An event-triggered fault-tolerant control method for state-constrained multi-agent systems

Abstract

The application discloses a state-constrained multi-agent event-triggered fault-tolerant control method, which comprises the following steps: firstly, constructing a state multi-agent mathematical model and a partial failure model of a controller; secondly, constructing a mathematical model of a state variable trigger function of a pth agent based on the state multi-agent mathematical model; then, combining the partial failure model of the controller and the mathematical model of the state variable trigger function, improving the controller of the pth agent by using the relationship between an adjacency matrix and a Laplacian matrix in graph theory, giving an adaptive law, and constructing an adaptive law model; finally, combining the trigger function and the adaptive law model, constructing a Lyapunov function, obtaining a sufficient condition for fault-tolerant control consistency, and completing fault-tolerant control. The multi-agent model can realize disturbance fault-tolerant constraint consistency under a time-varying topology with a variable number of agents.

Description

Technical Field

[0001] This invention belongs to the field of fault-tolerant control technology, specifically relating to an event-triggered fault-tolerant control method for state-constrained multi-agent systems. Background Technology

[0002] In the past decade or so, multi-agent models have been widely applied. With the development of artificial intelligence and big data networks, multi-agent models have shown great potential in solving various problems such as information dissemination, sensor networks, coordination, meeting points, vehicle platooning cooperative control, and power grid systems. On the one hand, they can communicate with their interconnected partners through communication protocols, ultimately reaching a unified protocol for shared values ​​among each agent. On the other hand, compared with single-agent models, networked multi-agent models are more efficient, and more and more people are conducting research on multi-agent models. Therefore, research on consensus control is of great significance.

[0003] In practical applications, the state of agents is often constrained, affecting their normal operation. For example, due to physical limitations, agents can only maintain consistency within a specific range, and the topology of the communication network between agents can dynamically change due to various factors. Two scenarios may occur: first, the number of agents in a multi-agent model remains constant, but the system's communication topology may change; second, both the number of agents and the communication topology in the multi-agent model change. Therefore, without implementing appropriate control strategies, controlling consensus is a significant challenge in communication topology changes caused by variations in the number of agents. Summary of the Invention

[0004] To address existing problems, this invention proposes an event-triggered fault-tolerant control method for state-constrained multi-agent models. First, an integrated design of an event-triggered disturbance observer and an event-triggered fault-tolerant controller is proposed to solve the coupling problem between external disturbances and actuator failures in multi-agent models. Second, considering the variation in the number of agents, a pulse-time-dependent Lyapunov function is introduced, providing a sufficient condition to ensure the consistency of disturbance suppression and fault-tolerant constraints. Under this condition, the consistency of fault-tolerant constraints in time-varying multi-agent models under an event-triggered mechanism can be achieved. The technical solution of this 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, It is the controller input of the p-th agent. ω represents the state variable of the p-th agent. p(t) is the external perturbation of the p-th agent, u p (t) represents the controller of the p-th intelligent agent that needs to be constructed, ρ p (t) represents the partial failure coefficient of the p-th agent, ρ p and This represents a partial failure coefficient ρ p The upper and lower bounds of (t).

[0008] Step (2) Based on the state-based multi-agent mathematical model, construct the mathematical model of the state variable trigger function of the p-th agent:

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

[0011] Introducing the error function for the p-th 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, constructing the disturbance observer and fault-tolerant controller of the p-th agent, and giving its adaptive law. Construct the following adaptive law model:

[0015]

[0016] Where, S p This represents a known constant matrix for the p-th agent, O p (t) represents the auxiliary function of the interference observer of the p-th agent, N p This represents the feedback gain of the interference observer for the p-th agent. K represents the estimated partial failure coefficient of the p-th agent. n(k) u represents the controller gain when the number of agents is n(k). p (t k h) represents the p-th agent in 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. The interference ω for the p-th agent p The estimated value of (t), where Ω is the trigger function introduced for the p-th agent, and P Ω N represents the projection of the state of the p-th agent onto the trigger function Ω. p Let θ be the feedback gain of the p-th agent. d λ is a positive constant. Let be the estimated partial failure rate of the p-th agent. denoted as the difference between the observed interference value and the actual value for the p-th agent.

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

[0018] Constructing Lyapunov functions:

[0019]

[0020] Where Θ(t) represents the time-dependent impulse function, x q (t) represents the position state of the q-th agent, x p Z(t) represents the position state of the p-th agent. p Let x represent the known constant matrix of the p-th agent. n(k) This represents the position and state when the number of agents is n(k). W p The known constant matrix corresponding to the p-th agent; The derivative of the state position function of the p-th agent at time s; τ p Let be the network-induced delay corresponding to the p-th agent.

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

[0022]

[0023] Where 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 when the multi-agent model accepts new agents.

[0024] The beneficial effects of this invention are: in multi-agent models, the sufficient condition for consistency of fault-tolerant control and the construction of Lyapunov functions ensure the stability of the model, and also possess H... ∞ Performance meets the sufficient conditions for achieving consistency under fault-tolerant constraints and obtaining consistency. In general, multi-agent models can still achieve consistency under time-varying topologies with a variable number of agents, despite the presence of disturbance-resistant and fault-tolerant constraints. Attached Figure Description

[0025] Figure 1 Overall Flow of Event-Triggered Fault-Tolerant Control for State-Constrained Multi-Agent Systems

[0026] Figure 2 This represents the communication topology of the multi-agent system in the first state.

[0027] Figure 3 This represents the communication topology for multiple agents in the second state.

[0028] Figure 4 This represents the communication topology for multiple agents in the third state.

[0029] Figure 5 For the first agent actuator partial failure rate and perturbation estimation;

[0030] Figure 6 For the partial failure rate and perturbation estimation of the second agent's actuator;

[0031] Figure 7 For the partial failure rate and perturbation estimation of the third agent's actuator;

[0032] Figure 8 For the fourth agent's actuator partial failure rate and perturbation estimation;

[0033] Figure 9 For the partial failure rate and perturbation estimation of the fifth agent's actuator;

[0034] Figure 10 For the partial failure rate and perturbation estimation of the sixth agent's actuator;

[0035] Figure 11 The trigger interval for each agent's trigger;

[0036] Figure 12 This refers to the trajectory of state changes in a multi-agent model under the action of the invented controller. Detailed Implementation

[0037] The invention will be further described in detail below with reference to the examples shown in the accompanying drawings. A state-constrained multi-agent event-triggered fault-tolerant control method, such as... 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, It is the controller input of the p-th agent. ω represents the state variable of the p-th agent. p (t) is the external perturbation of the p-th agent, u p (t) represents the controller of the p-th intelligent agent that needs to be constructed, ρ p (t) represents the partial failure coefficient of the p-th agent, ρ p and This represents a partial failure coefficient ρ p The upper and lower bounds of (t).

[0041] Step (2) Construct the mathematical model of the state variable trigger function of the p-th 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] Where, κ d ∈[0,1] is a constant value defined by the trigger function, R represents any positive definite matrix, and x p (tk h) and x p (t k (h+νh) describes the previous and current sample data, respectively. k Let represent the time corresponding to any sampling point k of the p-th agent, h represent the sampling period of the p-th agent, and ν represent the velocity of the p-th agent.

[0043] To address the network latency encountered by the p-th agent during information transmission in the mathematical model of the state variable trigger function, an error function for 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) Considering that disturbances and faults are coupled, the partial failure model of the controller constructed in step (1) and the state variable triggering function in step (2) are combined. Using the relationship between the Kronecker product, the adjacency matrix and the Laplacian matrix in graph theory, the disturbance observer and fault-tolerant controller of the p-th agent are constructed, and its adaptive law is given. Construct the following model:

[0047]

[0048] Where, S p This represents a known constant matrix for the p-th agent, O p (t) represents the auxiliary function of the interference observer of the p-th agent, N p This represents the feedback gain of the interference observer for the p-th agent. K represents the estimated partial failure coefficient of the p-th agent. n(k) u represents the controller gain when the number of agents is n(k). p (t k h) represents the p-th agent in 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. The interference ω for the p-th agent p The estimated value of (t), where Ω is the trigger function introduced for the p-th agent, and P Ω N represents the projection of the state of the p-th agent onto the trigger function Ω. p Let θ be the feedback gain of the p-th agent. dλ is a positive constant. Let be the estimated partial failure rate of the p-th agent. denoted as the difference between the observed interference value and the actual value for the p-th agent.

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

[0050]

[0051] Where Θ(t) represents the time-dependent impulse function, x q (t) represents the position state of the q-th agent, x p Z(t) represents the position state of the p-th agent. p Let x represent the known constant matrix of the p-th agent. n(k) This represents the position and state when the number of agents is n(k). W p The known constant matrix corresponding to the p-th agent; The derivative of the state position function of the p-th agent at time s; τ p Let be the network-induced delay corresponding to the p-th agent.

[0052] To eliminate the impact of topological changes and variations in the number of agents on constraint consistency, a piecewise linear function and a novel performance index for LMI that satisfies performance requirements are introduced into the Lyapunov function. By taking its derivative, D can be obtained. + When V(t) < 0, the multi-agent model is stable, and a sufficient condition for consistency of fault-tolerant control is obtained:

[0053]

[0054] Where λ, μ>1, α1, and 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 when the multi-agent model accepts new agents.

[0055] The effectiveness of the proposed control algorithm will be verified through simulation examples below:

[0056] In a multi-agent model, the number of agents can 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 consisting of the same number of nodes.

[0057] The communication topology diagrams for states 1, 2, and 3, corresponding to the Laplace matrices L1 and L2, are described below:

[0058]

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

[0060] In the simulation, some faults are selected as follows: ρ 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 represents the fault range.

[0065] Additionally, select the external perturbation constant matrix parameter S for agents 1 to 6. i For i = 1, 2, ..., 6, the following choices are made:

[0066]

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

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

[0069]

[0070] exist Figure 2 In this communication topology, there are 4 nodes, and the edge weight between the nodes is 1. Nodes 1, 2, 3, and 4 form a ring structure, which realizes the information transmission between the nodes. Figure 3 In this example, the communication topology is expanded to 5 nodes, with each edge having a weight of 1. The new node 5 is connected to nodes 1 and 4, representing the impact of the addition of the new agent on the original system's topology. Figure 4In this communication topology, there are still 5 nodes, and the edge weights are all 1. When the new node 6 is added, node 3 leaves, reflecting the dynamic changes in the system's communication structure caused by the addition or removal of agents.

[0071] Figures 5-10 The curves represent the perturbation estimates and partial failure rate estimates for different agents under two different actual perturbations and actual partial failure rates, respectively.

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

[0073] Figure 6 : 0-1.7 seconds, according to Figure 1 In the communication topology, agent 2 joins the model and participates in completing the work. At 0.6 seconds, agent 2 fails; at 0.1 seconds, agent 2 experiences a disturbance; 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 disturbance estimate 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 In the communication topology, agent 3 joins the model and participates in completing the work. From 4.1 to 12 seconds, agent 3 leaves the model. At 0.6 seconds, agent 3 experiences a failure. At 0.1 seconds, agent 3 experiences a disturbance. In the first case, the estimated partial failure rate coincides with the actual partial failure rate at about 1.6 seconds, and the estimated disturbance coincides with the actual estimate at about 0.5 seconds. In the second case, the estimated partial failure rate coincides with the actual failure rate at about 2.1 seconds, and the estimated disturbance coincides with the actual disturbance at about 2.5 seconds.

[0075] Figure 8 : 0-1.7 seconds, according to Figure 1In the communication topology, agent 4 joins the model and participates in completing the work. At 1 second, agent 4 fails; at 0.3 seconds, agent 4 experiences a disturbance; 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 disturbance estimate 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] Figure 9 At 1.8-4 seconds, according to Figure 2 In the communication topology, agent 5 joins the model and participates in completing the work. At 1.9 seconds, agent 5 fails; at 0.1 seconds, agent 5 experiences a disturbance; and at 12 seconds, agent 5 begins to leave the model. In the first case, around 4.2 seconds, the estimated partial failure rate coincides with the actual partial failure rate, and around 4.4 seconds, the estimated disturbance coincides with the actual disturbance estimate. In the second case, around 6 seconds, the estimated partial failure rate coincides with the actual partial failure rate, and the estimated disturbance coincides with the actual disturbance.

[0077] Figure 10 : 4.1-12 seconds, according to Figure 3 In the communication topology, agent 6 joins the model and participates in completing the work. At 4.3 seconds, agent 6 fails. At 4 seconds, agent 6 experiences a disturbance. 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 about 9 seconds, and the disturbance estimate coincides with the actual disturbance estimate at about 5 seconds. In the second case, the estimated partial failure rate coincides with the actual partial failure rate at about 10 seconds, and the disturbance estimate coincides with the actual disturbance at about 5 seconds.

[0078] Figure 11 This represents the trigger interval of the event triggers for each agent. During the three consensus events, the trigger intervals of each agent in each stage significantly changed from dense to sparse, indicating that the event triggers effectively reduced the communication frequency of the agents.

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

[0080] This invention studies a design method for event-triggered fault-tolerant control technology in state-constrained multi-agent systems. Utilizing an event-triggered mechanism, an improved method for achieving interference-resistant, fault-tolerant constraint consistency in multi-agent models with a variable number of agents is proposed. First, an integrated event-triggered perturbation observer and fault-tolerant controller for each agent is designed to reduce network congestion and estimate perturbations and actuator partial failures. Second, a time-varying impulse Lyapunov function dependent on the number of agents is proposed to overcome the topology switching problem caused by changes in the number of agents, and sufficient conditions for achieving event-triggered perturbation and suppressing fault-tolerant constraint consistency are given. Under these conditions, the multi-agent model can achieve fault-tolerant constraint consistency even when the number of nodes in the model changes continuously. Finally, the effectiveness of the proposed method is verified through specific case simulations.

Claims

1. A state-constrained multi-agent event-triggered fault-tolerant control method, characterized in that, Includes the following steps: Step 1: Construct a state-based multi-agent mathematical model and a partial failure model of the controller, as follows: in, It is the controller input of the p-th agent. ω represents the state variable of the p-th agent. p (t) is the external perturbation of the p-th agent, u p (t) is the controller of the p-th intelligent agent constructed, ρ p (t) represents the partial failure coefficient of the p-th agent. ρ p and This represents a partial failure coefficient ρ p The upper and lower bounds of (t); Step 2: Based on the state-based multi-agent mathematical model, construct the mathematical model of the state variable trigger function of the p-th agent; Step 3: Combining the partial failure model of the controller and the mathematical model of the state variable trigger function, and utilizing the relationship between the adjacency matrix and the Laplacian matrix in graph theory, the controller for the p-th agent is improved, and its adaptive law is given. Construct an adaptive law model; Step 4: Combining the trigger function and the adaptive law model, construct the Lyapunov function to obtain sufficient conditions for the consistency of fault-tolerant control, and complete the fault-tolerant control.

2. The event-triggered fault-tolerant control method for state-constrained multi-agent systems according to claim 1, characterized in that, The mathematical model for constructing the state variable triggering function of the p-th 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 Where, κ d ∈[0,1] is a constant value defined by the trigger function, R represents any positive definite matrix, and x p (t k h) and x p (t k h+νh) describes the previous and current sample data respectively; t k Let represent the time corresponding to any sampling point k of the p-th agent, h represent the sampling period of the p-th agent, and ν represent the velocity of the p-th agent; Introducing the error function for the p-th 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.

3. The event-triggered fault-tolerant control method for state-constrained multi-agent systems according to claim 2, characterized in that, The specific process of constructing the adaptive law model is as follows: By combining the partial failure model of the controller and the state variable triggering function, and utilizing the relationship between the adjacency matrix and the Laplacian matrix in graph theory, the controller of the p-th agent is improved. A disturbance observer and fault-tolerant controller for the p-th agent are constructed, and their adaptive law is given. Constructing an adaptive law model: Where, S p This represents a known constant matrix for the p-th agent, O p (t) represents the auxiliary function of the interference observer of the p-th agent, N p This represents the feedback gain of the interference observer for the p-th agent. K represents the estimated partial failure coefficient of the p-th agent. n(k) u represents the controller gain when the number of agents is n(k). p (t k h) represents the p-th agent in 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. The interference ω for the p-th agent p The estimated value of (t), where Ω is the trigger function introduced for the p-th agent, and P Ω N represents the projection of the state of the p-th agent onto the trigger function Ω. p Let θ be the feedback gain of the p-th agent. d λ is a positive constant. Let be the estimated partial failure rate of the p-th agent. denoted as the difference between the observed interference value and the actual value for the p-th agent.

4. The event-triggered fault-tolerant control method for state-constrained multi-agent systems according to claim 3, characterized in that, The specific implementation process of step 4 is as follows: By combining the trigger function and the adaptive law model, a Lyapunov function V(t) is constructed, and sufficient conditions for the consistency and stability of the fault-tolerant control of the multi-agent model are obtained: Where Θ(t) represents the time-dependent impulse function, x q (t) represents the position state of the q-th agent, x p Z(t) represents the position state of the p-th agent. p Let x represent the known constant matrix of the p-th agent. n(k) W represents the position state when the number of agents is n(k); p The known constant matrix corresponding to the p-th agent; The derivative of the state position function of the p-th agent at time s; τ p The network-induced delay is the network-induced delay for the p-th agent. By introducing a piecewise linear function and a novel performance index, LMI, that satisfies system performance into the Lyapunov function, and by taking its derivative, we obtain D. + When V(t) < 0, the multi-agent model is stable, and a sufficient condition for consistency of fault-tolerant control is obtained: Where 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 when the multi-agent model accepts new agents.

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