Event triggering fault-tolerant control method of state constraint multi-agent

Abstract

The invention discloses an event-triggered fault-tolerant control method for state-constrained multi-agent. The method comprises the following steps: firstly, constructing a state multi-agent mathematical model and a partial failure model of a controller; secondly, on the basis of the state multi-agent mathematical model, constructing a mathematical model of a state variable trigger function of the pth agent; then, in combination with a partial failure model of the controller and a mathematical model of a state variable trigger function, the controller of the pth agent is improved by utilizing the relation between an adjacent matrix and a Laplacian matrix in a graph theory, an adaptive law of the controller is given, and an adaptive law model is constructed; and finally, constructing a Lyapunov function in combination with the trigger function and the adaptive law model to obtain a sufficient condition of fault-tolerant control consistency and complete fault-tolerant control. The multi-agent model disclosed by the invention can still realize the consistency of anti-interference fault-tolerant constraints under the time-varying topology with variable number of agents.

Description

Technical Field

[0001] The present invention belongs to the technical field of fault-tolerant control, and in particular relates to an event-triggered fault-tolerant control method for state-constrained multi-agents. Background Art

[0002] In the past decade, multi-agent models have been widely used. With the development of artificial intelligence and big data network era, multi-agent models have shown great potential in solving various problems such as information dissemination, sensor networks, coordination, rendezvous points, vehicle formation cooperative control and power grid systems. On the one hand, it can communicate with its interconnected peers through communication protocols and finally reach a unified agreement on the shared value of each agent; on the other hand, compared with single agent models, networked multi-agent models are more efficient, and more and more people have started to study multi-agent models. Therefore, it is of great significance to study consistency control.

[0003] In practical applications, the state of an agent is often subject to constraints that affect its normal operation. For example, due to the limitations of the physical environment, agents can only maintain consistency within a specific range, and the topology of the communication network between agents will also change dynamically due to various factors. The following two situations may occur: first, the number of agents in the multi-agent model remains unchanged, but the communication topology of the system may change; second, both the number of agents and the communication topology in the multi-agent model change. Therefore, without the implementation of appropriate control strategies, controlling consensus is a huge challenge in the change of communication topology caused by the change in the number of agents. Summary of the invention

[0004] In view of the existing problems, the present invention proposes an event-triggered fault-tolerant control method for state-constrained multi-agents. First, an integrated design of an event-triggered disturbance observer and an event-triggered fault-tolerant controller is proposed to solve the problem of coupling between external disturbances and partial actuator failures in the multi-agent model; secondly, considering the change in the number of agents, a pulse time-dependent Lyapunov function is introduced to give a sufficient condition to ensure the consistency of disturbance suppression fault-tolerant constraints. Under this condition, the consistency of fault-tolerant constraints of the time-varying multi-agent model under the event-triggered mechanism can be achieved. The technical solution of the present invention includes the following steps:

[0005] Step (1) construct the following state multi-agent mathematical model and partial failure model of the controller:

[0006]

[0007] in, is the controller input of the pth agent, represents the state variable of the pth agent, ω p(t) is the external disturbance of the p-th agent, u p (t) is the controller of the p-th agent to be constructed, ρ p (t) is the partial failure coefficient of the p-th agent, ρ p and represents the partial failure coefficient ρ p (t) is the upper and lower bounds of

[0008] Step (2) Based on the state multi-agent mathematical model, a mathematical model of the state variable triggering function of the pth agent is constructed:

[0009] Ω=[x p (t k h+νh)-x p (t k h)] T R[x p (t k h+νh)-x p (t k h)]-κ d x p (t k h+νh) T Rx p (t k h+νh)>0

[0010] Among them, κ d ∈[0,1] is the constant value defined by the trigger function, R represents any positive definite matrix, x p (t k h) and x p (t k h+νh) respectively describe the previous and current sample data, t k represents the time corresponding to any sampling point k of the p-th agent, h represents the sampling period of the p-th agent, and ν represents the speed of the p-th agent.

[0011] Introduce the error function of the pth agent:

[0012]

[0013] Where τ(t) is the network-induced delay of the p-th agent.

[0014] Step (3) combines the partial failure model of the controller and the mathematical model of the state variable trigger function, and uses the relationship between the adjacency matrix and the Laplacian matrix in graph theory to improve the controller of the p-th agent, construct the disturbance observer and fault-tolerant controller of the p-th agent, and give its adaptive law Construct the following adaptive law model:

[0015]

[0016] Among them, S p represents the known constant matrix of the p-th agent, O p (t) represents the auxiliary function of the disturbance observer of the p-th agent, N p represents the feedback gain of the disturbance observer of the p-th agent, represents the estimated value of the partial failure coefficient of the p-th agent, K n(k) represents the controller gain corresponding to the number of agents n(k), u p (t k h) represents the pth agent at t k The control input at time h, L 0,n(k) (t)+ΔL n(k) (t) is the sum of the constant part of the Laplacian matrix and the bounded time-varying part of the Laplacian matrix, is the interference ω of the p-th agent p (t), Ω is the trigger function introduced to the pth agent, P Ω represents the projection of the state of the pth agent on the trigger function Ω, N p is the feedback gain of the p-th agent, θ d ,λ is a positive constant, is the estimated value of the partial failure rate of the p-th agent, is the difference between the interference observation value and the actual value of the pth agent.

[0017] Step (4) combines the trigger function and the adaptive law model to construct the Lyapunov function, obtain the sufficient conditions for the consistency of fault-tolerant control, and complete the fault-tolerant control.

[0018] Construct a Lyapunov function:

[0019]

[0020] Where Θ(t) represents the time-dependent pulse function, x q (t) represents the position state of the qth agent, x p (t) represents the position state of the pth agent, Z p represents the known constant matrix of the p-th agent, x n(k) W represents the position state when the number of agents is n(k). p is the known constant matrix corresponding to the p-th agent; The derivative of the state position of the pth agent at the sth moment; τ p is the network induced delay corresponding to the p-th agent.

[0021] Introducing piecewise linear function and a new performance index of LMI that satisfies system performance into Lyapunov function, by taking its derivative, we can get D + V(t)<0, at this time the multi-agent model is stable, and the sufficient condition for fault-tolerant control consistency is obtained:

[0022]

[0023] Among them, λ,μ>1, α1, α2 are all positive scalars, δ1 is the maximum norm value when the multi-agent model does not allow the addition of new agents, and δ2 is the minimum norm value of the multi-agent model to accept new agents.

[0024] Beneficial effects of the present invention: In the multi-agent model, the sufficient conditions for fault-tolerant control consistency and the construction of Lyapunov function ensure the stability of the model and have H ∞ Performance, achieve fault-tolerant constraint consistency and obtain sufficient conditions for consistency. In general, the multi-agent model can still achieve the consistency of disturbance-resistant fault-tolerant constraints under a time-varying topology with a variable number of agents. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The overall process of event-triggered fault-tolerant control for state-constrained multi-agents

[0026] Figure 2 It is the communication topology of multiple agents in the first state;

[0027] Figure 3 is the communication topology of multiple agents in the second state;

[0028] Figure 4 The communication topology of multiple agents in the third state;

[0029] Figure 5 Estimation of partial failure rate and disturbance of actuators for the first agent;

[0030] Figure 6 Estimation of partial failure rate and disturbance of actuators for the second agent;

[0031] Figure 7 Estimation of partial failure rate and disturbance of actuators for the third agent;

[0032] Figure 8 Partial failure rate and disturbance estimation of actuators for the fourth agent;

[0033] Fig. 9 Estimation of the actuator partial failure rate and disturbance for the fifth agent;

[0034] Fig.10 The actuator partial failure rate and disturbance estimation for the sixth agent;

[0035] Fig.11 is the triggering interval of each agent’s trigger;

[0036] Fig.12 It is the state change trajectory of the multi-agent model under the action of the invented controller. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with the examples shown in the accompanying drawings. Figure 1 As shown, the specific steps include:

[0038] Step (1) construct the following state multi-agent mathematical model and partial failure model of the controller:

[0039]

[0040] in, is the controller input of the pth agent, represents the state variable of the pth agent, ω p (t) is the external disturbance of the p-th agent, u p (t) is the controller of the p-th agent to be constructed, ρ p (t) is the partial failure coefficient of the p-th agent, ρ p and represents the partial failure coefficient ρ p (t) is the upper and lower bounds of

[0041] Step (2) Construct a mathematical model of the state variable trigger function of the pth agent: Ω = [x p (t k h+νh)-x p (t k h)] T R[x p (t k h+νh)-x p (t k h)]-κ d x p (t k h+νh) T Rx p (t k h+νh)>0

[0042] Among them, κ d ∈[0,1] is the constant value defined by the trigger function, R represents any positive definite matrix, x p (tk h) and x p (t k h+νh) respectively describe the previous and current sample data. k represents the time corresponding to any sampling point k of the p-th agent, h represents the sampling period of the p-th agent, and ν represents the speed of the p-th agent.

[0043] In order to solve the network delay encountered by the p-th agent in the process of transmitting information in the mathematical model of the state variable trigger function, the error function of the p-th agent is introduced:

[0044]

[0045] Where, τ(t) = tt k h-vh is the network-induced delay of the p-th agent.

[0046] Step (3) takes into account that disturbance and fault are coupled, combines the partial failure model of the controller in step (1) and the state variable trigger function in step (2), and uses the relationship between the Kronecker product, the adjacency matrix and the Laplacian matrix in graph theory to construct the disturbance observer and fault-tolerant controller of the pth agent, and gives its adaptive law Build the following model:

[0047]

[0048] Among them, S p represents the known constant matrix of the p-th agent, O p (t) represents the auxiliary function of the disturbance observer of the p-th agent, N p represents the feedback gain of the disturbance observer of the p-th agent, represents the estimated value of the partial failure coefficient of the p-th agent, K n(k) represents the controller gain corresponding to the number of agents n(k), u p (t k h) represents the pth agent at t k The control input at time h, L 0,n(k) (t)+ΔL n(k) (t) is the sum of the constant part of the Laplacian matrix and the bounded time-varying part of the Laplacian matrix, is the interference ω of the p-th agent p (t), Ω is the trigger function introduced to the pth agent, P Ω represents the projection of the state of the pth agent on the trigger function Ω, N p is the feedback gain of the p-th agent, θ d,λ is a positive constant, is the estimated value of the partial failure rate of the p-th agent, is the difference between the interference observation value and the actual value of the pth agent.

[0049] Step (4) combines the trigger function and adaptive law model in step (3) to construct the Lyapunov function:

[0050]

[0051] Where Θ(t) represents the time-dependent pulse function, x q (t) represents the position state of the qth agent, x p (t) represents the position state of the pth agent, Z p represents the known constant matrix of the p-th agent, x n(k) W represents the position state when the number of agents is n(k). p is the known constant matrix corresponding to the p-th agent; The derivative of the state position of the pth agent at the sth moment; τ p is the network induced delay corresponding to the p-th agent.

[0052] In order to eliminate the influence of topological changes and changes in the number of agents on constraint consistency, a new performance index of piecewise linear function and LMI that satisfies performance is introduced into the Lyapunov function. By taking its derivative, we can get D + V(t)<0, at this time the multi-agent model is stable, and the sufficient condition for fault-tolerant control consistency is obtained:

[0053]

[0054] Among them, λ, μ>1, α1, α2 are all positive scalars, δ1 is the maximum norm value when the multi-agent model does not allow the addition of new agents, and δ2 is the minimum norm value of the multi-agent model to accept new agents.

[0055] The following simulation example is used to verify the effectiveness of the proposed control algorithm:

[0056] The number of agents in a multi-agent model will change with different task stages. Multi-agent models with the same number of nodes can have different communication topologies. The configuration of the initial number of nodes can be modified to achieve the configuration of a multi-agent model composed of the same number of nodes.

[0057] The communication topology diagrams of state 1, state 2, and state 3 correspond to the Laplace matrices L1 and L2, which are described as follows:

[0058]

[0059] Since the number of agents in state 2 and state 3 is the same, the problem of switching topology in state 3 is solved by the uncertainty of topology, which is represented by L2+ΔL2.

[0060] In the simulation, some faults are selected as follows: im (t),i=1,2,...,6,m=1,2,

[0061] 0.5≤ρ 1m (t)≤1,0.7≤ρ 2m (t)≤1,

[0062] 0.5≤ρ 3m (t)≤1,0.5≤ρ 4m (t)≤1,0.7≤ρ 5m (t)≤1,0.6≤ρ 6m (t)≤1.

[0063] in,

[0064] 0.5≤ρ 1m (t)≤1,0.7≤ρ 2m (t)≤1,0.5≤ρ 3m (t)≤1,0.5≤ρ 4m (t)≤1,0.7≤ρ 5m (t)≤1,0.6≤ρ 6m (t)≤1 is the fault range.

[0065] Also select the external perturbation constant matrix parameters S of agents 1 to 6 i ,i=1,2,...,6,select as follows:

[0066]

[0067] λ=0.4, μ=4.8, δ1=4, δ2=15, β2=16.

[0068] The gains of the disturbance observer and controller are calculated as:

[0069]

[0070] exist Figure 2 In the figure, the communication topology contains 4 nodes, and the edge weights between nodes are all 1. Nodes 1, 2, 3, and 4 form a ring structure, which realizes the information transmission between nodes. Figure 3 In the figure, the communication topology is expanded to 5 nodes, and the edge weights are all 1. The new node 5 is connected to nodes 1 and 4, indicating the topological impact of the addition of the new agent on the original system. Figure 4In the example, the communication topology still contains 5 nodes, and the edge weights are all 1. When the new node 6 is added, node 3 exits, reflecting the dynamic changes of the system communication structure caused by the addition or exit of the intelligent agent.

[0071] Figure 5-Figure 10 The curves of the disturbance estimation and partial failure rate estimation of different agents under two different actual disturbances and actual partial failure rates are shown respectively, where:

[0072] Figure 5 : 0-1.7 seconds, according to Figure 2 Communication topology structure, agent 1 joins the model and participates in completing the work. At 0.6 seconds, agent 1 fails, at 0.1 seconds, agent 1 is disturbed, and at 12 seconds, agent 1 begins to leave the model. In the first case, the estimated partial failure rate of agent 1 coincides with the actual partial failure rate at around 5.2 seconds, and the estimated disturbance coincides with the actual disturbance value. In the second case, the estimated partial failure rate of agent 1 coincides with the actual partial failure rate at around 4.8 seconds, and the estimated disturbance coincides with the actual disturbance.

[0073] Figure 6 : 0-1.7 seconds, according to Figure 1 Communication topology structure, Agent 2 joins the model and participates in completing the work. At 0.6 seconds, Agent 2 fails, at 0.1 seconds, Agent 2 is disturbed, and at 12 seconds, Agent 2 begins to leave the model. In the first case, the estimated partial failure rate coincides with the actual partial failure rate at around 4 seconds, and the estimated disturbance coincides with the actual disturbance estimate at around 4.2 seconds. In the second case, the estimated partial failure rate coincides with the actual partial failure rate at around 8 seconds, and the disturbance estimate coincides with the actual disturbance.

[0074] Figure 7 : 0-1.7 seconds, according to Figure 1 Communication topology structure, agent 3 joins the model and participates in completing the work. At 4.1-12 seconds, agent 3 leaves the model. At 0.6 seconds, agent 3 fails. At 0.1 seconds, agent 3 is disturbed. In the first case, the estimated value of the partial failure rate at around 1.6 seconds coincides with the actual estimated value of the partial failure rate, and the estimated value of the disturbance at around 0.5 seconds coincides with the actual estimated value. In the second case, the estimated value of the partial failure rate at around 2.1 seconds coincides with the actual estimated value of the failure rate, and the estimated value of the disturbance at around 2.5 seconds coincides with the actual disturbance value.

[0075] Figure 8 : 0-1.7 seconds, according to Figure 1Communication topology structure, agent 4 joins the model and participates in completing the work. At 1 second, agent 4 fails, at 0.3 seconds, agent 4 is disturbed, and at 12 seconds, agent 4 begins to leave the model. In the first case, the estimated partial failure rate coincides with the actual partial failure rate at around 4 seconds, and the estimated disturbance coincides with the actual disturbance estimate at around 0.2 seconds. In the second case, the estimated partial failure rate coincides with the actual partial failure rate at around 6.2 seconds, and the disturbance estimate coincides with the actual disturbance.

[0076] Fig. 9 : 1.8-4 seconds, according to Figure 2 Communication topology structure, agent 5 joins the model and participates in completing the work. At 1.9 seconds, agent 5 fails, at 0.1 seconds, agent 5 is disturbed, and at 12 seconds, agent 5 begins to leave the model. In the first case, the estimated partial failure rate coincides with the actual partial failure rate at around 4.2 seconds, and the estimated disturbance coincides with the actual disturbance estimate at around 4.4 seconds. In the second case, the estimated partial failure rate coincides with the actual partial failure rate at around 6 seconds, and the disturbance estimate coincides with the actual disturbance.

[0077] Fig.10 : 4.1-12 seconds, according to Figure 3 Communication topology structure, agent 6 joins the model and participates in completing the work. At 4.3 seconds, agent 6 fails, at 4 seconds, agent 6 is disturbed, and at 12 seconds, agent 5 begins to leave the model. In the first case, the estimated partial failure rate coincides with the actual partial failure rate at around 9 seconds, and the estimated disturbance coincides with the actual disturbance estimate at around 5 seconds. In the second case, the estimated partial failure rate coincides with the actual partial failure rate at around 10 seconds, and the estimated disturbance coincides with the actual disturbance at around 5 seconds.

[0078] Fig.11 It represents the triggering interval of the event trigger of each agent. During the period when the agents completed the three consensuses, the triggering interval of each agent in each stage obviously changed from dense to sparse, indicating that the event trigger effectively reduced the communication frequency of the agents.

[0079] Fig.12 It shows the path of the multi-agent model under the action of the controller of the present invention when the actuator encounters partial failure and is subject to external interference. It can be divided into three stages: In the initial stage (0-1.7 seconds), Agent 1, Agent 2, Agent 3, and Agent 4 work together to complete the work and according to Figure 1 The topological structure of the fault-tolerant constraint is successfully reached in region A. In the second stage (1.8-4 seconds), agent 5 is introduced into the model. Figure 2The topological structure of the model is associated, and a consensus on fault-tolerant constraints is successfully reached in region B. In the third stage (4.1-12 seconds), agent 6 is introduced into the model, and agent 3 leaves the model. At this time, a fault-tolerant consensus is successfully reached in region C. Considering the external interference specified by the model, at 0.6 seconds, agents 1 and 3 fail; at 0.7 seconds, agents 2 and 4 fail; at 1.9 seconds, agent 5 fails; at 4.3 seconds, agents 6 and 7 fail. Fig.11 It can be seen that even in the presence of external disturbances, partial failure of actuators, and changing number of nodes in the model, the multi-agent model can reach consensus within the constraint set under the specified event-triggered controller.

[0080] This paper studies the design method of event-triggered fault-tolerant control technology for state-constrained multi-agents. Using the event-triggered mechanism, the method of achieving anti-interference fault-tolerant constraint consistency in a multi-agent model with a variable number of agents is improved. First, an integration of event-triggered disturbance observer and fault-tolerant controller for each agent is designed to reduce network congestion, estimate disturbances and partial actuator failures; secondly, a time-varying pulse Lyapunov function that depends on the number of agents is proposed to overcome the topology switching problem caused by the change in the number of agents, and sufficient conditions for achieving event-triggered disturbances and suppressing fault-tolerant constraint consistency are given. Under these conditions, the multi-agent model can achieve fault-tolerant constraint consistency even if the number of nodes in the model keeps changing. Finally, the effectiveness of this method is verified through simulation of specific examples.

Claims

1. An event-triggered fault-tolerant control method for state-constrained multi-agents, characterized in that: The following steps are involved: Step 1: Construct a state multi-agent mathematical model and a partial failure model of the controller; Step 2: Based on the state multi-agent mathematical model, construct a mathematical model of the state variable trigger function of the pth agent; Step 3: Combine the partial failure model of the controller and the mathematical model of the state variable trigger function, use the relationship between the adjacency matrix and the Laplacian matrix in graph theory to improve the controller of the pth agent, and give its adaptive law Constructing adaptive law models; Step 4: Combine the trigger function and the adaptive law model to construct the Lyapunov function, obtain the sufficient conditions for the consistency of fault-tolerant control, and complete the fault-tolerant control.

2. The event-triggered fault-tolerant control method of state-constrained multi-agent according to claim 1 is characterized in that: The construction state multi-agent mathematical model and the partial failure model of the controller are as follows: in, is the controller input of the pth agent, represents the state variable of the pth agent, ω p (t) is the external disturbance of the p-th agent, u p (t) is the controller of the p-th agent, ρp(t) is the partial failure coefficient of the p-th agent, ρ p and represents the partial failure coefficient ρ p (t) is the upper and lower bounds of the 3. The event-triggered fault-tolerant control method of state-constrained multi-agent according to claim 2, characterized in that: The mathematical model for constructing the state variable trigger function of the pth agent is as follows: Ω=[x p (t k h+νh)-x p (t k h)] T R[x p (t k h+νh)-x p (t k h)]-κ d x p (t k h+νh) T Rx p (t k h+νh)>0 Among them, κ d ∈[0,1] is the constant value defined by the trigger function, R represents any positive definite matrix, x p (t k h) and x p (t k h+νh) respectively describe the previous and current sample data; t k represents the time corresponding to any sampling point k of the p-th agent, h represents the sampling period of the p-th agent, and ν represents the speed of the p-th agent; Introduce the error function of the pth agent: l p (t) = x p (t k h+νh)-x p (t k h)=x p (t-τ(t))-x p (t k h),ν=1,2,…(3)where τ(t) is the network-induced delay of the p-th agent.

4. The event-triggered fault-tolerant control method of state-constrained multi-agent according to claim 3 is characterized in that: The specific process of constructing the adaptive law model is as follows: Combining the partial failure model of the controller and the state variable trigger function, the controller of the p-th agent is improved by using the relationship between the adjacency matrix and the Laplacian matrix in graph theory, and the disturbance observer and fault-tolerant controller of the p-th agent are constructed, and its adaptive law is given. Constructing the adaptive law model: Among them, S p represents the known constant matrix of the p-th agent, O p (t) represents the auxiliary function of the disturbance observer of the p-th agent, N p represents the feedback gain of the disturbance observer of the p-th agent, represents the estimated value of the partial failure coefficient of the p-th agent, K n(k) represents the controller gain corresponding to the number of agents n(k), u p (t k h) represents the pth agent at t k The control input at time h, L 0,n(k) (t)+ΔL n(k) (t) is the sum of the constant part of the Laplacian matrix and the bounded time-varying part of the Laplacian matrix, is the interference ω of the p-th agent p (t), Ω is the trigger function introduced to the pth agent, P Ω represents the projection of the state of the pth agent on the trigger function Ω, N p is the feedback gain of the p-th agent, θ d ,λ is a positive constant, is the estimated value of the partial failure rate of the p-th agent, is the difference between the interference observation value and the actual value of the pth agent.

5. The event-triggered fault-tolerant control method of state-constrained multi-agent according to claim 4, characterized in that: The specific implementation process of step 4 is as follows: Combining the trigger function and the adaptive law model, the Lyapunov function V(t) is constructed, and the sufficient conditions for the consistency stability of the fault-tolerant control of the multi-agent model are obtained: Where Θ(t) represents the time-dependent pulse function, x q (t) represents the position state of the qth agent, x p (t) represents the position state of the pth agent, Z p represents the known constant matrix of the p-th agent, x n(k) represents the position state when the number of agents is n(k); W p is the known constant matrix corresponding to the p-th agent; The derivative of the state position of the pth agent at the sth moment; τ p is the network-induced delay corresponding to the p-th agent; Introducing piecewise linear function and a new performance index of LMI that satisfies system performance into Lyapunov function, and by taking its derivative, we get D + V(t)<0, at this time the multi-agent model is stable, and the sufficient condition for fault-tolerant control consistency is obtained: Among them, λ,μ>1, α1, α2 are all positive scalars, δ1 is the maximum norm value when the multi-agent model does not allow the addition of new agents, and δ2 is the minimum norm value of the multi-agent model to accept new agents.

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