A novel design method for event-triggered dynamic compensator control protocol

Abstract

The present invention discloses a novel event-triggered dynamic compensator control protocol design method, comprising the following steps: (1) determining that the network connection structure of each subsystem is a strongly connected graph; all eigenvalues ​​of the matrix S are on the negative real axis; i ,B i ), and (A i , C mi ) are respectively controllable and observable; (H i , S) does not have to be observable; the following matrix equation has a solution #imgabs0#graph theory: Let G = (V, E, A) be a weighted directed graph, where V = {1, 2, ..., N} is the node set; #imgabs1# is the edge set, node i represents the i-th agent, an edge of G is represented by (i, j), indicating a unidirectional information transmission from node i to node j, if there is a root node in a directed graph. In the present invention, all error terms of the system can converge to 0, and the final state of the system tends to be stable. Under the action of the new dynamic compensator, the heterogeneous system can suppress interference or track signals to the external system, and finally achieve output consistency.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed multi-agent research, and in particular to a design method for a novel event-triggered dynamic compensator control protocol. Background Art

[0002] In recent years, the problem of consistent stability control of random multi-agent systems has attracted much attention due to its wide range of civil and military applications. Its applications involve various fields of national economy and people's livelihood, such as national power grid system, mobile communication network, urban transportation network, etc. Its normal operation has an important impact on national economic development and social stability. The key to the consistency problem is to make all nodes in the network converge to a common value from the information of limited neighboring agents to achieve the global goal of the entire multi-agent system.

[0003] Among them, heterogeneous output regulation systems have received attention in the research field of multi-agent systems. This system can follow external signals or suppress external interference signals, so as to achieve consistency in the output of each subsystem. In current research, only the external signal is considered to be fully observable, that is, some subsystems can fully observe the state of the external system. This situation is unrealistic. Because in reality, due to technical limitations and / or the high cost of existing measurement equipment, it is impractical to directly measure all dynamic variable information. In this case, a subsystem often measures part of the external signal, and then through mutual communication and coordinated control of each subsystem, a complete estimation of the external signal is achieved, so that the heterogeneous system achieves consistency in the output state under the action of the external signal. The event-triggered control method aims to reduce the waste of resources caused by frequent communication between systems. The characteristic of the event-triggered control method is that the communication between the subsystems will not occur every moment, but only at the moment when the trigger condition is met, which can greatly reduce the communication frequency between the subsystems. Summary of the invention

[0004] The purpose of the present invention is to provide a novel design method of event-triggered dynamic compensator control protocol to solve the problems raised by the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A design method for a novel event-triggered dynamic compensator control protocol includes the following steps:

[0007] (1) Determine the network connection structure of each subsystem as a strong interconnection diagram; matrix All eigenvalues ​​are on the negative real axis; ,and They are respectively controllable and observable; It does not have to be significant; the following matrix equation has a solution

[0008]

[0009] Graph theory: Let G = (V, E, A) be a weighted directed graph, where V = {1,2,...,N} is the node set; E⊆V×V is the edge set, node i represents the i-th agent, an edge of G is represented by (i, j), which represents the unidirectional information transmission from node i to node j. If a directed graph has a root node and the root node has directed paths to all other nodes in the graph, then a directed graph is said to contain a spanning tree. The weighted adjacency matrix A = [aij]∈RN×N represents the structure of the graph. If there is information communication between nodes j and i, it is represented by aij = 1, otherwise it is represented by aij = 0. A strongly connected graph means that there is always a directed path from node i to node j in the graph network;

[0010] (2) Establish a heterogeneous multi-agent system output regulation system model:

[0011] ;

[0012] (3) The process of using directed graphs to confirm the communication topology relationship between agents in a leaderless multi-agent system is as follows:

[0013] Error variables of dynamic compensators and external systems ; Define event trigger state error variable The next moment Determined by the event triggering protocol, where the event triggering protocol is

[0014]

[0015] in , Trigger thresholds for dynamic events. is a positive definite matrix, the constant The following lemma is satisfied.

[0016] Lemma 1: If G is a strongly connected directed graph, there will always be a positive definite matrix and constant Make

[0017]

[0018] in , , and .

[0019] Error variables of dynamic compensators and external systems Available error status The derivative of

[0020]

[0021] Select the Lyapunov function

[0022] , and then differentiate dV for the selected V,

[0023]

[0024] in .

[0025] We can get the following lemma

[0026] Lemma 2: The graph G is a strongly connected graph, and the eigenvalues ​​of the matrix S are non-negative real numbers. ,and are respectively controllable and observable. And the matrices S and H can be orthogonalized by the matrix T i Decompose into

[0027]

[0028] It is the observable part. The index Converges to 0. Coupling gain satisfy

[0029]

[0030] in , In addition, the gain matrix , They are

[0031]

[0032] From Lemma 2, we can see that the error ε converges exponentially to 0. Therefore, the new state compensator can perfectly observe the state of the external system.

[0033] Set system status and observer status The error is: , and derive it

[0034]

[0035] because is the Hurwitz matrix, the error ε exponentially converges to 0, so the error Converges to 0.

[0036] Set system status and external systems The error is , and derive it

[0037]

[0038] because is the Hurwitz matrix, the error ε exponentially converges to 0, and the error converges to 0, so the error term Converges to 0, further, the system error

[0039]

[0040] The error ε exponentially converges to 0, the error Converges to 0, error converges to 0, so the error Converges to 0.

[0041] Preferably, in step (2), is the state vector of the continuous-time linear multi-agent system; ymi(t) represents the output of the system; v is the external system; is the control input of the ith agent (distributed random consensus control protocol); Ei, Fmi, Fi are constant matrices, where the external system state is:

[0042] .

[0043] Preferably, in step (2), S, H are constant matrices, and the output feedback control protocol for each multi-agent dynamic event trigger is:

[0044]

[0045] in ; is the observer state; is the state of the dynamic compensator; zi is the relative estimated state, which is a piecewise constant vector and will update the current state at the next event triggering moment; is a constant, , is the observer gain matrix, where The state equation is

[0046] .

[0047] The novel event-triggered dynamic compensator control protocol design method provided by the present invention has the following beneficial effects:

[0048] In the present invention, all error terms of the system can converge to 0, and the final state of the system tends to be stable. Under the action of the new dynamic compensator, the heterogeneous system can suppress interference or track signals to the external system, and finally achieve output consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The figure is a schematic diagram of the overall process of the design method of the present invention. DETAILED DESCRIPTION

[0050] Example

[0051] See also Figure 1 The design method of the novel event-triggered dynamic compensator control protocol provided by the present invention comprises the following steps:

[0052] (1) Establishing a heterogeneous multi-agent system output regulation system model:

[0053]

[0054] in, is the state vector of the continuous-time linear multi-agent system; y mi (t) represents the output of the system; v is the external system; is the control input of the ith agent (distributed random consensus control protocol); E i ,F mi ,F i is a constant matrix. The external system state is:

[0055]

[0056] S,H is a constant matrix.

[0057] For each multi-agent dynamic event, the output feedback control protocol is triggered:

[0058]

[0059] in ; Represents the moment when each event is triggered; is the observer state; is the state of the new dynamic compensator; iis the relative estimated state, which is a piecewise constant vector and will update the current state at the next event triggering time; coupling gain , the observer gain matrix , the observer gain matrix The following inequality is satisfied:

[0060]

[0061] in , The gain matrix can be determined , They are

[0062]

[0063] in The state equation is

[0064]

[0065] The event triggering protocol is:

[0066]

[0067] in , is the dynamic event triggering threshold. The positive definite matrix and constant Satisfies the following inequality, is an arbitrary constant.

[0068]

[0069] in , , and .

[0070] (2) Determine the network connection structure of each subsystem as a strong interconnection graph; matrix All eigenvalues ​​are on the negative real axis; ,and They are respectively controllable and observable; It does not have to be significant; the following matrix equation has a solution

[0071]

[0072] Graph theory: Let G = (V, E, A) be a weighted directed graph, where V = {1,2,...,N} is the node set; E⊆V×V is the edge set. Node i represents the i-th agent, and an edge of G is represented by (i, j), which indicates a unidirectional information transmission from node i to node j. If a directed graph has a root node and the root node has directed paths to all other nodes in the graph, then the directed graph is said to contain a spanning tree. The weighted adjacency matrix A = [a ij ]∈R N×N Represents the structure of the graph. If there is information communication between nodes j and i, it is represented by a ij = 1, otherwise it means a ij = 0. A strongly connected graph means that there is always a directed path from node i to node j in the graph network.

[0073] The novel event-triggered dynamic compensator control protocol provided by the present invention establishes a stability criterion for the heterogeneous output regulation system, and constructs the error variables of the dynamic compensator and the external system. The Lyapunov function proves that the error system It will converge to 0 over time, so the new event-triggered dynamic compensator achieves perfect estimation of the state of the external system through the coordinated control of each subsystem. Finally, it is theoretically proved that the output state of the heterogeneous system tends to be consistent.

Claims

1. A design method for a novel event-triggered dynamic compensator control protocol, characterized in that: The following steps are involved: (1) Determine the network connection structure of each subsystem as a strong interconnection diagram; matrix All eigenvalues ​​are on the negative real axis; ,and They are respectively controllable and observable; It does not have to be significant; the following matrix equation has a solution ; ； Graph theory: Let G = (V, E, A) be a weighted directed graph, where V = {1,2,...,N} is the node set; E⊆V ×V is the edge set, node i represents the i-th agent, an edge of G is represented by (i, j), indicating a unidirectional information transmission from node i to node j. If a directed graph has a root node and the root node has directed paths to all other nodes in the graph, then a directed graph is said to contain a spanning tree, and the weighted adjacency matrix Represents the structure of the graph. If there is information communication between nodes j and i, it is represented as a ij = 1, otherwise it means a ij = 0, a strongly connected graph means that there is always a directed path from node i to node j in the graph network; (2) Establish a heterogeneous multi-agent system output regulation system model: ； (3) The process of using directed graphs to confirm the communication topology relationship between agents in a leaderless multi-agent system is as follows: Error variables of dynamic compensators and external systems ; Define event trigger state error variable , the next moment Determined by the event triggering protocol, where the event triggering protocol is ； in , is the dynamic event trigger threshold, is a positive definite matrix, the constant The following lemma is satisfied, Lemma 1: If G is a strongly connected directed graph, there will always be a positive definite matrix and constant Make ； in , , and , Error variables of dynamic compensators and external systems Available error status The derivative of ; Select the Lyapunov function , and then differentiate dV for the selected V, ; in , We can get the following lemma Lemma 2: The graph G is a strongly connected graph, and the eigenvalues ​​of the matrix S are non-negative real numbers. ,and are respectively controllable and observable, and the matrices S and H can be orthogonalized by the matrix T i Decompose into ； is the observable part, the error The index Converges to 0, the coupling gain satisfy ； in , , and the gain matrix , They are ； From Lemma 2, we can see that the error ε converges exponentially to 0; so the new state compensator can perfectly observe the state of the external system; Set system status and observer status The error is: , and derive it ； because is the Hurwitz matrix, the error ε exponentially converges to 0, so the error Converges to 0; Set system status and external systems The error is , and derive it ； because is the Hurwitz matrix, the error ε exponentially converges to 0, and the error converges to 0, so the error term Converges to 0, further, the system error , ； The error ε exponentially converges to 0, the error Converges to 0, error converges to 0, so the error Converges to 0; In step (2), is the state vector of the continuous-time linear multi-agent system; y mi (t) represents the output of the system; For external systems; is the control input of the ith agent; Ei, Fmi, Fi are constant matrices, where the external system state is: ； In step (2), S and H are constant matrices. The output feedback control protocol for each multi-agent dynamic event trigger is: ； in ; is the observer state; is the state of the dynamic compensator; z i is the relative estimated state, which is a piecewise constant vector and will update the current state at the next event triggering time; is a constant, , is the observer gain matrix, where The state equation is .

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