CN113110055A - 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

Info

Publication number
CN113110055A
CN113110055A CN202110425443.5A CN202110425443A CN113110055A CN 113110055 A CN113110055 A CN 113110055A CN 202110425443 A CN202110425443 A CN 202110425443A CN 113110055 A CN113110055 A CN 113110055A
Authority
CN
China
Prior art keywords
time
lag
switching system
switching
adaptive
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110425443.5A
Other languages
Chinese (zh)
Other versions
CN113110055B (en
Inventor
王振华
孔杰
程婷婷
牛奔
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong Normal University
Original Assignee
Shandong Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shandong Normal University filed Critical Shandong Normal University
Priority to CN202110425443.5A priority Critical patent/CN113110055B/en
Publication of CN113110055A publication Critical patent/CN113110055A/en
Application granted granted Critical
Publication of CN113110055B publication Critical patent/CN113110055B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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 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. 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, and designs a common adaptive neural output feedback controller for all subsystems by adopting an adaptive backstepping method, thereby proving 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.
Drawings
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 invention1，
Figure BDA0003029519950000031
A waveform diagram;
FIG. 3 is a state variable ζ obtained by simulation provided in embodiment 1 of the present invention2，
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 present 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 kinetic 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 ═ ζ1,ζ2,...,ζn]T∈RnU belongs to R, y belongs to R and is respectively the system state, input and output; output variable y ═ ζ of system1Can be directly measured, and the state variable ζ of the system2,...,ζnCannot be measured directly, i 1,2p,i(·)，qp,i(. a) an unknown continuous smooth nonlinear function satisfying fp,i(0)＝0，qp,i(0) 0; t represents time, τiIs an unknown constant time delay; σ (t) [ [0, ∞) → Γ ═ 1,2,. ·, M } represents the switching signal.
Introducing a switching observer:
Figure BDA0003029519950000052
wherein the content of the first and second substances,ζiin order to be in the state of the system,
Figure BDA0003029519950000061
is ζiI 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, lp,i、lp,nIs a normal number that needs to be designed.
By definition
Figure BDA0003029519950000062
Equation (1) of dynamics is modified as:
Figure BDA0003029519950000063
wherein e ═ e1,e2,...,en]T；
Fp(ζ)＝[fp,1(ζ),fp,2(ζ),...,fp,n(ζ)]T；
Dp(ζ(t-τ))＝[qp,1(ζ(t-τ1)),qp,2(ζ(t-τ2)),...,qp,n(ζ(t-τn))]T；
Figure BDA0003029519950000064
For 1 ≦ i ≦ n, p ∈ Γ, the normal number l is chosenp,iThus, matrix ApIs a Hurwitz matrix, which means that for a given positive definite matrix QpThere is a positive definite matrix PpSo that equation (4) holds:
ApPp+PpAp＝-Qp (4)
assume that 1: for i ═ 1, 2., n, and p ∈ Γ, the nonlinear function fp,i(·)、qp,i(. DEG) satisfies the following inequality:
Figure BDA0003029519950000065
definition 1: for the switching signal sigma (T) and any time T ≧ T ≧ 0, Nσp(T, T) represents the p-th subsystem in the time interval [ T, T [ ]]The number of times of switching; t isp(T, T) represents the p-th subsystem in the time interval [ T, T [ ]]The time of operation; if normal number N0pAnd τapSatisfy the requirement of
Figure BDA0003029519950000066
The switching signal σ (t) is said to have MDADT τap。
Introduction 1: for coordinate transformation
Figure BDA0003029519950000067
The inequality (6) holds:
Figure BDA0003029519950000068
wherein the content of the first and second substances,
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) WTS(ζ)；
Wherein ζ ∈ ΩZIs an input vector; w ═ ω1,...ωl]∈Rl，l>1 is the weight of the radial basis function neural network; γ (ζ) is an error, and | γ (ζ) | ≦ δ, and S (ζ) | [ S ≦ S1(ζ),s2(ζ),...,sn(ζ)]TExpressing the vector of basis functions, selecting a Gaussian function having the form
Figure BDA0003029519950000072
Wherein o isi＝[oi1,oi2,...,oin]TIs center, viIs 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)＝WTS(ζ)+γ(ζ),|γ(ζ)|≤δ (7)
wherein the optimal weight W*The selection is as follows:
Figure BDA0003029519950000073
2, leading: let
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 isiAnd muiAre respectively a positive design parameter, Si(Zi) Is a neural network basis function vector;
Figure BDA0003029519950000081
Figure BDA0003029519950000082
is ρiIs estimated.
(1) Designing a Lyapunov function:
Vp＝Vpe+Vpz+Vρ (12)
wherein, Vpe＝eTPpe+Vp1 (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 isiIs an unknown constant time delay;
Figure BDA00030295199500000814
is a design constant; h ispIn order to design the constants of the two-phase,
Figure BDA0003029519950000088
e＝[e1,...,en]T，
Figure BDA0003029519950000089
αiis virtual control;
Figure BDA00030295199500000810
is unknownA function.
(2) Obtained by equation (3):
Figure BDA00030295199500000811
to simplify the expression, ζτ＝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 VpzCalculation 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 content of the first and second substances,
Figure BDA00030295199500001012
Figure BDA00030295199500001013
wherein the content of the first and second substances,
Figure BDA00030295199500001014
ρi＝max{||Wp,i||2,p∈Γ}。
designing virtual control alphan：
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
tk+1＝inf{t>tk||e(t)|≥δ|u(t)|+η} (42)
where e (t) is a measurement error, t (t) -u (t) is a measurement errorkDenotes the kth trigger time, tk+1Represents 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:
Vp(t)≤ηpVl(t),ηp>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 00 and define
Figure BDA0003029519950000133
Is a time [0, T]The time of the inner switching is the time of the inner switching,
Figure BDA0003029519950000134
order to
Figure BDA0003029519950000135
For piecewise differentiable functions, at time intervals tj,tj+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 deltamin＝min{δpP ∈ 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
therefore, the temperature of the molten metal is controlled,if modality-dependent mean 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 { tk+1-tk}≥t*. Obtained by e (t) v (t) u (t):
Figure BDA00030295199500001510
from equation (40) we obtain:
Figure BDA00030295199500001511
because of the fact that
Figure BDA00030295199500001512
Is znAnd alphanAnd 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
f1,2＝0.2ζ2sin(ζ1ζ2)，
q1,1(ζ)＝(0.25ζ1(t-τ1)ζ2(t-τ1))/(1+ζ1(t-τ2)2+ζ2(t-τ2)2)
q1,2(ζ)＝(0.5ζ1(t-τ1)ζ2(t-τ1))/(1+ζ1(t-τ2)2+ζ2(t-τ2)2)
Figure BDA0003029519950000163
q2,1(ζ)＝(0.25ζ1(t-τ1)2sin(ζ2(t-τ1)))
q2,2(ζ)＝(0.25ζ1(t-τ1)2sinζ2(t-τ1)),τ1＝τ2＝1
in the simulation experiment, the present embodiment selects suitable parameters as follows:
l1,1＝3.2,l1,2＝5.5,l2,1＝3.3,l2,2＝5.4,δ＝0.9,θ＝1,
Figure BDA0003029519950000164
μ＝15,mp,i＝hp,i＝0.05
ε＝0.5,a1＝0.1920,a2＝0.2215,λ1＝2.5233,λ2＝3.4103,η1＝6.37296,η2＝8.6818
Figure BDA0003029519950000165
μ1＝0.1,μ2＝0.2,r1＝r2＝15,k1＝25,k2＝15,ω1＝ω2＝0.05
matrix A1And A2Is a Herviz matrix, by selecting Q110I and Q212I, a positive definite matrix can be obtained:
Figure BDA0003029519950000166
the initial conditions were chosen as: zeta1(0)＝-0.1,ζ2(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 31，
Figure BDA0003029519950000168
ζ2，
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
is shown in the figure of the waveform of (c),FIGS. 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 processors, digital signal processors DSP, application specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and so on. 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 (10)

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;
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.
2. The adaptive event-triggered output feedback control method for time-lapse switching systems according to claim 1, wherein the switching state observer is:
Figure FDA0003029519940000011
therein, ζiIn order to be in the state of the system,
Figure FDA0003029519940000012
is ζiI is more than or equal to 1 and less than or equal to n, and p belongs to gamma; y is the system output, u is the control input, lp,i、lp,nIs a normal number that needs to be designed.
3. The adaptive event-triggered output feedback control method of a time-lag switching system as claimed in claim 1, wherein said Lyapunov-Krasovskii functional is:
Figure FDA0003029519940000013
Figure FDA0003029519940000014
wherein t is time; tau isiIs an unknown constant time delay;
Figure FDA0003029519940000021
is a design constant; h ispIn order to design the constants of the two-phase,
Figure FDA0003029519940000022
e＝[e1,...,en]T，
Figure FDA0003029519940000023
αiis virtual control;
Figure FDA0003029519940000024
is an unknown function.
4. The adaptive event-triggered output feedback control method for skew switching systems as claimed in claim 1, wherein said event-triggering mechanism is:
Figure FDA0003029519940000025
tk+1＝inf{t>tk||e(t)|≥δ|u(t)|+η}
where e (t) is a measurement error, t (t) -u (t) is a measurement errorkDenotes the kth trigger time, tk+1Represents the (k + 1) th trigger moment; 0 < delta < 1, mu, eta and
Figure FDA0003029519940000026
are positive design parameters.
5. 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.
6. The adaptive event-triggered output feedback control method for skew switching system as claimed in claim 1, wherein the virtual control function and the adaptation rate are defined as follows:
Figure FDA0003029519940000027
Figure FDA0003029519940000028
wherein k isi、μi、ωiAnd riAre respectively the design parameter, Si(Zi) Is a neural network basis function vector;
Figure FDA0003029519940000029
Figure FDA00030295199400000210
is ρiIs estimated.
7. 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.
8. 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 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.
9. 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 1-7.
10. A computer-readable storage medium storing computer instructions which, when executed by a processor, perform the method of any one of claims 1 to 7.
CN202110425443.5A 2021-04-20 2021-04-20 Self-adaptive event trigger output feedback control method and system of time-lag switching system Expired - Fee Related CN113110055B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110425443.5A CN113110055B (en) 2021-04-20 2021-04-20 Self-adaptive event trigger output feedback control method and system of time-lag switching system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110425443.5A CN113110055B (en) 2021-04-20 2021-04-20 Self-adaptive event trigger output feedback control method and system of time-lag switching system

Publications (2)

Publication Number Publication Date
CN113110055A true CN113110055A (en) 2021-07-13
CN113110055B CN113110055B (en) 2022-08-26

Family

ID=76719172

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110425443.5A Expired - Fee Related CN113110055B (en) 2021-04-20 2021-04-20 Self-adaptive event trigger output feedback control method and system of time-lag switching system

Country Status (1)

Country Link
CN (1) CN113110055B (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859725A (en) * 2022-05-09 2022-08-05 广东工业大学 Self-adaptive event trigger control method and system for nonlinear system
CN115016273A (en) * 2022-06-14 2022-09-06 中国科学院数学与系统科学研究院 Predefined time stability control method and system for single-link mechanical arm
CN115589319A (en) * 2022-10-09 2023-01-10 四川大学 Synchronization and attack processing method of time-lag switching system based on observer
CN115793465A (en) * 2022-12-08 2023-03-14 广西大学 Self-adaptive control method of spiral climbing pruner
CN116628862A (en) * 2023-07-19 2023-08-22 浙江大学海南研究院 Dynamic positioning event triggering robust H of mass-switching unmanned ship ∞ Filtering method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105244875A (en) * 2015-10-28 2016-01-13 上海大学 Network multi-area electric power system load frequency control method based on self-adaptive event trigger mechanism
US9296474B1 (en) * 2012-08-06 2016-03-29 The United States of America as represented by the Administrator of the National Aeronautics & Space Administration (NASA) Control systems with normalized and covariance adaptation by optimal control modification
CN107957683A (en) * 2017-11-07 2018-04-24 浙江工业大学 A kind of delay compensation method of the networking reversible pendulum system with input constraint

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9296474B1 (en) * 2012-08-06 2016-03-29 The United States of America as represented by the Administrator of the National Aeronautics & Space Administration (NASA) Control systems with normalized and covariance adaptation by optimal control modification
CN105244875A (en) * 2015-10-28 2016-01-13 上海大学 Network multi-area electric power system load frequency control method based on self-adaptive event trigger mechanism
CN107957683A (en) * 2017-11-07 2018-04-24 浙江工业大学 A kind of delay compensation method of the networking reversible pendulum system with input constraint

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
JIAO LIU等: "Output feedback L1 finite-time control of switched positive delayed systems with MDADT", 《NONLINEAR ANALYSIS: HYBRID SYSTEMS》 *
JIE KONG等: "Adaptive event-triggered output-feedback control for switched nonlinear systems with time-varying delays: A modified MDADT method", 《WILEY》 *
丛？咽麽？徐君祥: "时滞切换系统稳定性分析与镇定―Lyapunov函数方法", 《控制理论与应用》 *
刘娟 等: "基于MDADT的多变时滞切换正系统异步输出跟踪控制", 《沈阳大学学报(自然科学版)》 *
杜雨薇等: "事件触发下混合时滞神经网络的状态估计", 《应用数学和力学》 *
段长杰 等: "基于事件触发的不确定时滞切换系统的有限时间稳定", 《纺织高校基础科学学报》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114859725A (en) * 2022-05-09 2022-08-05 广东工业大学 Self-adaptive event trigger control method and system for nonlinear system
CN114859725B (en) * 2022-05-09 2024-04-05 广东工业大学 Nonlinear system self-adaptive event trigger control method and system
CN115016273A (en) * 2022-06-14 2022-09-06 中国科学院数学与系统科学研究院 Predefined time stability control method and system for single-link mechanical arm
CN115589319A (en) * 2022-10-09 2023-01-10 四川大学 Synchronization and attack processing method of time-lag switching system based on observer
CN115589319B (en) * 2022-10-09 2023-10-24 四川大学 Synchronization and attack processing method of time-lag switching system based on observer
CN115793465A (en) * 2022-12-08 2023-03-14 广西大学 Self-adaptive control method of spiral climbing pruner
CN116628862A (en) * 2023-07-19 2023-08-22 浙江大学海南研究院 Dynamic positioning event triggering robust H of mass-switching unmanned ship ∞ Filtering method
CN116628862B (en) * 2023-07-19 2024-04-02 浙江大学海南研究院 Dynamic positioning event triggering robust H of mass-switching unmanned ship ∞ Filtering method

Also Published As

Publication number Publication date
CN113110055B (en) 2022-08-26

Similar Documents

Publication Publication Date Title
CN113110055B (en) Self-adaptive event trigger output feedback control method and system of time-lag switching system
Li et al. Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems
Liu et al. Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems
Qiu et al. Event-triggered adaptive fuzzy fault-tolerant control for stochastic nonlinear systems via command filtering
Hua et al. Neural network observer-based networked control for a class of nonlinear systems
Sahoo et al. Stochastic optimal regulation of nonlinear networked control systems by using event-driven adaptive dynamic programming
Lu et al. Adaptive fuzzy output feedback control for nonlinear systems based on event-triggered mechanism
Zhao et al. Unified mapping function-based neuroadaptive control of constrained uncertain robotic systems
Gao et al. Event-triggering based adaptive neural tracking control for a class of pure-feedback systems with finite-time prescribed performance
Wang et al. Event-driven optimal control for uncertain nonlinear systems with external disturbance via adaptive dynamic programming
Ibeas et al. Robust sliding control of SEIR epidemic models
Wang et al. Event-triggered cooperative adaptive neural control for cyber–physical systems with unknown state time delays and deception attacks
CN108594643B (en) Performance-guaranteed control method for all-state limited strict feedback system
Wang et al. Event-triggered model-parameter-free trajectory tracking control for autonomous underwater vehicles
Hsu Adaptive dynamic RBF neural controller design for a class of nonlinear systems
CN113459083B (en) Self-adaptive fixed time control method and system for mechanical arm under event trigger
CN114859725A (en) Self-adaptive event trigger control method and system for nonlinear system
Sahoo et al. Event-based optimal regulator design for nonlinear networked control systems
CN114690634A (en) Nonlinear multi-agent system finite time consistency control method based on state constraint pulse control strategy
CN112255916B (en) Finite time real-time control method of time delay nonlinear time-varying system
He et al. Aperiodic event-triggered model predictive control for perturbed LTI systems: A PID based approach
Yuan et al. Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions
CN114371618A (en) Extended state observer compensation method based on neural network and active disturbance rejection controller
Zhang et al. Output-constrained fixed-time coordinated control for multi-agent systems with event-triggered and delayed communication
CN114500383B (en) Intelligent congestion control method, system and medium for space-earth integrated information network

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20220826