CN116009392B - Quantizer-based asynchronous event trigger control method, quantizer-based asynchronous event trigger control device, quantizer-based asynchronous event trigger control equipment and medium - Google Patents
Quantizer-based asynchronous event trigger control method, quantizer-based asynchronous event trigger control device, quantizer-based asynchronous event trigger control equipment and medium Download PDFInfo
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Abstract
The embodiment of the invention discloses a quantizer-based asynchronous event trigger control method, a quantizer-based asynchronous event trigger control device, a quantizer-based asynchronous event trigger control equipment and a quantizer-based asynchronous event trigger control medium, which relate to the technical field of controllers, wherein the method comprises the following steps: (1) establishing a controlled object model; (2) establishing a state observer-based controller; (3) Establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer; (4) Establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon; (5) And detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs. According to the embodiment of the application, the controlled object model, the controller based on the state observer, the quantizer and the asynchronous event trigger control mechanism based on the quantizer are built in the nonlinear networked control system, so that stability of the nonlinear networked control system can be guaranteed and Zeno phenomenon can be avoided when a resource channel is limited.
Description
Technical Field
The present invention relates to the field of controller technologies, and in particular, to a quantizer-based asynchronous event trigger control method, apparatus, device, and medium.
Background
The nonlinear networked control system is a control system which connects a controlled object (physical equipment), a sensor, a controller and an actuator and can share communication under limited channel transmission resources, and has considerable advantages in terms of maintenance cost and design flexibility compared with the traditional point-to-point control. In addition, nonlinear networked control systems have been widely used in various industrial applications, such as intelligent transportation, power grids, unmanned aerial vehicles, and the like. In a nonlinear networked control system, however, limited channel transmission resources can affect the transmission of signals.
In order to save transmission resources, event trigger control can be used in a network control system to overcome the limitation of a channel, and event trigger control mechanisms are divided into two types: fixed threshold strategies and relative threshold strategies, wherein the fixed threshold strategy focuses on the use of a comparison of a fixed function with a function (such as an error function, a state function, or an output function) with system dynamics related variables; the relative threshold strategy focuses on the comparison between two dynamic functions related to system dynamics; however, the two types of event trigger control mechanisms are easy to generate a Zeno phenomenon in a nonlinear networked control system when channel resources are limited, so that the stability of the system is affected.
Disclosure of Invention
The embodiment of the invention provides a quantizer-based asynchronous event trigger control method, a quantizer-based asynchronous event trigger control device, quantizer-based asynchronous event trigger control equipment and a quantizer-based asynchronous event trigger control medium, and aims to solve the problem that a non-linear network control system is prone to Zeno phenomenon when channel resources are limited, so that the system is unstable.
In a first aspect, an embodiment of the present invention provides a quantizer-based asynchronous event trigger control method, including:
(1) Establishing a controlled object model:
wherein ,i e { 1., -, n-1 is the state, output and quantity of the controlled object model, and is t E [ tau ] j ,τ j+1 ) When (I)>Is the trigger time of the controlled object channel of the controller, < >>For control input +.>Is a nonlinear function vector;
(2) Establishing a controller based on a state observer;
(3) Establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer;
(4) Establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon;
(5) And detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs.
In a second aspect, an embodiment of the present invention further provides an asynchronous event trigger control apparatus based on a quantizer, including:
the building module is used for building a controlled object model; establishing a controller based on a state observer; establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer; establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon;
the detection module is used for detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs.
In a third aspect, an embodiment of the present invention further provides a computer device, which includes a memory and a processor, where the memory stores a computer program, and the processor implements the method when executing the computer program.
In a fourth aspect, embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.
The embodiment of the invention provides a quantizer-based asynchronous event trigger control method, a quantizer-based asynchronous event trigger control device, a quantizer-based asynchronous event trigger control equipment and a quantizer-based asynchronous event trigger control medium. Wherein the method comprises the following steps: (1) establishing a controlled object model; (2) establishing a state observer-based controller; (3) Establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer; (4) Establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon; (5) And detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs. According to the technical scheme provided by the embodiment of the invention, the controlled object model, the controller based on the state observer, the quantizer and the asynchronous event trigger control mechanism based on the quantizer are built in the nonlinear networked control system, so that the stability of the nonlinear networked control system can be ensured and the Zeno phenomenon can be avoided when a resource channel is limited.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a system diagram of a quantizer-based asynchronous event trigger control method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a process of an event trigger mechanism of an asynchronous event trigger control method based on a quantizer according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a quantizer-based asynchronous event trigger control scheme according to an embodiment of the present invention 1 (t)，x 1 (t k )，x 2 (t)，x 2 (t k )，z 2(t) and z2 (τ j ) A change track diagram;
fig. 4 is a diagram of a trigger time t of a P-C channel under the action of an event trigger control mechanism in an asynchronous event trigger control method based on a quantizer according to an embodiment of the present invention k And trigger time tau of C-P channel j Observer-based controller output u (t) and sampling controller output u (τ) j ) Is of the change track of (a)A figure;
FIG. 5 is a schematic block diagram of a quantizer-based asynchronous event trigger control device provided by an embodiment of the present invention;
fig. 6 is a schematic block diagram of a computer device provided by an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the terms "comprises" and "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that 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. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
As used in this specification and the appended claims, the term "if" may be interpreted as "when..once" or "in response to a determination" or "in response to detection" depending on the context. Similarly, the phrase "if a determination" or "if a [ described condition or event ] is detected" may be interpreted in the context of meaning "upon determination" or "in response to determination" or "upon detection of a [ described condition or event ]" or "in response to detection of a [ described condition or event ]".
Referring to fig. 1, fig. 1 is a schematic diagram of a system of a quantizer-based asynchronous event trigger control method according to an embodiment of the present invention, in fig. 1, on an output channel from a controlled object to a controller, an output of the controlled object is y (t), which is obtained by encoding, quantizing and triggering an asynchronous event by a quantizer-based asynchronous event trigger control mechanism, i.e., y (t)Transmitting through a network; the discrete signal can then be finally converted into a continuous signal +_ by decoding it by a decoder and using a zero order holder>To the observer-based controller. And the signal transmission process of the input channel from the controller to the controlled object is similar to the signal transmission process of the output channel from the controlled object to the controller, thereby completing the whole asynchronous event trigger control based on the quantizer of the system.
The method for controlling asynchronous event triggering based on the quantizer structure comprises the following specific steps:
step 1: establishing a controlled object model:
wherein ,is a system state->Is the system output, i e { 1..2, n-1} represents the number of system states, only x } 1 (t) can be observed through the system outputTo, at t.epsilon.tau j ,τ j+1 ) In the time-course of which the first and second contact surfaces,
is the trigger time of the controller-controlled object channel,is a control input of the controller and is provided with a control signal,is a nonlinear function vector, nonlinear function g i (x (t)) (i ε {1,2,., n-1 }) and g n (x (t)) is a local Lipschitz function.
Due to system stateThe observer-based controller in the embodiments of the present invention can provide control signals for both the controlled object to controller (P-C) channel (output channel) and the controller to controlled object (C-P) channel (input channel). The system output y (t) and the control signal u (t) are quantized before transmission over the network, and the quantizers on the output channel and the input channel are independent of each other. Based on the system structure and mutually independent quantizer characteristics, event trigger control of related quantizers is respectively designed, so that the stability of a nonlinear networked control system model under a limited channel is realized.
Step 2: establishing a state observer-based controller:
wherein Is the state of the controller. At t E [ t ] k ,t k+1 ) During the course of this time period,is the trigger moment on the output channel, +.>Is the signal received by the decoder, h i Is positive constant, +.>Is the output of the controller. Nonlinear function->Is a local Lipschitz function, +.>Satisfy the following requirements Is a positive constant.
When meeting the requirementsTime of day
||z(t)-z(τ j )||＜ηM c (t)
Wherein η is a positive constant, ψ i And (t) is an auxiliary power variable. τ j For the trigger time between the controller and the controlled object channel. At t E [ tau ] j ,τ j+1 ) Within the range, psi i (t) satisfies:
thus, the auxiliary power variable ψ i Kinetic compliance of (t):
and is defined as follows:
Ξ(t)＝[x 1 (t),...,x n (t),ψ 1 (t),...,ψ n-1 (t)] T
step 3: establishing a quantizer and an event trigger control mechanism based on the quantizer:
first, a binary encoder-based dynamic quantizer is constructed and />
wherein , and />Is the quantized signal. c s[k] and cc [j]Is a P-C channel (when t e t k ,t k+1 ) And C-P channels (when t E [ tau ] j ,τ j+1 ) A) the center point. c s[k] and cc [j]The updates of (2) are as follows:
wherein ,Ms (t k+1) and Mc (τ j+1 ) Is the trigger time t k+1 and τj+1 Time M s(t) and Mc The value of (t). M is M s(t) and Mc (t) is a dynamic quantizer parameter representing a quantization error threshold, which updates the rulesThe method comprises the following steps:
is the initial value. /> and />Representing the corresponding target. ρ s ,ρ c ∈(0,1]Is a scaled-down parameter. /> and />Is the signal obtained by the following encoder:
is a signum function, satisfying:
and />A variable calculated by the following formula:
based on the analysis described above, the range of dynamic quantization may be changed in accordance with the dynamic change of the quantized signal. On P-C channel, t E [ t ] k ,t k+1 ) The quantization range is [ c ] s [k]-M s (t),c s [k]+M s (t)]The method comprises the steps of carrying out a first treatment on the surface of the On the C-P channel, the quantization range is [ C ] c [k]-M c (t),c c [k]+M c (t)]。
Secondly, according to the independent transmission of the signal in the output channel and the input channel and the dynamic quantizer based on the binary encoder, an asynchronous event trigger control mechanism based on the quantizer is established, and quantization errors and event trigger errors can be limited within quantization error thresholds, so that the signal can be transmitted in a network only when jumping between different quantization levels.
For the output channel, the quantizer-based event trigger control mechanism is:
t k+1 ＝inf{t＞t k |||y(t)-y(t k )||≥M s (t)}
the first trigger time is t 0 ＝0，M s And (t) is the threshold of quantization error and trigger error.
For the input channel, the quantizer-based event trigger control mechanism is:
τ j+1 ＝inf{t＞τ j |||u(t)-u(τ j )||≥M c (t)}
the first trigger time is tau 0 ＝0。M c And (t) is the threshold of quantization error and trigger error.
To better describe the asynchronous event trigger control mechanism based on the quantizer structure, fig. 2 demonstrates the trigger procedure by taking the P-C channel as an example.
Next, a dynamic quantizer and a quantizer-based asynchronous event trigger control mechanism for the above design are proposed based on the received signal and />Is a decoding strategy of (2):
wherein , and />For decoder at corresponding trigger time t k+1 and τj+1 And decoding the signal. The discrete signal is then converted to a continuous signal using a zero-order holder (ZOH). Thus, at t ε [ t ] k+1 ,t k+2) and t∈[τj+1 ,τ j+2 ) Within the scope, there are:
finally, observer-based controllers, encoders, decoders, and quantizer-based asynchronous event trigger control mechanisms according to the previous designs, at t e [ tau ] j ,τ j+1 ) Within the scope, the nonlinear network control system can be re-expressed as:
and define
g(x(t))＝[g 1 (x(t)),...,g n (x(t))] T
The following analysis will focus mainly on the reconstructed model.
Step 4: and establishing sufficient conditions for ensuring stability of the nonlinear networked control system and avoiding the Zeno phenomenon.
In step 3, if the nonlinear networked control system has the encoder, the decoder and the observer-based controller designed in step 2 and step 3, and under the dynamic quantization of the output channel and the input channel based on the binary encoder, the asynchronous event trigger control mechanism based on the quantizer can meet these conditions, so that the stability of the nonlinear networked control system can be ensured.
Assuming the nonlinear networked control system described above, there is a local Lipschitz ISS-Lyapunov function V (XI (t)) that satisfies:
wherein ,γ(·) and Is positive K ∞ The function, δ (·) is a continuous positive function. Assuming constants alpha > 0 and theta i > 0 (i.e {1,2,.,. Fwdarw.n-1 }) exists, beta. 1(·) and β2 (. Cndot.) is a positive continuous function. The method can obtain the following steps:
by this assumption, we can get the value of T.epsilon. [ tau ] j ,τ j+1 ) During the period, there are:
taking into account the event trigger condition τ j+1 ＝inf{t＞τ j |||u(t)-u(τ j )||≥M c (t) } can be obtained
In addition, because||z(t)-z(τ j )||＜ηM c (t) if the scalar ε (0, 1) is present, the Lyapunov function described above is +.>The method can be as follows:
wherein ,
β 3 (M c (t))＝αM c (t),
at t E [ tau ] j ,τ j+1 ) Definition of periodr＞0。
Selecting r small enough c > 0, makeWhen it is, it can get +.> and />From these above derivations and analyses, we can get after simplification:
therefore, the stability of the nonlinear networked control system in the step 3 is proved, and a sufficient condition for the stability of the nonlinear networked control system is established.
Step 5: and detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs.
The stability of the nonlinear networked control system and whether the Zeno phenomenon occurs are detected, and sufficient conditions for the nonlinear networked control system to avoid the Zeno phenomenon need to be proved, so that the Zeno phenomenon (namely, the situation of infinite triggering in a limited time period) cannot occur in the system under the action of the designed asynchronous event triggering control method based on the quantizer structure.
Since the system is quantized asynchronously on the output channel and the input channel, it is proved in two parts that u (t) is guaranteed not to appear as a Zeno phenomenon on the observer-controlled object channel (input channel). It was then demonstrated that the Zeno phenomenon can also be avoided on the controlled object-observer channel (output channel). Ensuring that the system does not generate Zeno phenomenon, namely ensuring that delta exists t＞0 and Δτ > 0, can let t k+1 -t k ≥Δ t and τj+1 -τ j ≥Δ τ 。
(1) Observer-controlled object (input channel) channel:
according to z (t) -z (τ) j )||＜ηM c (t) to obtain ||z (τ) j )-z(t)||≤||z(τ j )-z(τ j+1 )||＝ηM c (t)。
Taking τ into account j+1 Trigger time M of (2) c (t) thereforeThus, at t ε [ t ] k ,t k+1) and t∈[τj ,τ j+1 ) Within the scope, from the designed observer-based controller and decoder, it is possible to derive:
taking z into account 1 The piecewise continuous nature of (t) is divided into two parts as discussed below.
Case one: when i=1, at t e [ t ] k ,t k+1) and t∈[τj ,τ j+1 ) Within the scope, there are:
from the previous analysis of the stability of a nonlinear networked system, the system has a bounded state that is asymptotically stable. Let g (x (t)). Ltoreq.lambda. s (x(t))||x(t)||，λ s (. Cndot.) is a non-decreasing function, and therefore, again, based on the stability of the system, it is possible to obtain:
wherein Is constant (I)>As a non-decreasing function. In combination, it can be inferred that:
and a second case: when i=2,..n, at t e [ t. k ,t k+1) and t∈[τj ,τ j+1 ) Within the scope, there are:
thus combined with the front surface, can obtain
From analysis of the stability of a nonlinear networked system
wherein , and />Is a positive constant. According to the above analysis, define->It can be concluded that:
wherein ,is a non-decreasing function. />When taking the appropriate value, there areThus (2)
Definition of the definitionBy combining both cases, we can obtain τ j+1 -τ j ≥Δ τ And > 0, it is also proved that the system does not appear Zeno phenomenon on the observer-controlled object channel.
(2) Controlled object-observer channel (output channel):
definition e y (t)＝y(t)-y(t k ). From the event trigger mechanism designed previously, it can be derived that:
||y(t k+1 )-y(t k )||＝M s (t)
from the previous analysis of the stability of a nonlinear networked system, the system has a bounded state asymptotically stabilized. Thus, it is apparent that x 2(t) and g1 (x (t)) are all bounded. Definition of the definitionTherefore, we have:
definition of the definitionThe following can be easily foundThe formula is always true:
therefore, it is verified that the Zeno phenomenon does not occur in the system on the controlled object-observer channel.
The application example provided by the invention is a mechanical arm system described by taking a Lagrangian equation as a dynamic equation, and the invention is applied to the mechanical arm system shown in the following dynamic equation:
wherein q (t) andthe angle and angular velocity of the rigid links, respectively. B is a damping coefficient. J is the moment of inertia of the servo motor. M is the mass of the connecting rod and g is the gravitational acceleration. L is the length of the robotic arm from the joint axis to the centroid. Definition x 1 (t) =q (t) and +.>When j=1, ">At this time, the robotic arm system may become:
wherein the initial condition x 1 (0)＝2,x 2 (0) = -2. Quantization parameter c s [0]＝2,c c [0]＝-40ρ s =0.4 and ρ c =0.7 at t e [ τ ] j ,τ j+1) and t∈[tk ,t k+1 ) During the period, the observer-based controller is designed to:
wherein ,ψ1 (t) satisfyThe parameter is selected as h 1 ＝6。
FIG. 3 shows the system state x 1 (t) and trigger sampling State x 1 (t k ) In addition, system state x 2 (t) trigger sampling State x 2 (t k ) Observer-based controller state z 2 (t) and sampling State z 2 (τ j ) The relationship between these is also reflected in fig. 3. FIG. 4 shows observer-based controller output u (t) and sampling controller output u (τ) j ) Is a trajectory of (a). P-C channel t k And C-P channel τ j As shown in fig. 4, as can be seen from fig. 3 and 4, the number of trigger events on the P-C channel is 3, and the number of trigger events on the C-P channel is 52. The minimum sampling intervals for the P-C channel and the C-P channel are 0.351 and 0.01, respectively.
It should be noted that, in the embodiment of the present invention, the quantization result, the event triggering result and the stability result of the established nonlinear quantized event triggering control model may also be displayed.
Fig. 5 is a schematic block diagram of an asynchronous event trigger control device 200 based on a quantizer according to an embodiment of the present invention. As shown in fig. 5, the present invention further provides a quantizer-based asynchronous event trigger control device 200, corresponding to the quantizer-based asynchronous event trigger control method above. The quantizer-based asynchronous event trigger control apparatus 200, which may be configured in a server, includes a unit for performing the quantizer-based asynchronous event trigger control method described above. Specifically, referring to fig. 5, the quantizer-based asynchronous event trigger control device 200 includes a setup module 201 and a detection module 202.
The building module 201 is configured to build a controlled object model; establishing a controller based on a state observer; establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer; establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon; the detection module 202 is configured to detect stability of the nonlinear networked control system and whether a Zeno phenomenon occurs.
The detailed implementation manner of the quantizer-based asynchronous event trigger control device 200 in the embodiment of the present invention corresponds to the quantizer-based asynchronous event trigger control method described above, and will not be described herein.
The quantizer-based asynchronous event trigger control means described above may be implemented in the form of a computer program that is executable on a computer device as shown in fig. 6.
Referring to fig. 6, fig. 6 is a schematic block diagram of a computer device according to an embodiment of the present application. The computer device 300 is a server.
Referring to fig. 6, the computer device 300 includes a processor 302, a memory, and a network interface 305 connected by a system bus 301, wherein the memory may include a storage medium 303 and an internal memory 304.
The storage medium 303 may store an operating system 3031 and a computer program 3032. The computer program 3032, when executed, may cause the processor 302 to perform a quantizer-based asynchronous event trigger control method.
The processor 302 is used to provide computing and control capabilities to support the operation of the overall computer device 300.
The internal memory 304 provides an environment for the execution of a computer program 3032 in the storage medium 303, which computer program 3032, when executed by the processor 302, causes the processor 302 to perform a quantizer-based asynchronous event trigger control method.
The network interface 305 is used for network communication with other devices. Those skilled in the art will appreciate that the architecture shown in fig. 6 is merely a block diagram of a portion of the architecture in connection with the present application and is not intended to limit the computer device 300 to which the present application is applied, and that a particular computer device 300 may include more or fewer components than shown, or may combine certain components, or have a different arrangement of components.
Wherein the processor 302 is configured to run a computer program 3032 stored in a memory to implement any embodiment of a quantizer-based asynchronous event trigger control method.
It should be appreciated that in embodiments of the present application, the processor 302 may be a central processing unit (Central Processing Unit, CPU), the processor 302 may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSPs), application specific integrated circuits (Application Specific Integrated Circuit, ASICs), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. Wherein the general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
Those skilled in the art will appreciate that all or part of the flow in a method embodying the above described embodiments may be accomplished by computer programs instructing the relevant hardware. The computer program may be stored in a storage medium that is a computer readable storage medium. The computer program is executed by at least one processor in the computer system to implement the flow steps of the embodiments of the method described above.
Accordingly, the present invention also provides a storage medium. The storage medium may be a computer readable storage medium. The storage medium stores a computer program. The computer program, when executed by a processor, causes the processor to perform any of the embodiments of the quantizer-based asynchronous event trigger control method described above.
The storage medium may be a U-disk, a removable hard disk, a Read-Only Memory (ROM), a magnetic disk, or an optical disk, or other various computer-readable storage media that can store program codes.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps described in connection with the embodiments disclosed herein may be embodied in electronic hardware, in computer software, or in a combination of the two, and that the elements and steps of the examples have been generally described in terms of function in the foregoing description to clearly illustrate the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. 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 invention.
The integrated unit may be stored in a storage medium if implemented in the form of a software functional unit and sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention is essentially or a part contributing to the prior art, or all or part of the technical solution may be embodied in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a terminal, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention.
In the foregoing embodiments, the descriptions of the embodiments are focused on, and for those portions of one embodiment that are not described in detail, reference may be made to the related descriptions of other embodiments.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (6)
1. A quantizer-based asynchronous event trigger control method, comprising:
(1) Establishing a controlled object model:
wherein ,i e { 1., -, n-1 is the state, output and quantity of the controlled object model, and is t E [ tau ] j ,τ j+1 ) When (I)>Is the trigger time of the controlled object channel of the controller, < >>For control input +.>Is a nonlinear function vector;
(2) Establishing a controller based on a state observer;
(3) Establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer;
(4) Establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon;
(5) Detecting the stability of a nonlinear networked control system and whether a Zeno phenomenon occurs;
wherein the establishing a state observer based controller comprises:
establishing a state observer-based controller:
wherein Is the state of the controller, at t e [ t ] k ,t k+1 ) During (I)>Is the trigger moment on the output channel, +.>Is the signal received by the decoder, h i Is positive constant, +.>Is the output of the controller, nonlinear function +.>Is a local Lipschitz function, +.>Satisfy the following requirements Is a positive constant;
when meeting the requirementsTime of day
||z(t)-z(τ j )||＜ηM c (t)
Wherein η is a positive constant, ψ i (t) is an auxiliary power variable τ j For the trigger time between the controller and the controlled object channel, at t E [ [τ j ,τ j+1 ) Within the range, psi i (t) satisfies:
wherein the establishing quantizer and quantizer-based asynchronous event trigger control mechanism comprises:
construction of binary encoder based dynamic quantizerR→R and />R→R：
wherein , and />Is the quantized signal, c s[k] and cc [j]Is a P-C channel (when t e t k ,t k+1 ) And C-P channels (when t E [ tau ] j ,τ j+1 ) A) a center point;
establishing an asynchronous event trigger control mechanism based on a quantizer according to independent transmission of signals in an output channel and an input channel and a dynamic quantizer based on a binary encoder;
wherein, the method establishes an asynchronous event trigger control mechanism based on a quantizer according to independent transmission of signals in an output channel and an input channel and based on a dynamic quantizer of a binary encoder, and comprises the following steps:
for the output channel, the quantizer-based asynchronous event trigger control mechanism is:
t k+1 ＝inf{t＞t k |||y(t)-y(t k )||≥M s (t)}
t k is the trigger time of the controlled object channel of the controller, and the first trigger time is t 0 ＝0，M s (t) is a threshold of quantization error and trigger error;
for the input channel, the quantizer-based asynchronous event trigger control mechanism is:
τ j+1 ＝inf{t＞τ j |||u(t)-u(τ j )||≥M c (t)}
τ j is the triggering time of the controlled object channel of the controller, and the first triggering time is tau 0 ＝0，M c (t) is a threshold of quantization error and trigger error;
wherein, in the asynchronous event trigger control mechanism based on the quantizer, the method further comprises:
an encoder:
wherein , and />Is the signal encoded by the encoder, sgn (& gt)>Is a signum function, satisfying:
and />A variable calculated by the following formula:
a decoder:
wherein ,Ms (t k+1) and Mc (τ j+1 ) Is the trigger time t k+1 and τj+1 Time M s(t) and Mc A value of (t); and />For decoder at corresponding trigger time t k+1 and τj+1 A decoded signal;
reconstructing a nonlinear networked control system model:
wherein ,and gamma (t) is an auxiliary variable, +.>Is the input of the controlled object and the controller, z 1 (τ j )...z n-1 (τ j ) Representing the controller state z 1 (t)...z n-1 (t) at trigger time τ j The value of time, t.epsilon.tau j ,τ j+1 )。
2. The method of claim 1, wherein establishing sufficient conditions to ensure stability of the nonlinear-networked control system comprises:
the nonlinear networked control system model has a local Lipschitz ISS-Lyapunov function V (xi (t)) that satisfies:
wherein, gamma (& gt) andis positive K ∞ The function, delta (·) is a continuous positive function, assuming constants alpha > 0 and theta i > 0 (i.e {1,2,.,. Fwdarw.n-1 }) exists, beta. 1(·) and β2 (. Cndot.) is a positive continuous function, then:
under the dynamic quantization of an output channel and an input channel based on a binary encoder, the asynchronous event trigger control condition based on the quantizer is satisfied, and the stability of a nonlinear networked control system can be ensured.
3. The method of claim 2, wherein detecting stability and the presence of a Zeno phenomenon in a nonlinear networked control system comprises:
detecting whether delta exists in nonlinear networked control system t＞0 and Δτ > 0, can let t k+1 -t k ≥Δ t and τj+1 -τ j ≥Δ τ ；
If the non-linear networked control system exists, the non-linear networked control system is stable in the observer-controlled object channel and the controlled object-observer channel system, and the Zeno phenomenon can not occur.
4. An asynchronous event trigger control device based on a quantizer, comprising:
the building module is used for building a controlled object model; establishing a controller based on a state observer; establishing a quantizer and an asynchronous event trigger control mechanism based on the quantizer; establishing sufficient conditions for ensuring stability of a nonlinear networked control system and avoiding a Zeno phenomenon;
the detection module is used for detecting the stability of the nonlinear networked control system and whether the Zeno phenomenon occurs;
the building module is specifically configured to build a controller based on a state observer, and includes:
establishing a state observer-based controller:
wherein Is the state of the controller, at t e [ t ] k ,t k+1 ) During (I)>Is the trigger moment on the output channel, +.>Is the signal received by the decoder, h i Is positive constant, +.>Is the output of the controller, nonlinear function +.>Is a local Lipschitz function, +.>Satisfy the following requirements Is a positive constant;
when meeting the requirementsTime of day
||z(t)-z(τ j )||＜ηM c (t)
Wherein η is a positive constant, ψ i (t) is an auxiliary power variable τ j For the trigger time between the controller and the controlled object channel, t is E [ tau ] j ,τ j+1 ) Within the range, psi i (t) satisfies:
wherein the establishing quantizer and quantizer-based asynchronous event trigger control mechanism comprises:
construction of binary encoder based dynamic quantizerR→R and />R→R：
wherein , and />Is the quantized signal, c s[k] and cc [j]Is a P-C channel (when t e t k ,t k+1 ) And C-P channels (when t E [ tau ] j ,τ j+1 ) A) a center point;
establishing an asynchronous event trigger control mechanism based on a quantizer according to independent transmission of signals in an output channel and an input channel and a dynamic quantizer based on a binary encoder;
wherein, the method establishes an asynchronous event trigger control mechanism based on a quantizer according to independent transmission of signals in an output channel and an input channel and based on a dynamic quantizer of a binary encoder, and comprises the following steps:
for the output channel, the quantizer-based asynchronous event trigger control mechanism is:
t k+1 ＝inf{t＞t k |||y(t)-y(t k )||≥M s (t)}
t k is the trigger time of the controlled object channel of the controller, and the first trigger time is t 0 ＝0，M s (t) is quantization
Threshold of error and trigger error;
for the input channel, the quantizer-based asynchronous event trigger control mechanism is:
τ j+1 ＝inf{t＞τ j |||u(t)-u(τ j )||≥M c (t)}
τ j is the controlled object of the controllerThe triggering time of the channel is tau 0 ＝0，M c (t) is a threshold of quantization error and trigger error;
wherein, in the asynchronous event trigger control mechanism based on the quantizer, the method further comprises:
an encoder:
wherein , and />Is the signal encoded by the encoder, sgn (& gt)>Is a signum function, satisfying:
and />A variable calculated by the following formula:
a decoder:
wherein ,Ms (t k+1) and Mc (τ j+1 ) Is the trigger time t k+1 and τj+1 Time M s(t) and Mc A value of (t); and />For decoder at corresponding trigger time t k+1 and τj+1 A decoded signal;
reconstructing a nonlinear networked control system model:
wherein ,and gamma (t) is an auxiliary variable, +.>Is the input of the controlled object and the controller, z 1 (τ j )...z n-1 (τ j ) Representing the controller state z 1 (t)...z n-1 (t) at trigger time τ j The value of time, t.epsilon.tau j ,τ j+1 )。
5. A computer device, characterized in that it comprises a memory on which a computer program is stored and a processor which, when executing the computer program, implements the method according to any of claims 1-3.
6. A computer-readable storage medium, characterized in that the storage medium stores a computer program which, when executed by a processor, implements the method according to any of claims 1-3.
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