A design method of dynamic event-driven consistency protocol under switching topology

Abstract

This invention relates to the field of distributed multi-agent research technology and discloses a design method for a dynamic event-driven consensus protocol under a switching topology, comprising the following steps: S1, constructing the agent network structure and dynamic equations of the multi-agent network using Markov functions; S2, establishing an event-triggered mechanism for communication between agents; S3, constructing a Brownian motion model of measurement errors; S4, constructing a consensus control protocol for the multi-agent network under a Markov switching topology. This design method for a dynamic event-driven consensus protocol under a switching topology, when considering the random dynamics of topology switching, allows some followers to obtain the leader's state information and exchange information with their neighbors, coordinating control to suppress noise and achieve state consistency with the leader. A novel dynamic event-triggered control mechanism is used to determine the communication frequency between nodes, establish appropriate communication timing, avoid communication congestion, and thus save energy.

Description

Technical Field

[0001] This invention relates to the field of distributed multi-agent research technology, specifically to a design method for a dynamic event-driven consensus protocol under topology switching. Background Technology

[0002] In recent years, the consensus stability control problem of stochastic multi-agent systems has attracted much attention due to its wide range of civilian and military applications. Its applications cover various sectors of national economy and people's livelihood, such as the national power grid system, mobile communication networks, and urban transportation networks. Their normal operation has a significant impact on national economic development and social stability. The key to the consensus problem is to move from information from limited neighboring agents to achieving the global goal of the entire multi-agent system, so that all nodes in the network converge to a common value. However, communication between the agents in the system can also introduce noise interference problems.

[0003] Therefore, to improve the stability and reliability of multi-agent systems, the impact of noise on data transmission needs to be considered during the design of control protocol algorithms. It is worth noting that the design of relevant consensus control protocols requires real-time system state information, but neglects the interference signals of multiplicative noise present in real-world systems. Multiplicative noise better reflects the interference of the environment on information from neighbors, and its intensity depends on the state of the multi-agent system. Furthermore, in practical applications, agents occasionally disconnect or reconnect, forming a time-varying communication network, which is a problem that needs to be considered compared to a fixed topology. Therefore, this paper investigates and designs a dynamic event-triggered protocol to ensure that the system state of followers remains consistent with that of the leader system in the presence of multiplicative noise and topology switching. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a design method for a dynamic event-driven consensus protocol under topology switching. When considering the random dynamics of topology switching, some followers obtain the leader's state information and exchange information with their neighbors to coordinate control, thereby suppressing noise and achieving state consistency with the leader. A novel dynamic event triggering control mechanism is used to determine the communication frequency between nodes, establish appropriate communication timing, avoid communication congestion, and thus save energy. Compared with static event triggering mechanisms, dynamic event triggering mechanisms can dynamically adjust the triggering threshold based on the current system information (state, error). As the system state converges to consistency, the triggering threshold gradually decreases, and the event triggering interval lengthens, thereby effectively reducing communication frequency and saving energy.

[0006] (II) Technical Solution

[0007] To achieve the aforementioned energy-saving effect, this invention provides the following technical solution: a design method for a dynamic event-driven consensus protocol under topology switching, comprising the following steps:

[0008] S1. Constructing agent network structure and multi-agent dynamic equations using Markov functions.

[0009] The infinitesimal generator of the Markov process {(), t≥0} is Ξ=[]×m, which can be given by the transition probability.

[0010]

[0011] Where, q rs Let q be the transition rate from mode r to mode s, satisfying q rs ≥0.

[0012] S2. Event-triggered mechanism for establishing communication between agents

[0013] The system dynamics model of the leader:

[0014]

[0015] Follower system dynamics model:

[0016] The event triggering protocol is as follows:

[0017]

[0018]

[0019] Measurement error

[0020] Internal dynamic variable μ i satisfy

[0021]

[0022] S3. Construct a Brownian motion model for measurement error.

[0023] The measurement information of each intelligent agent system is

[0024] y ji ()=x j ()+f ij ( j ()-x i ()) ij ()#(5).

[0025] S4. Constructing a consensus control protocol for multi-agent systems under Markov switching topology.

[0026] In the case of random topology switching, to reduce the impact of measurement noise and take into account the event-triggered strategy, the consistency control protocol is as follows:

[0027]

[0028] S5. Constructing an error model for the agent and leader.

[0029] Constructing an error model with the leader e i ()=x i ()-x0()

[0030]

[0031] S6. Establish the Lyapunov function model

[0032] Choosing Lyapunov functions make

[0033] Differentiation yields

[0034]

[0035] S7. By proving that the Lyapunov function is bounded and convergent, the range of system parameters is determined.

[0036] The selected parameters are determined by using Lyapunov functions.

[0037]

[0038] in,

[0039] S8. Achieve alignment with the leader's state.

[0040] In the event trigger controller u i Under this effect, the states of followers and leaders eventually reached a mean square consistency, thus suppressing interference.

[0041] Preferably, in step S1, the network connection structure of each node is established as an undirected graph; for nonlinear systems, there exist nonnegative constants. satisfy

[0042]

[0043] Preferably, in step S2, f(·) is an unknown nonlinear system.

[0044] Preferably, in step S3, ξ ij The measurement noise between system i and system j satisfies the Brownian motion characteristics. There exists ε such that ||f ij (x)||≤ε||x||.

[0045] Preferably, in step S4, the next state update time satisfy

[0046]

[0047] Preferably, in step S6, wherein,

[0048] Preferably, in step S6, it can be deduced that...

[0049]

[0050] Combining (1)-(7) we have

[0051]

[0052] To achieve alignment between the state of followers and leaders.

[0053] Preferably, in step S7, the event triggering protocol satisfies

[0054]

[0055] in,

[0056]

[0057]

[0058] (III) Beneficial Effects

[0059] Compared with existing technologies, this invention provides a design method for a dynamic event-driven consensus protocol under topology switching, which has the following advantages:

[0060] 1. The design method of dynamic event-driven consensus protocol under the switching topology. When considering the random dynamics of the topology switching, some followers obtain the leader's state information and exchange information with their neighbors to coordinate control, thereby suppressing noise and achieving consistency with the leader's state.

[0061] 2. The design method of dynamic event-driven consensus protocol under the switching topology: a new dynamic event triggering control mechanism is used to determine the communication frequency between nodes, establish appropriate communication timing, avoid communication congestion, and thus save energy.

[0062] 3. The design method of the dynamic event-driven consistency protocol under the switching topology, compared with the static event triggering mechanism, can dynamically adjust the triggering threshold by combining the current system information (state, error). As the system state converges to consistency, the triggering threshold will gradually decrease and the event triggering interval will be extended, thereby effectively reducing the communication frequency and saving energy. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the process structure of the present invention;

[0064] Figure 2 This is a schematic diagram of the switching topology of the network graph of the present invention;

[0065] Figure 3 This is a schematic diagram of the mean square error of the present invention. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Example 1:

[0068] Please see Figure 1 This invention provides a technical solution: a design method for a dynamic event-driven consensus protocol under topology switching, comprising the following steps:

[0069] S1. Constructing agent network structure and multi-agent dynamic equations using Markov functions.

[0070] The infinitesimal generator of the Markov process {(), t≥0} is Ξ=[]×m, which can be given by the transition probability.

[0071]

[0072] Where, q rs Let q be the transition rate from mode r to mode s, satisfying q rs ≥0.

[0073] The network connection structure of each node is established as an undirected graph; for nonlinear systems, there exist nonnegative constants. satisfy

[0074]

[0075] S2. Event-triggered mechanism for establishing communication between agents

[0076] The system dynamics model of the leader:

[0077]

[0078] Follower system dynamics model:

[0079]

[0080] The event triggering protocol is as follows:

[0081]

[0082] Measurement error

[0083] Internal dynamic variable μ i satisfy

[0084]

[0085] f(·) is an unknown nonlinear system.

[0086] S3. Construct a Brownian motion model for measurement error.

[0087] The measurement information of each intelligent agent system is

[0088] y ji (t)=x j (t)+f ij (x j (t)-x i (t))ξ ij (t)#(5).

[0089] ξ ij The measurement noise between system i and system j satisfies the Brownian motion characteristics. There exists ε such that ||f ij (x)||≤ε||x||.

[0090] Preferably, in step S4, the next state update time satisfy

[0091]

[0092] S4. Constructing a consensus control protocol for multi-agent systems under Markov switching topology.

[0093] In the case of random topology switching, to reduce the impact of measurement noise and take into account the event-triggered strategy, the consistency control protocol is as follows:

[0094]

[0095] S5. Constructing an error model for the agent and leader.

[0096] Constructing an error model with the leader e i ()=x i ()-x0()

[0097]

[0098] S6. Establish the Lyapunov function model

[0099] Choosing Lyapunov functions make

[0100] Differentiation yields

[0101]

[0102] in, It can be deduced that

[0103]

[0104] Combining (1)-(7) we have

[0105]

[0106] To achieve alignment between the state of followers and leaders.

[0107] S7. By proving that the Lyapunov function is bounded and convergent, the range of system parameters is determined. The selected parameters satisfy the Lyapunov function.

[0108]

[0109] in, Event triggering protocol satisfied

[0110]

[0111] in,

[0112]

[0113]

[0114] S8. Achieve alignment with the leader's state.

[0115] In the event trigger controller u i Under this effect, the states of followers and leaders eventually reached a mean square consistency, thus suppressing interference.

[0116] Example 2:

[0117] Please see Figure 2 picture Figure 3 Furthermore, in conjunction with Example 1, it is obtained that,

[0118] (1) Establish the system dynamics model:

[0119] Leader:

[0120] Followers:

[0121] Given the Markov switching topology {σ(t), t≥0}, the consensus control protocol for each multi-agent is as follows:

[0122]

[0123] Among them, the measurement information y ji (t)=x j (t)+f ij (x j (t)-x i (t))ξ ij (t); ξ ij The measurement noise between system i and system j satisfies the Brownian motion characteristics. There exists ε such that ||f ij (x)||≤ε||x||.

[0124] The event triggering protocol is as follows:

[0125]

[0126] Measurement error Internal dynamic variable μ i satisfy:

[0127]

[0128] Next status update time satisfy:

[0129]

[0130] The system parameters satisfy:

[0131]

[0132]

[0133]

[0134] in

[0135]

[0136]

[0137] The mean square error of the system converges to 0, as follows: Figure 3 As shown.

[0138] (2) Establish the network connection structure of each node as a randomly switching topology. Figure 2 For nonlinear systems, there exist nonnegative constants. satisfy

[0139]

[0140] Graph theory related knowledge: Let G = (V, E, A) be a weighted directed graph, where V = {1, 2, ..., N} is the set of nodes; Let G be the edge set. Node i represents the i-th agent, and an edge of G is denoted by (i,j), representing a one-way information transfer 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 This represents the structure of the graph. If there is 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. If G is an undirected graph, (i,j) is a bidirectional information transmission process. Here, this invention emphasizes that the information between agents is bidirectional.

[0141] The design method of the dynamic event-driven consensus protocol under the switching topology considers the random dynamics of the topology switching. Some followers obtain the leader's state information and exchange information with their neighbors to coordinate control, thereby suppressing noise and achieving consistency with the leader's state. A novel dynamic event triggering control mechanism is used to determine the communication frequency between nodes, establish appropriate communication timing, avoid communication congestion, and thus save energy. Compared with the static event triggering mechanism, the dynamic event triggering mechanism can dynamically adjust the triggering threshold based on the current system information (state, error). As the system state converges to consistency, the triggering threshold will gradually decrease, and the event triggering interval will be extended, thereby effectively reducing the communication frequency and saving energy.

[0142] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A design method for a dynamic event-driven consensus protocol under topology switching, characterized in that, Includes the following steps: S1. Constructing agent network structures and multi-agent dynamic equations using Markov functions. Markov processes The infinitesimal generator is It can be given by the transition probability. in, For modality To mode The transfer rate satisfies ; S2. Event-triggered mechanism for establishing communication between agents The system dynamics model of the leader: Follower system dynamics model: ； The event triggering protocol is as follows: Measurement error , ; Internal dynamic variables satisfy ； S3. Construct a Brownian motion model for measurement error. The measurement information of each intelligent agent system is ； S4. Constructing a consensus control protocol for multi-agent systems under Markov switching topology. In the case of random topology switching, to reduce the impact of measurement noise and take into account the event-triggered strategy, the consistency control protocol is as follows: ； S5. Constructing an error model for the agent and leader. Constructing an error model with the leader S6. Establish the Lyapunov function model Choosing Lyapunov functions ,make , Differentiation yields ； S7. By proving that the Lyapunov function is bounded and convergent, the range of system parameters is determined. The selected parameters are determined by using Lyapunov functions. in, ; S8. Achieve alignment with the leader's state. In the event triggering controller Under this effect, the states of followers and leaders eventually reached a mean square consistency, thus suppressing interference. In step S7, the event triggering protocol satisfies in, 。 2. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S1, the network connection structure of each node is established as an undirected graph; for nonlinear systems, there exist nonnegative constants. satisfy 。 3. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S2 It is an unknown nonlinear system.

4. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S3 The measurement noise between system i and system j satisfies the Brownian motion characteristics. ,exist Make .

5. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S4, the next state update time satisfy 。 6. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S6, wherein, .

7. The design method of a dynamic event-driven consensus protocol under topology switching according to claim 1, characterized in that, In step S6, it can be deduced that Combination have To achieve alignment between the state of followers and leaders.

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