110055B
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王振华
孔杰
程婷婷
牛奔
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Shandong Normal University
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Abstract

The invention discloses a self-adaptive event trigger output feedback control method and a self-adaptive event trigger output feedback control system for a time-lag switching system, wherein the method comprises the following steps: determining a kinetic equation of the time-lag switching system; estimating unknown state variables according to a switching state observer, and converting a dynamic equation to obtain a state error equation; compensating time lag of a state error equation by a Lyapunov-Krasovski functional, and constructing a virtual controller by defining a virtual control rate and a self-adaptive rate; under an event trigger mechanism, the time-lag switching system is controlled based on the virtual controller, so that any MDADT in signals of the time-lag switching system is bounded during switching. By fusing an event trigger control strategy and a backstepping control method, a self-adaptive event trigger controller is constructed, and the problem of resource waste caused by the traditional time-driven control method is solved; the modality-dependent mean residence time method is also more suitable for practical applications than other methods.

Description

Self-adaptive event trigger output feedback control method and system of time-lag switching system
Technical Field
The invention relates to the technical field of switching systems, in particular to a self-adaptive event trigger output feedback control method and system of a time-lag switching system.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The switching system is a hybrid system consisting of a finite number of continuous or discrete time subsystems and switching rules that control the subsystems to be active. Many practical systems often contain both discrete events and continuous events, so modeling practical systems with switching systems has a wide range of application prospects.
The traditional time-driven control strategy is widely applied to the control design process, and is characterized in that the output of an actual controller is continuously transmitted to a system, but the waste of communication resources is caused; in addition, while some research efforts are currently being made in adaptive control of handover systems, most of the research efforts do not use event-triggered control strategies nor do they use an improved modality-dependent mean residence time (MDADT) approach.
Disclosure of Invention
In order to solve the problems, the invention provides a self-adaptive event trigger output feedback control method and a self-adaptive event trigger output feedback control system of a time-lag switching system.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, the present invention provides a feedback control method for adaptive event triggered output of a time lag switching system, including:
determining a kinetic equation of the time-lag switching system;
estimating unknown state variables according to a switching state observer, and converting a dynamic equation to obtain a state error equation;
compensating time lag of a state error equation by a Lyapunov-Krasovski functional, and constructing a virtual controller by defining a virtual control rate and an adaptive rate;
under an event trigger mechanism, the time-lag switching system is controlled based on the virtual controller, so that the time of switching under any MDADT in signals of the time-lag switching system is bounded.
In a second aspect, the present invention provides an adaptive event triggered output feedback control system for a dead-time switching system, comprising:
a dynamics modeling module configured to determine a dynamics equation of the time-lapse switching system;
the state estimation module is configured to estimate an unknown state variable according to the switching state observer, so that a state error equation is obtained by converting the dynamic equation;
the controller building module is configured to build a virtual controller by defining a virtual control rate and an adaptive rate according to the time lag of a state error equation compensated by a Lyapunov-Krasovski functional;
and the trigger module is configured to control the time-lapse switching system based on the virtual controller under the event trigger mechanism so as to enable the time-lapse switching system to be bounded when switching at any MDADT in the signals.
In a third aspect, the present invention provides an electronic device comprising a memory and a processor, and computer instructions stored on the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method of the first aspect is performed.
In a fourth aspect, the present invention provides a computer readable storage medium for storing computer instructions which, when executed by a processor, perform the method of the first aspect.
Compared with the prior art, the invention has the beneficial effects that:
(1) different from the public Lyapunov function method, the Duoyapunov function method and the average residence time method adopted by other inventions, the invention adopts an improved MDADT method to research the event-triggered adaptive neural output feedback control of a class of time-lag switching non-strict feedback nonlinear systems.
(2) Unlike classical time-driven control strategies, in which the output of the controller is continuously transmitted to the system, the control strategy proposed by the present invention transmits the output to the system only when the event-triggered error reaches a predefined threshold, effectively saving communication resources.
(3) The invention constructs a switching observer to solve the difficulty caused by an undetectable state, designs a common self-adaptive neural output feedback controller for all subsystems by adopting a self-adaptive backstepping method, and proves that all signals in a switching closed-loop system are bounded under any MDADT switch.
(4) According to the invention, the self-adaptive event trigger controller is constructed by fusing the event trigger control strategy and the backstepping control method, so that the problem of resource waste caused by the traditional time drive control method is solved, and compared with other methods, the modal-dependent average residence time method is more suitable for practical application.
Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
Fig. 1 is a flowchart of an adaptive event triggered output feedback control method for a time lag switching system according to embodiment 1 of the present invention;
FIG. 2 shows a simulated state variable ζ according to embodiment 1 of the present invention 1 ，
Figure BDA0003029519950000031
A waveform diagram;
FIG. 3 is a state variable ζ obtained by simulation provided in embodiment 1 of the present invention 2 ，
Figure BDA0003029519950000041
A waveform diagram;
FIG. 4 shows the simulated adaptive rates provided in embodiment 1 of the present invention
Figure BDA0003029519950000042
A waveform diagram;
FIG. 5 shows the simulated adaptive rates provided in embodiment 1 of the present invention
Figure BDA0003029519950000043
A waveform diagram;
fig. 6 is a waveform diagram of a controller and an actuator v (t), u (t) obtained by simulation provided in embodiment 1 of the present invention;
FIG. 7 is a waveform diagram of simulated event triggered time intervals provided in embodiment 1 of the present invention;
fig. 8 is a waveform diagram of a switching signal σ (t) obtained by simulation provided in embodiment 1 of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. 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.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise, and it should be understood that the terms "comprises" and "comprising", and any variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The embodiments and features of the embodiments of the invention may be combined with each other without conflict.
Example 1
As shown in fig. 1, the present embodiment provides a feedback control method for adaptive event triggered output of a skew switching system, which includes the following steps:
(1) determining a kinetic equation of the time-lag switching nonlinear system;
(2) estimating an unknown system state variable according to the switching state observer, and converting the dynamic equation to obtain a state error equation;
(3) compensating time lag of a state error equation by a Lyapunov-Krasovski functional, and defining a virtual control rate and an adaptive rate by a backstepping method and an intelligent approximation technology so as to construct a virtual controller;
(4) designing an event trigger controller to reduce communication resources;
(5) under an event trigger mechanism, the time-lag switching system is controlled based on the virtual controller, so that the time of switching under any MDADT in signals of the time-lag switching system is bounded.
The following describes in detail the implementation process of the adaptive event triggered output feedback control method of the time-lag switching nonlinear system according to this embodiment.
The kinetic equation for switching a nonlinear system in consideration of time lag is as follows:
Figure BDA0003029519950000051
wherein i is a system state dimension, i ═ 1.., n-1; ζ ═ ζ 1 ,ζ 2 ,...,ζ n ] T ∈R n U belongs to R, y belongs to R and is respectively the system state, input and output; ζ is the output variable y of the system 1 Can be directly measured, and the state variable ζ of the system 2 ,...,ζ n Cannot be measured directly, i 1,2 p,i (·)，q p,i (. a) an unknown continuous smooth nonlinear function satisfying f p,i (0)＝0，q p,i (0) 0; t represents time, τ i Is an unknown constant time delay; σ (t) [ [0, ∞) → Γ ═ 1,2,. ·, M } represents the switching signal.
Introducing a switching observer:
Figure BDA0003029519950000052
therein, ζ i In order to be in the state of the system,
Figure BDA0003029519950000061
is ζ i I is more than or equal to 1 and less than or equal to n, p belongs to gamma, y is the output of the system, u is the control input, l p,i 、l p,n Is a normal number that needs to be designed.
By definition
Figure BDA0003029519950000062
Equation of dynamics (1) is deformed as:
Figure BDA0003029519950000063
wherein e ═ e 1 ,e 2 ,...,e n ] T ；
F p (ζ)＝[f p,1 (ζ),f p,2 (ζ),...,f p,n (ζ)] T ；
D p (ζ(t-τ))＝[q p,1 (ζ(t-τ 1 )),q p,2 (ζ(t-τ 2 )),...,q p,n (ζ(t-τ n ))] T ；
Figure BDA0003029519950000064
For 1 ≦ i ≦ n, p ∈ Γ, the normal number l is chosen p,i Thus, matrix A p Is a Hurwitz matrix, which means that for a given positive definite matrix Q p There is a positive definite matrix P p So that equation (4) holds:
A p P p +P p A p ＝-Q p (4)
assume that 1: for i ═ 1, 2., n, and p ∈ Γ, the nonlinear function f p,i (·)、q p,i (. cndot.) satisfies the following inequality:
Figure BDA0003029519950000065
definition 1: for the switching signal sigma (T) and any time T ≧ T ≧ 0, N σp (T, T) represents the p-th subsystem in the time interval [ T, T [ ]]The number of times of switching; t is p (T, T) represents the p-th sub-system in the time interval [ T, T ]]The time of operation; if normal number N 0p And τ ap Satisfy the requirement of
Figure BDA0003029519950000066
The switching signal σ (t) is said to have MDADT τ ap 。
Introduction 1: for coordinate transformation
Figure BDA0003029519950000067
The inequality (6) holds:
Figure BDA0003029519950000068
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003029519950000071
radial basis function neural network approximation
Radial basis function neural networks are used to handle arbitrary unknown continuous functions, i.e. f (ζ) W T S(ζ)；
Wherein ζ ∈ Ω Z Is an input vector; w ═ ω 1 ,...ω l ]∈R l ，l>1 is the weight of the radial basis function neural network; gamma (zeta) is an error, and | gamma (zeta) | < delta, and S (zeta) | [ S ≦ S 1 (ζ),s 2 (ζ),...,s n (ζ)] T Expressing the vector of basis functions, selecting a Gaussian function having the form
Figure BDA0003029519950000072
Wherein o is i ＝[o i1 ,o i2 ,...,o in ] T Is center, v i Is the width of the gaussian function.
For any given γ >0, if the neuron number is large enough, an unknown continuous function f (ζ) is approximated by the following radial basis function neural network:
f(ζ)＝W T S(ζ)+γ(ζ),|γ(ζ)|≤δ (7)
wherein the optimal weight W * The selection is as follows:
Figure BDA0003029519950000073
2, leading: let a
Figure BDA0003029519950000074
As a vector of basis functions, wherein,
Figure BDA0003029519950000075
then, for any positive number k ≦ q, the following inequality is satisfied:
Figure BDA0003029519950000076
based on the analysis process, a backstepping method is utilized to realize the design process of the self-adaptive event trigger controller, and specifically: giving a control design process of the self-adaptive backstepping technology, defining a virtual control function and a self-adaptive rate:
Figure BDA0003029519950000077
Figure BDA0003029519950000078
wherein k is i And mu i Are respectively a positive design parameter, S i (Z i ) Is a neural network basis function vector;
Figure BDA0003029519950000081
Figure BDA0003029519950000082
is ρ i Is estimated.
(1) Designing a Lyapunov function:
V p ＝V pe +V pz +V ρ (12)
wherein, V pe ＝e T P p e+V p1 (13)
Figure BDA0003029519950000083
Figure BDA0003029519950000084
Figure BDA0003029519950000085
Figure BDA0003029519950000086
Wherein the content of the first and second substances,
Figure BDA0003029519950000087
and the formulas (14) and (16) are designed Lyapunov-Krasovski functional; t is time; tau is i Is an unknown constant time delay;
Figure BDA00030295199500000814
is a design constant; h is p In order to design the constants of the two-phase,
Figure BDA0003029519950000088
e＝[e 1 ,...,e n ] T ，
Figure BDA0003029519950000089
α i is a virtual control;
Figure BDA00030295199500000810
is an unknown function.
(2) Obtained by equation (3):
Figure BDA00030295199500000811
to simplify the expression, ζ τ ＝ζ(t-τ)，
Figure BDA00030295199500000812
According to assumption 1, there are:
Figure BDA00030295199500000813
Figure BDA0003029519950000091
according to the Young's inequality, there are:
Figure BDA0003029519950000092
wherein the content of the first and second substances,
Figure BDA0003029519950000093
Figure BDA0003029519950000094
Figure BDA0003029519950000095
wherein the content of the first and second substances,
Figure BDA0003029519950000096
substituting equations (19) - (23) into equation (18) yields:
Figure BDA0003029519950000097
(3) to simplify V pz Calculation of the derivative, defining:
Figure BDA0003029519950000098
definition of
Figure BDA0003029519950000099
To obtain
Figure BDA00030295199500000910
Figure BDA00030295199500000911
Wherein the content of the first and second substances,
Figure BDA0003029519950000101
further, we will
Figure BDA0003029519950000102
Expressed as:
Figure BDA0003029519950000103
wherein the content of the first and second substances,
Figure BDA0003029519950000104
further, in the present invention,
Figure BDA0003029519950000105
the derivative of (d) is expressed as:
Figure BDA0003029519950000106
wherein the content of the first and second substances,
Figure BDA0003029519950000107
combining equations (28) and (29), we obtain:
Figure BDA0003029519950000108
using neural networks
Figure BDA0003029519950000109
Approximating unknown functions
Figure BDA00030295199500001010
It is possible to obtain:
Figure BDA00030295199500001011
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00030295199500001012
Figure BDA00030295199500001013
wherein the content of the first and second substances,
Figure BDA00030295199500001014
ρ i ＝max{||W p,i || 2 ,p∈Γ}。
designing virtual control alpha n ：
Figure BDA00030295199500001015
Obtaining:
Figure BDA0003029519950000111
substituting equations (11), (32), and (34) into (30) yields:
Figure BDA0003029519950000112
(4) combining equations (24) and (35) yields:
Figure BDA0003029519950000113
obtained according to equation (11):
Figure BDA0003029519950000114
the following steps are provided:
Figure BDA0003029519950000115
finally, the following is obtained:
Figure BDA0003029519950000116
wherein the content of the first and second substances,
Figure BDA0003029519950000117
(5) designing an event trigger controller:
the actual controller design is as follows:
Figure BDA0003029519950000118
the event trigger mechanism is designed as follows:
Figure BDA0003029519950000121
t k+1 ＝inf{t>t k ||e(t)|≥δ|u(t)|+η} (42)
where e (t) is a measurement error, t (t) -u (t) is a measurement error k Denotes the kth trigger time, t k+1 Represents the (k + 1) th trigger moment; 0 < delta < 1, mu, eta and
Figure BDA0003029519950000122
is a positive design parameter.
Obtained by the formula (42)
Figure BDA0003029519950000123
Wherein the content of the first and second substances,
Figure BDA0003029519950000124
is a time-varying parameter, satisfies
Figure BDA0003029519950000125
Thus, the following results were obtained:
Figure BDA0003029519950000126
obtained by equation (43):
Figure BDA0003029519950000127
substituting (39) into equation (44) yields:
Figure BDA0003029519950000128
by means of the selection of the,
Figure BDA0003029519950000129
Figure BDA00030295199500001210
equation (45) is rewritten as:
Figure BDA00030295199500001211
order to
Figure BDA0003029519950000131
Obtaining:
V p (t)≤η p V l (t),η p >1 (47)
theorem 1: considering a switching system (1), if it is assumed that 1 holds, a switching observer (2), a virtual control rate (10), an adaptation rate (11) and an event trigger mechanism (42) are selected and a modality-dependent mean dwell time is satisfied
Figure BDA0003029519950000132
All signals that result in switching the closed loop system are bounded.
And (3) proving that: for arbitrary T>0，Let t 0 0 and define
Figure BDA0003029519950000133
Is a time [0, T]The time of the handover in (d) is,
Figure BDA0003029519950000134
order to
Figure BDA0003029519950000135
For piecewise differentiable functions, at time intervals t j ,t j+1 ) It is possible to obtain:
Figure BDA0003029519950000136
combining equations (49) and (47) yields:
Figure BDA0003029519950000137
thereby obtaining:
Figure BDA0003029519950000141
thus, it is possible to obtain:
Figure BDA0003029519950000142
where Ψ (p) is a set of s, satisfying σ (t) s )＝p，
Figure BDA0003029519950000143
And delta min ＝min{δ p P ∈ Γ } satisfies
Figure BDA0003029519950000144
By using
Figure BDA0003029519950000151
For arbitrary
Figure BDA0003029519950000152
To obtain
Figure BDA0003029519950000153
By definition 1, we obtain:
Figure BDA0003029519950000154
thus, there are:
Figure BDA0003029519950000155
bringing (54) into (52) results in:
Figure BDA0003029519950000156
thus, if the modality-dependent average residence time is satisfied
Figure BDA0003029519950000157
Figure BDA0003029519950000158
Will converge to a small neighborhood of near zero, ensuring that the signal switching the closed loop system is bounded.
Since the knowless phenomenon usually occurs in event-triggered mechanisms, for
Figure BDA0003029519950000159
Presence of t * >0 satisfies { t k+1 -t k }≥t * . Obtained by e (t) v (t) -u (t):
Figure BDA00030295199500001510
from equation (40) we obtain:
Figure BDA00030295199500001511
because of
Figure BDA00030295199500001512
Is z n And alpha n And thus all signals are bounded. Thus exist
Figure BDA00030295199500001513
So that
Figure BDA00030295199500001514
Integrating equation (56) yields:
Figure BDA00030295199500001515
thus obtaining
Figure BDA00030295199500001516
Thereby avoiding the fano phenomenon.
To demonstrate the effectiveness of an event-triggered controller, the following simulation experiment was conducted.
The model of the time-lapse switching nonlinearity is as follows:
Figure BDA0003029519950000161
wherein: p e Γ ═ 1,2},
Figure BDA0003029519950000162
f 1,2 ＝0.2ζ 2 sin(ζ 1 ζ 2 )，
q 1,1 (ζ)＝(0.25ζ 1 (t-τ 1 )ζ 2 (t-τ 1 ))/(1+ζ 1 (t-τ 2 ) 2 +ζ 2 (t-τ 2 ) 2 )
q 1,2 (ζ)＝(0.5ζ 1 (t-τ 1 )ζ 2 (t-τ 1 ))/(1+ζ 1 (t-τ 2 ) 2 +ζ 2 (t-τ 2 ) 2 )
Figure BDA0003029519950000163
q 2,1 (ζ)＝(0.25ζ 1 (t-τ 1 ) 2 sin(ζ 2 (t-τ 1 )))
q 2,2 (ζ)＝(0.25ζ 1 (t-τ 1 ) 2 sinζ 2 (t-τ 1 )),τ 1 ＝τ 2 ＝1
in the simulation experiment, the present embodiment selects suitable parameters as follows:
l 1,1 ＝3.2,l 1,2 ＝5.5,l 2,1 ＝3.3,l 2,2 ＝5.4,δ＝0.9,θ＝1,
Figure BDA0003029519950000164
μ＝15,m p,i ＝h p,i ＝0.05
ε＝0.5,a 1 ＝0.1920,a 2 ＝0.2215,λ 1 ＝2.5233,λ 2 ＝3.4103,η 1 ＝6.37296,η 2 ＝8.6818
Figure BDA0003029519950000165
μ 1 ＝0.1,μ 2 ＝0.2,r 1 ＝r 2 ＝15,k 1 ＝25,k 2 ＝15,ω 1 ＝ω 2 ＝0.05
matrix A 1 And A 2 Is a Herviz matrix, by selecting Q 1 10I and Q 2 12I, a positive definite matrix can be obtained:
Figure BDA0003029519950000166
the initial conditions were chosen as: zeta 1 (0)＝-0.1,ζ 2 (0)＝0.2,
Figure BDA0003029519950000167
The simulation results are shown in fig. 2-8, and the state variable ζ is given in fig. 2 and 3 1 ，
Figure BDA0003029519950000168
ζ 2 ，
Figure BDA0003029519950000169
Fig. 2 and 3 show that the switching state observer can well estimate the unknown system state; the adaptation rates are given in fig. 4 and 5
Figure BDA00030295199500001610
And
Figure BDA00030295199500001611
fig. 4 and 5 show that an event-triggered controller designed according to the adaptive back-step stability control method can guarantee that all variables in a closed-loop system are bounded; fig. 6 shows waveforms of the controller and the actuators v (t), u (t), and fig. 6 shows that event triggering can effectively save communication resources; fig. 7 shows a waveform diagram of the time interval of the event trigger, and fig. 8 shows a waveform diagram of the switching signal σ (t); the adaptive event trigger stability control method of the embodiment adopts an event trigger mechanism and a mode dependent average residence time method, and can solve the problem of network resource limitation; compared with a general control algorithm, the self-adaptive event triggering algorithm provided by the embodiment has obvious advantages, the used event triggering control strategy effectively improves the control efficiency, and the problem of communication constraint under limited network bandwidth is avoided. The improved MDADT method is more suitable for practical application.
Example 2
The present embodiment provides an adaptive event triggered output feedback control system of a skew switching system, including:
a dynamics modeling module configured to determine a dynamics equation of the time-lapse switching system;
the state estimation module is configured to estimate an unknown state variable according to the switching state observer, so that a state error equation is obtained by converting the dynamic equation;
the controller building module is configured to build a virtual controller by defining a virtual control rate and an adaptive rate according to the time lag of a state error equation compensated by a Lyapunov-Krasovski functional;
and the trigger module is configured to control the time-lapse switching system based on the virtual controller under the event trigger mechanism so as to enable the time-lapse switching system to be bounded when switching at any MDADT in the signals.
It should be noted that the modules correspond to the steps described in embodiment 1, and the modules are the same as the corresponding steps in the implementation examples and application scenarios, but are not limited to the disclosure in embodiment 1. It should be noted that the modules described above as part of a system may be implemented in a computer system such as a set of computer-executable instructions.
In further embodiments, there is also provided:
an electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, the computer instructions when executed by the processor performing the method of embodiment 1. For brevity, no further description is provided herein.
It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general purpose processor, a digital signal processor DSP, an application specific integrated circuit ASIC, an off-the-shelf programmable gate array FPGA or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include both read-only memory and random access memory, and may provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method described in embodiment 1.
The method in embodiment 1 may be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules in the processor. The software modules may be located in ram, flash, rom, prom, or eprom, registers, among other storage media as is well known in the art. The storage medium is located in a memory, and a processor reads information in the memory and completes the steps of the method in combination with hardware of the processor. To avoid repetition, it is not described in detail here.
Those of ordinary skill in the art will appreciate that the various illustrative elements, i.e., algorithm steps, described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (6)

1. A feedback control method for self-adaptive event trigger output of a time-lag switching system is characterized by comprising the following steps:
determining a kinetic equation of the time-lag switching system;
estimating unknown state variables according to a switching state observer, and converting a dynamic equation to obtain a state error equation; introducing a switching observer:
Figure FDA0003745425340000011
therein, ζ i In order to be in the state of the system,
Figure FDA0003745425340000012
is ζ i I is more than or equal to 1 and less than or equal to n, p belongs to gamma, y is the output of the system, u is the control input, l p,i 、l p,n Is a normal number required to be designed;
compensating time lag of a state error equation by a Lyapunov-Krasovski functional, and constructing a virtual controller by defining a virtual control rate and an adaptive rate;
Figure FDA0003745425340000013
Figure FDA0003745425340000014
the formulas (14) and (16) are designed Lyapunov-Krasovski functional; wherein t is time; tau is i Is an unknown constant time delay;
Figure DEST_PATH_FDA0003029519940000021
is a design constant; h is p In order to design the constants for the purpose of,
Figure FDA0003745425340000015
e＝[e 1 ，...，e n ] T ，
Figure FDA0003745425340000016
α i is virtual control;
Figure FDA0003745425340000017
is an unknown function;
defining a virtual control function and an adaptation rate:
Figure FDA0003745425340000018
Figure FDA0003745425340000019
wherein k is i And mu i Are respectively a positive design parameter, S i (Z i ) Is a neural network basis function vector;
Figure FDA0003745425340000021
Figure FDA0003745425340000022
is ρ i (ii) is estimated;
under an event trigger mechanism, controlling the time-lag switching system based on a virtual controller so as to enable the time-lag switching system to be bounded when switching is carried out under any MDADT in signals;
the event trigger mechanism is designed as follows:
Figure FDA0003745425340000023
t k+1 ＝inf{t＞t k ||e(t)|≥δ|u(t)|+η} (42)
wherein e (t) v (t) u (t) is a measurement error,t k denotes the kth trigger time, t k+1 Represents the (k + 1) th trigger moment; 0 < delta < 1, mu, eta is a positive design parameter.
2. The adaptive event-triggered output feedback control method for time-lag switching systems as claimed in claim 1, wherein the virtual controller is constructed by defining the virtual control rate and the adaptive rate through a back-stepping method and an intelligent approximation method based on a radial basis function neural network.
3. The adaptive event-triggered output feedback control method for a time-lag switching system as recited in claim 1, wherein an average dwell time threshold is preset, and when the time-lag switching system is controlled based on the virtual controller, the modal-dependent average dwell time of the time-lag switching system satisfies the average dwell time threshold, so that all signals of the time-lag switching system are bounded.
4. An adaptive event triggered output feedback control system for a time-lapse switching system, comprising:
a dynamics modeling module configured to determine a dynamics equation of the time-lapse switching system;
the state estimation module is configured to estimate unknown state variables according to the switching state observer so as to convert the dynamic equation to obtain a state error equation; introducing a switching observer:
Figure FDA0003745425340000031
therein, ζ i In order to be in the state of the system,
Figure FDA0003745425340000032
is ζ i I is more than or equal to 1 and less than or equal to n, p belongs to gamma, y is the output of the system, u is the control input, l p,i 、l p,n Is a normal number required to be designed;
the controller building module is configured to build a virtual controller by defining a virtual control rate and an adaptive rate according to the time lag of a state error equation compensated by a Lyapunov-Krasovski functional;
Figure FDA0003745425340000033
Figure FDA0003745425340000034
the formulas (14) and (16) are designed Lyapunov-Krasovski functional; wherein t is time; tau is i Is an unknown constant time delay;
Figure 85659DEST_PATH_FDA0003029519940000021
is a design constant; h is p In order to design the constants for the purpose of,
Figure FDA0003745425340000035
e＝[e 1 ，…，e n ] T ，
Figure FDA0003745425340000036
α i is virtual control;
Figure FDA0003745425340000037
is an unknown function;
defining the virtual control function and the adaptation rate:
Figure FDA0003745425340000038
Figure FDA0003745425340000039
wherein k is i And mu i Are respectively a positive design parameter, S i (Z i ) Is a neural network basis function vector;
Figure FDA00037454253400000310
Figure FDA00037454253400000311
is ρ i (ii) an estimate of (d);
the trigger module is configured to control the time-lag switching system based on the virtual controller under an event trigger mechanism so as to enable the time-lag switching system to be bounded when switching is carried out under any MDADT in signals of the time-lag switching system; the event trigger mechanism is designed as follows:
Figure FDA0003745425340000041
t k+1 ＝inf{t＞t k ||e(t)|≥δ|u(t)|+η} (42)
where e (t) is a measurement error, t (t) -u (t) is a measurement error k Denotes the kth trigger time, t k+1 Represents the (k + 1) th trigger moment; 0 < delta < 1, mu, eta is a positive design parameter.
5. An electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, the computer instructions when executed by the processor performing the method of any of claims 1-3.
6. A computer-readable storage medium storing computer instructions which, when executed by a processor, perform the method of any one of claims 1 to 3.
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