Method and system for designing control law of multi-channel networked control system with asymptotic stability

Abstract

The application relates to a kind of multi-channel networked control system asymptotic stability control law design method and system, comprising: establishing the first system model of networked control system with delay and packet loss simultaneously and equivalent expansion to the first system model to obtain the second system model;Establishing intermediate state and equivalent constraint condition to build the third system model;According to the expression of the control law designed by the third system model;Construct Riccati equation and obtain positive definite solution, substitute the positive definite solution into the expression of the control law, obtain the third system control law;Delete the channel information not transmitting information in the third system control law to obtain the first system control law;According to the first system control law, multi-channel information transmission can be carried out, so as to solve the problem of multiple transmission delay and random packet loss coexistence, improve the integrity of transmission information during channel transmission.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of data signal transmission, and particularly to a multi-channel networked control system asymptotic stability control law design method and system. BACKGROUND

[0002] In recent years, with the rapid development of wireless communication networks, computer technology and information technology, actuators and sensors in the system have developed into intelligent nodes with network communication functions, which can independently complete the perception, calculation, storage and interaction of part of the information. At the same time, in order to meet the needs of automatic control and remote control, the control system and the communication network have gradually integrated into one. Generally speaking, a networked control system is a closed-loop feedback control system composed of actuators, sensors and controllers connected by real-time serial networks. As a product of the integration of control technology and network communication technology, compared with the traditional point-to-point structure control system, the networked control system has the advantages of low cost, strong flexibility, high reliability, easy installation and maintenance, and information resource sharing, which makes the networked control system widely applied to industrial automation production, intelligent transportation network, aerospace, military and other fields, such as real-time monitoring and scheduling of urban transportation system, remote formation control of unmanned aerial vehicles, automatic control of aircraft navigation, precise guidance of tactical missiles, etc.

[0003] The networked control system is a distributed feedback system, in which multiple loops exchange information between different components (sensors, actuators, controllers) through some form of channel. As a flexible driving architecture in wireless sensor networks and Ad-hoc networks, the multi-path routing method has been widely used in various network management purposes, such as supporting demand-driven services, improving information reliability and ensuring control quality. Under the multi-path architecture, it is possible to build a set of different paths from a single sensor node to the destination. In recent years, extensive research has been conducted on communication and control problems in multi-path routing networks. However, it has been proven that the insertion of multi-path routing networks introduces some unavoidable communication defects, such as transmission delay and packet loss, which not only destroy the actual performance of the system, but also cause the instability of the entire system. In fact, simply relying on increasing network bandwidth to ensure the integrity of transmitted information not only increases communication costs, but also fundamentally solves the control problem under communication constraints. Therefore, the stability analysis of networked control systems with communication delay and / or data packet loss has important theoretical significance and application value, attracting the attention of many scholars. Since the communication delay will be represented as input or state time delay in network system modeling, and data packet loss may bring multiplicative noise to the system, such networked control systems also bring new challenges to the study of time-delay systems and stochastic systems, and many basic problems have not been well solved.

[0004] Based on the above analysis, it is found that the stability problem of the multi-channel networked control system with communication delay and data packet loss is a valuable research topic, and has important engineering background and practical significance. The present application mainly based on the random control theory of time delay system, further researches the stability problem of the networked control system, and proposes a control law design method and system for the asymptotic stability of the multi-channel networked control system. SUMMARY

[0005] The purpose of the present application is to provide a control law design method and system for the asymptotic stability of a multi-channel networked control system, which solves the problem of transmission delay and random packet loss in the channel, improves the integrity of the transmitted information in the channel, and makes the system stable under the designed control law.

[0006] To achieve the above purpose, the present application provides the following scheme:

[0007] A control law design method for the asymptotic stability of a multi-channel networked control system, comprising:

[0008] A multi-channel networked control system model with delay and packet loss is established, denoted as a first system model;

[0009] An information transmission channel is introduced to the first system model, and all the data of the information transmission channel is defined as packet loss, to obtain a second system model;

[0010] An intermediate state parameter is defined and an equivalent constraint condition is constructed, and a third system model is constructed according to the intermediate state parameter, the equivalent constraint condition and the second system model;

[0011] An expression of the control law is designed according to the third system model; a Riccati equation is constructed and a positive definite solution is obtained, and the positive definite solution is substituted into the expression of the control law to obtain the control law of the third system model, denoted as a third system control law;

[0012] The information of the information transmission channel in the third system control law is deleted to obtain the control law of the first system model, denoted as a first system control law;

[0013] According to the first system control law, multi-channel information transmission is performed.

[0014] The present application also provides a control law design system for the asymptotic stability of a multi-channel networked control system, comprising:

[0015] A first model establishment module is used to establish a multi-channel networked control system model with delay and packet loss, denoted as a first system model;

[0016] a second model establishing module, configured to introduce channels without information transmission into the first system model and define that all data of the channels without information transmission are all packet loss, so as to obtain a second system model;

[0017] a third model establishing module, configured to define intermediate state parameters and construct equivalent constraint conditions, and construct a third system model according to the intermediate state parameters, the equivalent constraint conditions and the second system model;

[0018] a third system control law designing module, configured to design an expression of a control law according to the third system model, construct Riccati equation and obtain a positive definite solution, and substitute the positive definite solution into the expression of the control law to obtain a control law of the third system model, which is recorded as a third system control law;

[0019] a first system control law designing module, configured to delete channel information without information transmission in the third system control law to obtain a control law of the first system model, which is recorded as a first system control law;

[0020] an information transmission module, configured to perform multi-channel information transmission according to the first system control law.

[0021] According to the embodiments of the present application, the following technical effects are provided.

[0022] The present application relates to a kind of multi-channel networked control system asymptotic stability control law design method and system, comprising: establishing the first system model of networked control system with delay and packet loss simultaneously and equivalent expansion to the first system model to obtain second system model;According to intermediate state parameters and equivalent constraint conditions, a third system model is constructed;According to the expression of the control law of the third system model is designed;Riccati equation is constructed and a positive definite solution is obtained, and the positive definite solution is substituted into the expression of the control law to obtain the third system control law;Delete the channel information without information transmission in the third system control law to obtain the first system control law;According to the first system control law, multi-channel information transmission is carried out.Thereby it can solve the problem that multiple transmission delay and random packet loss coexist, improve the integrity of transmission information when channel transmission, so that the system reaches stabilization under the designed control law. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0024] Figure 1A multi-channel networked control system asymptotic stability control law design method flow chart provided for the embodiment 1 of the present application;

[0025] Figure 2 The discrete time networked control system schematic diagram provided for the embodiment 1 of the present application;

[0026] Figure 3 A multi-channel networked control system asymptotic stability control law design system block diagram provided for the embodiment 2 of the present application. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0028] The purpose of the present application is to provide a multi-channel networked control system asymptotic stability control law design method, which can make the networked control system asymptotically mean square stable to solve the problem of coexistence of multiple transmission delays and random packet loss, and improve the integrity of the transmitted information during channel transmission.

[0029] In order to make the above-mentioned purposes, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0030] Embodiment 1

[0031] As shown in the figure, the present embodiment provides a multi-channel networked control system asymptotic stability control law design method, which comprises: Figure 1 S1: a multi-channel networked control system model with delay and packet loss is established, denoted as a first system model.

[0032] S1: a multi-channel networked control system model with delay and packet loss is established, denoted as a first system model.

[0033] The present embodiment mainly considers Figure 2 The described discrete time networked control system, the designed controller is located between the observer and the actuator. The role of the controller: issue control law, command and coordinate the work of each part. The role of the actuator: execute the control law transmitted through the multi-channel network. The role of the sensor: to observe and transmit data information in the control system.

[0034] Suppose that at any time t, the current state information x tMeanwhile, the controller and the actuator are connected through n unreliable parallel channels, and the data packet loss and communication delay may occur simultaneously in the process of transmitting control signals from the controller to the actuator. In particular, for the ith channel, i = 1, 2, …, n; d i The control input delay transmitted on the ith channel, and the control signal obtained by the actuator at time t is denoted as where, denotes the arrival process of the control signal ( modeled by a "binary random variable"), that is, a random process in the state space {0, 1}, denotes the successful arrival of the control signal to the actuator, denotes the packet loss of the control signal on the ith channel. Therefore, the networked control system with multi-channel communication delay and data packet loss can be represented as a stochastic system with multiple input time delays and multiplicative noise (first system model):

[0035]

[0036] where, x t denotes the state of the system at time t; denotes the control signal on the ith channel participating in information transmission; d i The control input delay transmitted on the ith channel satisfies 0≤d1<d2<…<d N A, B represent the matrix parameters of the system; N represents the number of channels participating in information transmission. Moreover, the packet loss probabilities of each channel are independent of each other, the packet loss processes of different channels are independent of each other, and the packet loss processes at different times are also independent of each other, that is, for any t≠s, i≠j are independent of each other, and A uniformly distributed implementation is as follows: p i ∈[0,1], p i is the packet loss probability of the ith path. For convenience, the system (1.1) can be simply denoted as

[0037] S2: Introducing channels that do not perform information transmission to the first system model and defining that all the data of the channels that do not perform information transmission are completely lost packet, to obtain a second system model.

[0038] ​That is, taking d1=1, d2=5 as an example, the original system (1.1) has two channels, wherein the control input delay of the first channel is 1, and the control input delay of the second channel is 5, then the number of channels needs to be expanded to 6, and the control input delays of the expanded channels are 0, d1, 2, 3, 4, d2 respectively. Since the expanded channels are virtual and do not actually transmit information, it is equivalent to assume that all information in the new channels (channels with control input delays of “0, 2, 3, 4”) is lost.

[0039] (1) The channels without information transmission are considered, and it is assumed that all information transmitted by these channels is lost. The networked control system is equivalently expanded, and the first type expression of the second system model is:

[0040]

[0041] Wherein, d N +1 is the total number of system channels, including channels participating in information transmission and channels without information transmission; represents the random process of control signal transmission of the channel with control input delay d at time t.

[0042] (2) The second type expression of the second system model is constructed by introducing a packet loss probability parameter and a parameter with multiplicative noise property in the first type expression of the second system model.

[0043] The expression of the packet loss probability parameter is:

[0044]

[0045] Wherein, represents the probability of packet loss of the channel with control input delay d at time t; p i represents the packet loss probability value; d i represents the control input delay transmitted by the i-th channel.

[0046] The expression of the parameter with multiplicative noise property is:

[0047]

[0048] Wherein, represents the expected value of ;

[0049]

[0050]

[0051] The system (2.1) can be further rewritten as a stochastic dynamic equation with both delay and multiplicative noise, i.e., the second type expression of the second system model is:

[0052]

[0053] where, represents the delay of the control input at time t, and represents the multiplicative noise of the channel. At this time, the total channel sum is d N +1( , and the range of d N is 0 ~ d

[0054] S3: Define the intermediate state parameter and construct the equivalent constraint condition to establish a constrained equivalent system, i.e., to construct a third system model.

[0055] By using the method of mathematical modeling, an intermediate state is introduced to establish a constrained equivalent system. First, the expression of the intermediate state parameter is defined as:

[0056]

[0057] Combining (2.2) and (3.1), y t can be transformed into a relationship that satisfies the following expression, i.e., the expression of the third system model:

[0058]

[0059] S4: According to the expression of the control law of the third system model, a Riccati equation is constructed and solved to obtain a positive definite solution. The positive definite solution is substituted into the expression of the control law to obtain the control law of the third system model, which is denoted as the third system control law.

[0060] Assumption (H1): The system matrix A is non-singular.

[0061] Assumption (H1) is a prerequisite condition for ensuring that the stability of the system (2.2) is equivalent to the stability of the time-lag-free system (3.2).

[0062] The rule for determining that (3.2) is asymptotically mean-square stabilizable is:

[0063] If for any positive definite matrices Q and R, the delay-dependent algebraic Riccati equation (4.1) has a unique positive definite solution P, and the auxiliary stochastic system (3.2) is asymptotically mean-square stabilizable.

[0064] The expression of the Riccati equation is:

[0065]

[0066]

[0067] where Q and R are positive definite matrices, respectively, and P is a positive definite solution.

[0068] The control law that makes the system (3.2) asymptotically mean-square stable, i.e., the expression of the third system control law is:

[0069]

[0070]

[0071] S5: Delete the channel information that is not transmitted in the third system control law to obtain the control law of the first system model, denoted as the first system control law.

[0072] Under the premise of assumption (H1), for any positive definite matrix Q and positive definite matrix R, the delay-dependent algebraic Riccati equation (5.1) has a unique positive definite solution when Then it can be determined that the system is asymptotically mean-square stabilizable.

[0073]

[0074] where the parameters are as follows, respectively:

[0075]

[0076] The stable control law (the first system control law) of the system can be designed as:

[0077]

[0078] where the parameters can be understood as the channel information that is not transmitted in the parameters P, D, and V. is the transpose of .

[0079] This part describes the process of deleting the channel information that is not transmitted in the third system control law. The formula form applied is basically the same, only the meaning of the parameters is different.

[0080] S6: Perform multi-channel information transmission according to the first system control law.

[0081] In the embodiment, the networked control system is equivalently expanded, and a dynamic equation of a multi-time-delay stochastic system is further rewritten, an intermediate state is introduced to establish a constrained equivalent system, and a control law is designed based on the equivalent system, so that the networked control system is asymptotically stable under the control law, and the problem of coexistence of multiple transmission delays and random packet loss is solved, and the integrity of transmitted information in channel transmission is improved.

[0082] Embodiment 2

[0083] As Figure 3 shown, the embodiment provides a control law design system for asymptotic stability of a multi-channel networked control system, comprising:

[0084] A first model establishing module M1 is configured to establish a model of a multi-channel networked control system with both delay and packet loss, and the model is denoted as a first system model.

[0085] A second model establishing module M2 is configured to introduce channels without information transmission into the first system model, and define that all data of the channels without information transmission are all lost packets, to obtain a second system model.

[0086] A third model establishing module M3 is configured to define an intermediate state parameter and construct an equivalent constraint condition, and construct a third system model according to the intermediate state parameter, the equivalent constraint condition and the second system model.

[0087] A third system control law design module M4 is configured to design an expression of a control law according to the third system model, construct a Riccati equation and solve a positive definite solution, substitute the positive definite solution into the expression of the control law, and obtain a control law of the third system model, which is denoted as a third system control law.

[0088] A first system control law design module M5 is configured to delete information of channels without information transmission in the third system control law to obtain a control law of the first system model, which is denoted as a first system control law.

[0089] An information transmission module M6 is configured to perform multi-channel information transmission according to the first system control law.

[0090] In the embodiments, each embodiment is described in a progressive manner, and each embodiment mainly describes differences from other embodiments, and the same or similar parts of each embodiment can be referred to each other.

[0091] The principles and implementation manners of the present application are described by using specific examples in the present application, and the above examples are only used to help understand the method of the present application and its core idea; meanwhile, for the general technical personnel in the art, the specific implementation manners and application ranges will be changed according to the idea of the present application. In conclusion, the content of the present specification should not be understood as the limitation of the present application.

Claims

1. A method for designing asymptotically stable control laws for a multi-channel networked control system, characterized in that, include: Establish a multi-channel networked control system model that simultaneously exhibits delay and packet loss, denoted as the first system model; By introducing channels that do not transmit information into the first system model and defining that all data in the channels that do not transmit information is lost, a second system model is obtained. Define intermediate state parameters and construct equivalent constraints. Construct a third system model based on the intermediate state parameters, the equivalent constraints, and the second system model. The expression for the control law is designed based on the third system model; the Riccati equation is constructed and solved to obtain a positive definite solution; the positive definite solution is substituted into the expression for the control law to obtain the control law for the third system model, denoted as the third system control law; The control law of the first system model is obtained by deleting the channel information that has not been transmitted in the third system control law, and is denoted as the first system control law. Multi-channel information transmission is performed according to the first system control law; The expression for the first system model is: in, Indicates in The state of the system at any given time; Indicates the first Control signals that participate in the information transmission channel For state space stochastic processes, Indicates control signal Successful transmission. Indicates the first Control signals participating in the information transmission channel Packet loss; Indicates the first Control input delay transmitted over a single channel; , The matrix parameters represent the system parameters; Indicates the number of channels involved in information transmission; Specifically, the first system model introduces channels that do not transmit information and defines all data on these channels as being lost, resulting in a second system model, which includes: By introducing channels that do not transmit information into the first system model and assuming that all data in the channels that do not transmit information is lost, a first type expression for the second system model is obtained. In the first type expression of the second system model, a packet loss probability parameter and a parameter with multiplicative noise properties are introduced to construct the second type expression of the second system model; The first type expression of the second system model is: in, It is the sum of system channels, including channels that participate in information transmission and channels that do not participate in information transmission; This indicates that the control input delay at time t is... The random process of control signal transmission in the channel.

2. The method according to claim 1, characterized in that, The expression for the packet loss probability parameter is: in, This indicates that the control input delay at time t is... The probability of packet loss in the channel; This represents the probability of packet loss. Indicates the first Control input delay transmitted over a single channel; The expression for the parameter with multiplicative noise properties is: in, express Expected value; The second type expression of the second system model is: 。 3. The method according to claim 1, characterized in that, The expression for the Riccati equation is: Where Q and R are positive definite matrices; P is a positive definite solution; The expression for the control law of the third system is: ； ； The expression for the first system control law is: 。 4. A system based on the method according to any one of claims 1 to 3, characterized in that, include: The first model building module is used to build a multi-channel networked control system model that simultaneously has delay and packet loss, denoted as the first system model; The expression for the first system model is: in, Indicates in The state of the system at any given time; Indicates the first Control signals that participate in the information transmission channel For state space stochastic processes, Indicates control signal Successful transmission. Indicates the first Control signals participating in the information transmission channel Packet loss; Indicates the first Control input delay transmitted over a single channel; , The matrix parameters represent the system parameters; Indicates the number of channels involved in information transmission; The second model building module is used to introduce channels that do not transmit information into the first system model and define that all data in the channels that do not transmit information are lost, so as to obtain the second system model. Specifically, the first system model introduces channels that do not transmit information and defines all data on these channels as being lost, resulting in a second system model, which includes: By introducing channels that do not transmit information into the first system model and assuming that all data in the channels that do not transmit information is lost, a first type expression for the second system model is obtained. In the first type expression of the second system model, a packet loss probability parameter and a parameter with multiplicative noise properties are introduced to construct the second type expression of the second system model; The first type expression of the second system model is: in, It is the sum of system channels, including channels that participate in information transmission and channels that do not participate in information transmission; This indicates that the control input delay at time t is... The random process of control signal transmission in the channel; The third model building module is used to define intermediate state parameters and construct equivalent constraints, and to construct a third system model based on the intermediate state parameters, the equivalent constraints, and the second system model. The third system control law design module is used to design the expression of the control law based on the third system model; construct the Riccati equation and solve it to obtain a positive definite solution; substitute the positive definite solution into the expression of the control law to obtain the control law of the third system model, which is denoted as the third system control law. The first system control law design module is used to delete the channel information that has not been transmitted in the third system control law to obtain the control law of the first system model, which is denoted as the first system control law. The information transmission module is used to perform multi-channel information transmission according to the first system control law.

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