A fault detection method and system for a nonlinear multi-agent system

Abstract

The application relates to a fault detection method and system of a nonlinear multi-agent system, and relates to the technical field of multi-agent fault detection.The method comprises the following steps: constructing a Lipshitz nonlinear system model according to each agent; determining a state observer according to a system state model and a system output model; determining a controller according to the state of the state observer and combined measurement variables; solving a linear matrix inequality by using a robust control theory according to the state observer and the controller to obtain a controller gain matrix and an observer gain matrix; determining an output vector according to the controller gain matrix, the controller and the system state model; determining an output vector estimated value according to the observer gain matrix and the state observer; determining a residual evaluation function according to the output vector estimated value and the output vector; and the residual evaluation function is used for detecting system faults.The application can realize the sensitivity of a residual signal to faults and the robustness of control output to faults.

Description

Technical Field

[0001] This invention relates to the field of multi-agent fault detection technology, and in particular to a fault detection method and system for nonlinear multi-agent systems. Background Technology

[0002] In the field of control, intelligent agents generally refer to entities with certain dynamics that can exchange information with other individuals in their vicinity. Multi-agent systems exist in numerous fields, such as distributed optimization, wireless sensor networks, mobile robot collaboration, drone / satellite swarm flight, and intelligent transportation systems.

[0003] With the increasing application of multi-agent systems, these systems are often affected by parameter uncertainties, communication noise, and unknown nonlinear dynamics. These problems can lead to communication delays or channel congestion, thus reducing communication quality. In recent years, distributed coordinated control of multi-agent systems has demonstrated increasingly important value and has begun to be widely accepted and applied. Unlike centralized control methods, the design of individual agents in distributed control is simple, and the failure of a single agent will not affect the overall function. These characteristics significantly reduce the design difficulty of individual agents and increase the overall system's anti-interference capability. On the other hand, with the rapid increase in the scale and complexity of control systems, failures are more likely to occur in real-world systems, potentially affecting system performance and even causing serious consequences. Especially for multi-agent systems, if one agent fails, the fault information will be transmitted to other agents through the communication topology, affecting the entire system. Therefore, fault detection in multi-agent systems is a significant problem.

[0004] Compared to linear systems, nonlinear systems are widely present in practical problems, such as robot or aircraft control systems containing trigonometric nonlinear terms. The study of nonlinear systems satisfying the Lipschitz condition has become a hot topic in the field of control. Summary of the Invention

[0005] The purpose of this invention is to provide a fault detection method and system for nonlinear multi-agent systems, so as to achieve the sensitivity of residual signals to faults and the robustness of control outputs to faults.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A fault detection method for a nonlinear multi-agent system includes:

[0008] A Lipschitz nonlinear system model is constructed for each agent; the Lipschitz nonlinear system model includes a system state model and a system output model.

[0009] The state observer is determined based on the system state model and the system output model;

[0010] The controller is determined based on the state of the state observer and the combined measured variables;

[0011] Based on the state observer and the controller, the linear matrix inequality is solved using robust control theory to obtain the controller gain matrix and the observer gain matrix.

[0012] The output vector is determined based on the controller gain matrix, the controller, and the system state model.

[0013] The output vector estimate is determined based on the observer gain matrix and the state observer.

[0014] The residual evaluation function is determined based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

[0015] The present invention also provides a fault detection system for a nonlinear multi-agent system, comprising:

[0016] The building module is used to construct a Lipschitz nonlinear system model for each agent; the Lipschitz nonlinear system model includes a system state model and a system output model;

[0017] A state observer determination module is used to determine a state observer based on the system state model and the system output model;

[0018] A controller determination module is used to determine the controller based on the state of the state observer and the combined measurement variables;

[0019] The solution module is used to solve linear matrix inequalities based on the state observer and the controller using robust control theory to obtain the controller gain matrix and the observer gain matrix.

[0020] An output vector determination module is used to determine the output vector based on the controller gain matrix, the controller, and the system state model.

[0021] An output vector estimate determination module is used to determine the output vector estimate based on the observer gain matrix and the state observer;

[0022] The residual evaluation function determination module is used to determine the residual evaluation function based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

[0023] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0024] This invention constructs a Lipschitz nonlinear system model for each agent; the Lipschitz nonlinear system model includes a system state model and a system output model; a state observer is determined based on the system state model and the system output model; a controller is determined based on the state of the state observer and combined measurement variables; linear matrix inequalities are solved using robust control theory based on the state observer and the controller to obtain the controller gain matrix and the observer gain matrix; an output vector is determined based on the controller gain matrix, the controller, and the system state model; an estimated value of the output vector is determined based on the observer gain matrix and the state observer; a residual evaluation function is determined based on the estimated value of the output vector and the output vector; the residual evaluation function is used to detect system faults, thereby achieving sensitivity of the residual signal to faults and robustness of the control output to faults. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a block diagram illustrating fault detection and consensus control via an event-triggered mechanism, as provided by the present invention.

[0027] Figure 2 A topology diagram of a multi-agent system provided by the present invention;

[0028] Figure 3 This is the first state of the controlled output when there is no fault, as provided by the present invention;

[0029] Figure 4 This is the second state of the controlled output provided by the present invention when there is no fault;

[0030] Figure 5 This is the first state of the fault-free state observer provided by the present invention;

[0031] Figure 6 This is the second state of the state observer provided by the present invention when there is no fault;

[0032] Figure 7 The triggering times of the four intelligent agents when there are no faults provided by this invention;

[0033] Figure 8 The residual signals of the four intelligent agents and their upper and lower bounds when there are no faults are provided by the present invention.

[0034] Figure 9This is the first state of the controlled output when nodes 1 and 2 of the present invention are faulty;

[0035] Figure 10 This is the second state of the controlled output provided by the present invention when nodes 1 and 2 are faulty;

[0036] Figure 11 This is the first state of the state observer provided by the present invention when nodes 1 and 2 are faulty.

[0037] Figure 12 This is the second state of the state observer provided by the present invention when nodes 1 and 2 are faulty;

[0038] Figure 13 The triggering times of the four agents when nodes 1 and 2 are faulty, as provided in this invention;

[0039] Figure 14 The residual signals and their upper and lower bounds of the four agents when nodes 1 and 2 are faulty, as provided in this invention;

[0040] Figure 15 The flowchart of the fault detection method for nonlinear multi-agent systems provided by the present invention is shown. Detailed Implementation

[0041] 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.

[0042] The purpose of this invention is to provide a fault detection method and system for nonlinear multi-agent systems, so as to achieve the sensitivity of residual signals to faults and the robustness of control outputs to faults.

[0043] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] like Figure 15 As shown, the present invention provides a fault detection method for a nonlinear multi-agent system, comprising:

[0045] Step 101: Construct a Lipschitz nonlinear system model for each agent; the Lipschitz nonlinear system model includes a system state model and a system output model.

[0046] Step 102: Determine the state observer based on the system state model and the system output model.

[0047] Step 103: Determine the controller based on the state of the state observer and the combined measurement variables.

[0048] Step 104: Solve the linear matrix inequality using robust control theory based on the state observer and the controller to obtain the controller gain matrix and the observer gain matrix.

[0049] Step 104 specifically includes:

[0050] Obtain the closed-loop system of multiple agents; reduce the order of the closed-loop system based on the Laplace matrix and the closed-loop system of multiple agents to obtain the reduced-order closed-loop system; transform the objective problem of the reduced-order closed-loop system to obtain the optimization problem; determine the linear matrix inequality based on the optimization problem using the Lyapunov function; determine the controller gain matrix and the observer gain matrix based on the linear matrix inequality, the state observer, and the controller.

[0051] Step 105: Determine the output vector based on the controller gain matrix, the controller, and the system state model.

[0052] Step 106: Determine the output vector estimate based on the observer gain matrix and the state observer.

[0053] Step 107: Determine the residual evaluation function based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

[0054] The expression for the controller is:

[0055]

[0056] Among them, u i (t) represents the controller, and K is the controller gain matrix. For combined measurement variables, t is the time of the continuous system. Let k be the trigger time of agent i. Let k be the (k+1)th trigger time of agent i, where k is the number of times agent i is triggered, and i is the i-th agent.

[0057] The expression for the combined measurement variables is:

[0058]

[0059] Where, q i (t) represents the combined measurement variable, N is the number of agents, j is the neighboring agent of agent i, and a ij This represents the connection weight between agent i and agent j. For agent i, the observer state, Let be the observer state of the neighboring intelligent agents of agent i.

[0060] like Figure 1 As shown, this invention proposes a fault detection method for nonlinear multi-agent systems with uncertainty based on event triggering. This method involves designing suitable controllers, state observers, and event triggering conditions, and employing a hybrid H- / H- architecture. ∞ The method makes the relevant residual signals sensitive to faults and the control output robust to faults, thus obtaining a linear matrix inequality that satisfies the optimization performance constraints. By solving the linear matrix inequality, the unknown controller gain matrix and observer gain matrix are obtained, enabling the system state to reach consistency, and the residual signals can detect faults. A distributed fault detection model for Lipschitz nonlinear systems is constructed, performing independent fault detection and isolation for each agent, improving the system's security, and thus solving the fault detection problem of nonlinear multi-agent systems with uncertain terms under event-triggered conditions. The specific steps are as follows:

[0061] Step 1: First, establish a Lipschitz nonlinear system model, including fault signals. Establish a state model and system output model for the Lipschitz nonlinear system containing uncertain variables and faults. Describe the information communication model between nodes using an undirected graph. Give the conditions satisfied by the Lipschitz nonlinear system and the conditions satisfied by the uncertain terms.

[0062] Consider a Lipschitz nonlinear system with N agents and nonlinear terms. The dynamics of each agent are expressed as follows:

[0063]

[0064] The dynamics of each agent are represented by the system state model and the system output model.

[0065] x i (t)∈R n ,y i (t)∈R m and u i (t)∈R l These represent the state vector, output vector, and control input, respectively. f is the derivative of agent i in state i, where i is agent i, n is the dimension of agent state, m is the dimension of agent output, l is the dimension of agent input, and t is agent system time; i (t)∈R p ΔA represents the fault signal of agent i, where p is the dimension of the fault signal of agent i; i (t) and ΔB i (t) represents the uncertainty of the system matrix and control matrix of the intelligent agent, which are difficult to obtain accurately, and respectively satisfy the following conditions: and δ is a positive scalar, I is the identity matrix, T denotes transpose, and φ(x) i (t) represents the nonlinear dynamics of agent i, where φ(·) is an unknown nonlinear Lipschitz function that satisfies (α is a positive scalar, R) n Let A represent an n-dimensional column vector, where a is a scalar, b is a scalar, A is the system matrix, B is the control matrix, C is the output matrix, and D is the output matrix. f Let B be the matrix representing the impact of the fault on the output. f Let A, B, C, B be the matrix representing the impact of the fault on the system state, and E be the nonlinear system matrix. Here, N represents the number of agents. Matrices A, B, C, B f D f E can be obtained accurately.

[0066] To describe the impact of faults on consistency performance, a common rule is used to define the controlled output function of agent i.

[0067]

[0068] This is the system output model. Note that this is in the event of a fault. So This is satisfied, meaning that the states of agents tend to be consistent when a fault exists. Here, j represents the neighboring agents of agent i, and x... j (t) represents the state of agent j.

[0069] Step 2: Design a state observer to observe the system state and residual signal. In practice, the system state may be difficult to measure; therefore, the relative output information of the system is used to design the state observer and residual signal. Based on the aforementioned nonlinear system model, the state observer and residual signal are designed according to the relative output information of the system and the observer. The state observer is used to observe the system state, i.e., x in equation (1) above. i (t) is used for observation, and its observer and residual signal are designed as follows:

[0070]

[0071] in, For the state of the observer of agent i, Let be the derivative of the observer state of agent i. For the output of the observer of agent i, y j (t) represents the output of the neighboring agents of agent i. N is the output of the observers of the neighboring agents of agent i. iLet r be the set of neighboring agents of agent i. i (t)∈R m Let H ∈ R represent the residual signal of agent i. n×m The observer gain matrix is ​​unknown. Let V represent the most recent trigger time of agent i. In a multi-agent system, each agent can be considered as a node, and the information transmission relationship between agents can be considered as an edge. G = (V, ε) represents a weighted graph with N nodes, where V = {v1, v2, ..., v...} N} represents the set of nodes in graph G, v N Let N be the node in graph G. Let N be the edge set of graph G, and let N be the neighborhood of node i. i ={v j ∈V|(v j ,v i )∈ε},v j For the j-th node, v i For the i-th node, S = [a ij ] is the adjacency matrix of graph G, where a ij >0 indicates node v i With v j The connection weights between them. ξ i (t) represents the system's relative output; This is the relative output of the observer.

[0072] Step 3: Design an event-triggered state feedback consistency controller that combines the measured variables and the nonlinear system.

[0073] Based on the state of the aforementioned observer, an event-triggered state feedback consistency controller for the combined measurement variables and the nonlinear system is designed. The combined measurement variables are designed as follows: Among them, a ij This represents the connection weights between agent i and agent j. The controller is designed as follows:

[0074]

[0075] Where K∈R l×n The controller gain matrix is ​​unknown. Let be the state of agent i at the most recent trigger moment of its observer. Let be the state of the observer of the neighboring intelligent agent i at the most recent trigger time.

[0076] Step 4: Define the event triggering conditions of the system and construct an event triggering mechanism to enable intermittent communication between each agent and its neighboring agents.

[0077] Based on the state observer, the event triggering conditions of the system are given, enabling each agent to communicate intermittently with its neighboring agents, specifically including:

[0078] 1. Define the state estimation error of agent i.

[0079] 2. Based on the state estimation error and combined measurement variables, design event triggering conditions.

[0080]

[0081] in, z i (t) is the relative trigger measurement variable, and σ is a known positive scalar.

[0082] 3. In order to calculate the time of the next trigger moment, an event triggering mechanism is constructed based on the designed event triggering condition formula (6) and the previous trigger moment of agent i:

[0083]

[0084] in, Let i be the time of the (k+1)th trigger. This represents the time of the k-th trigger of agent i (also the most recent trigger time). At time , the event triggering condition formula (6) is satisfied. At this time, agent i sends its information to neighboring agents and solves the linear matrix inequality to obtain the controller gain matrix and the observer gain matrix.

[0085] Step 5: Solve the linear matrix inequalities to obtain the controller gain matrix and the observer gain matrix.

[0086] Based on the state observer and the controller, solving the linear matrix inequalities yields the controller gain matrix K and the observer gain matrix H, specifically including:

[0087] 1. Describe a closed-loop system with multiple agents, with the following specific expression:

[0088]

[0089] in, For the Kronecker product, I N Represents the N-dimensional identity matrix. n Let n be the identity matrix, and define... For the state measurement error of a single system, The state measurement error of the closed-loop system, i.e. A column stack vector from i=1 to N; This is the derivative of the state measurement error of the closed-loop system. r is the residual function of agent i i (t) The column stack vector from i=1 to N; z sc z(t) is the controlled output function of agent i. sci (t) The column stack vector from i=1 to N; For agent i, the observer state A column stack vector from i=1 to i=N; The state estimation error of agent i is e i (t) The column stack vector from i=1 to i=N; For agent i, fault signal f i (t) is the column stack vector from i=1 to i=N; φ(x) = [φ T (x1),...,φ T (x N )] T For agent i, the nonlinear dynamic φ(x) i (t) is the column stack vector from i=1 to i=N; ΔA(t) = diag(ΔA1(t),...,ΔA N (t)), ΔB(t)=diag(ΔB1(t),...,ΔB N (t)), where diag(·) denotes a block diagonal matrix. L is the Laplace matrix of the undirected topological graph. c ∈R N×N It is a positive definite matrix with the following elements on the main diagonal: The remaining elements are For matrix L c For L, there exists an orthogonal matrix U = [U1 U2] ∈ R. N×N ,in make U T L c U = diag(I) N-1 ,0),U T LU = diag(L1, 0), where L1 is a positive definite matrix, 1 N ∈R N ΔA(t) represents a vector whose components are all 1. ΔA(t) is the uncertainty of the system matrix of the closed-loop system (7), and ΔB(t) is the uncertainty of the control matrix of the closed-loop system (7).

[0090] 2. Since 0 is a single eigenvalue of the Laplacian matrix L of the undirected topological graph, and the corresponding eigenvector is 1. N Based on the closed-loop system of the multiple intelligent agents, a reduced-order closed-loop system is obtained, as follows:

[0091]

[0092] in, After the order is reduced and The derivative of the combined quantities, After the order is reduced and The combination quantity, i.e. for A column stack vector from i=1 to i=N-1; for A column stack vector from i=1 to i=N-1; for A column stack vector from i=1 to i=N-1;

[0093] for A column stack vector from i=1 to i=N-1;

[0094] for A column stack vector from i=1 to i=N-1; for A column stack vector from i=1 to i=N-1. For L c With the n×n dimensional identity matrix I n The Kronecker product and e sc The product of (t), i.e. For L c With the n×n dimensional identity matrix I n Kronecker product and The product of, i.e. For U T With the n×n dimensional identity matrix I n Kronecker product and The product of, i.e. For U T With the n×n dimensional identity matrix I n Kronecker product and The product of, i.e. For U T With the n×n dimensional identity matrix I n The product of the Kronecker product and e(t), i.e. For U T With the p×p dimensional identity matrix I n The product of the Kronecker product and f(t), i.e. For UT With the m×m dimensional identity matrix I m The product of the Kronecker product and r(t), i.e. For U T With the n×n dimensional identity matrix I n The Kronecker product and z sc The product of (t), i.e.

[0095] For U T The i-th row and the n×n dimensional identity matrix I n Kronecker product and The product; For U T The i-th row and the n×n dimensional identity matrix I n Kronecker product and The product; For matrix L c The i-th row and the n×n dimensional identity matrix I n The Kronecker product and e sc The product of (t); For L c The i-th row and the n×n dimensional identity matrix I n Kronecker product and The product; For U T The i-th row and the n×n dimensional identity matrix I n The product of the Kronecker product and e(t); For U T The i-th row and the n×n dimensional identity matrix I n The product of the Kronecker product and f(t); For U T The i-th row and the m×m dimensional identity matrix I m The product of the Kronecker product and r(t); For U T With the n×n dimensional identity matrix I n The Kronecker product and z sc The product of (t).

[0096] make for The column stack vector from i=1 to i=N; I n It is an n×n identity matrix. for A column stack vector from i=1 to i=N; for A column stack vector from i=1 to i=N; for The column stack vector from i=1 to i=N; I p It is a p×p identity matrix; for The column stack vector from i=1 to i=N; I m It is an m×m identity matrix; for A column stack vector from i=1 to i=N.

[0097] The system matrix A of the reduced-order closed-loop system (8) cl for

[0098]

[0099] This is the estimation error matrix of the closed-loop system after order reduction.

[0100] This is the matrix showing the impact of the fault on the reduced-order system state. This is the residual output matrix after order reduction. This is represented as the reduced-order estimation error output matrix. This is the effect matrix of faults on residuals after order reduction. This is the reduced-order controlled output matrix.

[0101] Based on robust control theory and the small gain theorem, ΔA with the largest Euclidean norm is selected. i (t) and ΔB i The upper bounds of (t) are taken as ΔA′ and ΔB′ respectively, and the controller can also stabilize the system well.

[0102] 3. Based on robust control theory and the reduced-order closed-loop system (8), in order to reduce the impact of faults on the controlled output function and ensure the sensitivity of the residual signal to faults, these two multi-objective problems are transformed into H ∞ / H - The optimization problem, in which H is used ∞ The norm indicates the robustness of the control output to faults (robustness means that the system can maintain consistency under disturbances), and the H-exponent represents the sensitivity of the residual signal to faults. The specific equation is:

[0103] minmizeδ1γ-δ2β

[0104]

[0105] Where δ1 and δ2 represent the importance of targets (i) and (ii) respectively (δ1 > 0, δ2 > 0), and γ > 0 and β > 0 represent H respectively. ∞ And the H-index. This indicates the fault after order reduction in the closed-loop system (8). Residual after order reduction The closed-loop transfer function; This indicates the fault after order reduction in the closed-loop system (8). Controlled output after de-ranking The closed-loop transfer function.

[0106] 4. Based on the transformed H ∞ From the H-optimization problem (9) and the properties of the Lyapunov function, we can obtain the following linear matrix inequality (also known as LMI) (10). For the nonlinear system (1), given parameters α, σ, δ1 and δ2, if there exist positive scalars γ and β, the positive definite matrix... and Matrix X1, If F1, F2, and F3 satisfy the conditions in equation (10), then system (1) is stable. Therefore, the controller gain matrix K and the observer gain matrix H are obtained from equation (11), and the LMI is specifically:

[0107]

[0108] Where * denotes a symmetric element in the matrix; X is a block diagonal matrix composed of matrices X1, denoted as... Z i Composed of an n×n dimensional zero matrix and an n×n dimensional identity matrix, it is represented as λ i Let L be the non-zero eigenvalues ​​of the undirected graph Laplacian matrix L. For a matrix consisting of 0 and λ i An augmented matrix composed of the identity matrix; ΔA′ and ΔB′ are related to ΔA i The norm of (t) and ΔB i A matrix with the same upper bound on the norm of (t); B T ΔB is the transpose of matrix B; ′T Represented as the transpose of ΔB′

[0109] C rcli =[λ i C 0 m×n ], C ecli =-λ i C, C fcl =λ i D f C zcli =[I n I n ].

[0110] For the LMI mentioned above, to simplify, we only need to substitute the smallest non-zero eigenvalue of the undirected graph Laplacian matrix L. Furthermore, if the above inequality (10) is feasible, the controller gain matrix K and the observer gain matrix H can be obtained from the following equation:

[0111]

[0112] Specifically, please refer to the example: Consider Figure 2 The adjacency matrix S and Laplace matrix L of the described four-agent multi-agent system can be written as:

[0113]

[0114] The dynamic equations for each agent are as shown in equation (1), where,

[0115] C = [1 0], D f =5,

[0116]

[0117] The Lipschitz nonlinear function is φ(x) i )=-0.1sin(x i1 The initial state of the four agents is x1(0) = [-5 -1]. T x2(0) = [-7 -1] T x3(0) = [-1 -3] T x4(0) = [3 4] T Faults exist in both agent 1 and agent 2, and these faults are represented as follows:

[0118]

[0119] ΔA i The norm of (t) and ΔB i The upper bounds of (t) are taken as ΔA′ and ΔB′ respectively, and the controller can also stabilize the system well.

[0120] Choose appropriate ΔA′ and ΔB′. ||ΔA i (t)|| max =0.3,||ΔB i (t)|| max =0.6. Choose two constant matrices ΔA′ and ΔB′ such that their dimensions are equal to those of ΔA′ and ΔB′ respectively. i (t) and ΔB i (t) have the same dimension and satisfy ||ΔA′||=||ΔAi (t)|| max And ||ΔB′||=||ΔB i (t)|| max .

[0121] Therefore, choose

[0122] Choosing α = 11, δ = 1, σ = 0.03, δ1 = δ2 = 1, the eigenvalues ​​of the Laplace matrix L are calculated to be 0, 1, 1, and 4, with the smallest eigenvalue other than 0 being 1.

[0123] Calculate matrix X1 according to equation (10). F1, F2 and F3.

[0124] Let matrices A, B, B f E,C,D f and λ i Substituting 1 into equation (10), and using the MATLAB toolkit YALMIP, three solvers—fmincon, MOSEK, and CPLEX—to solve the problem, the result is as follows:

[0125] γ = 0.0352, β = 2.6780

[0126] F2=[-0.3985 0.0509], F3=[-0.9050 -0.4535],

[0127]

[0128]

[0129] The controller gain matrix K and the observer gain matrix H are calculated according to equation (11).

[0130] K = [-0.0712 0.0091],

[0131]

[0132] Step Six: Obtain residual evaluation results using the residual evaluation mechanism, thus obtaining an evaluation of the fault signal and the results of fault detection.

[0133] Substituting the controller gain matrix K into (4) yields the controller equation u. i (t), the controller equation u i Substituting (t) into (1) yields y i (t); the observer gain matrix H and the controller equation u i Substituting (t) into (3) yields Based on the definition of the residual function in equation (3) By ξ i (t) and Obtain the residual evaluation function The residual evaluation function is used to detect faults, specifically:

[0134] The residual evaluation function is J ri =r i (t). The upper and lower thresholds of the residual evaluation function are used under healthy system conditions, i.e., the fault signal f. i (t)=0 residual signal r i The upper and lower thresholds of (t) are used to represent this, and the upper and lower thresholds are respectively:

[0135]

[0136] Whether the system has malfunctioned is determined by the following mechanism:

[0137] or or f j (t)≠0,j∈N i

[0138] Otherwise, the system has not malfunctioned.

[0139] If the residual signal r of agent i i (t) and its neighboring intelligent agents j (j∈N) i The residual signal r j (t) satisfies the following conditions within the same time period. or and or Then it can be determined that agent i malfunctioned during this period.

[0140] The observer designed according to equation (3) is initialized to 0. The two states of the controlled output of the agent under fault-free conditions are obtained as follows: Figure 3 and Figure 4 As shown, it can be seen that the two states of the four agents have reached consistency; Figure 5 and Figure 6 It can be seen that the observer also achieved consistency when there was no fault.

[0141] The event triggering times of the 4 agents are as follows: Figure 7 As shown, each agent communicates intermittently, which greatly saves communication resources.

[0142] When there is no fault, the residual signals of the four agents and their upper and lower bounds are as follows: Figure 8As shown, this indicates that all four residual signals are within the range of the upper and lower thresholds. Figure 8 (a) in the diagram shows the residual signal of node 1 and its upper and lower bounds when there is no fault. Figure 8 (b) in the diagram shows the residual signal of node 2 and its upper and lower bounds when there is no fault. Figure 8 (c) in the diagram shows the residual signal of node 3 and its upper and lower bounds when there is no fault. Figure 8 (d) in the diagram represents the residual signal of node 4 without faults and its upper and lower bounds. The upper and lower bounds of the residual function threshold are respectively...

[0143]

[0144]

[0145] In the event of a fault, the two states of the controlled output of the agent are as follows: Figure 9 and Figure 10 As shown, it can be seen that the four agents still achieved consistency even when there was a fault. Figure 11 and Figure 12 This indicates that the designed state observer detected the occurrence of the fault; the event trigger times of the four agents are as follows: Figure 13 As shown, this indicates that the four agents still communicate intermittently. The residual signals of the four agents when a fault exists, and their upper and lower thresholds when there is no fault, are shown below. Figure 14 As shown. Figure 14 (a) in the diagram shows the residual signal of node 1 and its upper and lower bounds when a fault exists. Figure 14 (b) in the diagram shows the residual signal of node 2 and its upper and lower bounds when a fault exists. Figure 14 (c) in the diagram shows the residual signal of node 3 and its upper and lower bounds when a fault exists. Figure 14 (d) in the diagram represents the residual signal of node 4 and its upper and lower bounds when a fault exists.

[0146] Depend on Figure 14 It can be seen that during the period of 30s-40s, r1(t), r3(t), and r4(t) all exceed their respective lower bounds when there is no fault. and Since nodes 1, 3, and 4 are neighbors of node 2, it can be determined that node 2 failed between 30 and 40 seconds. Observing r1(t) and r2(t), it can be found that r1(t) exceeds its upper bound when there is no failure between 15 and 20 seconds. r2(t) exceeds its lower bound when there is no fault. Since node 2 is a neighbor of node 1, and the residual signals r3(t) and r4(t) of nodes 3 and 4, which are adjacent to node 2, did not exceed their respective threshold ranges during 15-20s, it can be determined that node 1 has a fault during 15-20s. Therefore, node 1 has a fault during 15-20s, and node 2 has a fault during 30-40s.

[0147] This invention proposes an event-triggered fault detection method for nonlinear multi-agent systems with faults and uncertainties. First, a state model and output model of the system are established, and a state observer's state model and output model are designed. Fault detection is performed by constructing residual signals using the relative outputs of the state observer, and event triggering conditions are given. By reducing the order of the closed-loop system, a linear matrix inequality that stabilizes the system is obtained. Then, this linear matrix inequality is solved to obtain the controller gain matrix and observer gain matrix. Finally, a residual evaluation mechanism is used to detect faults. This invention not only reduces the frequency of information exchange between agents and saves communication bandwidth, but also considers the uncertainties and nonlinearity of the system, making it practically significant.

[0148] The present invention also provides a fault detection system for a nonlinear multi-agent system, comprising:

[0149] A construction module is used to construct a Lipschitz nonlinear system model for each agent; the Lipschitz nonlinear system model includes a system state model and a system output model.

[0150] A state observer determination module is used to determine a state observer based on the system state model and the system output model.

[0151] The controller determination module is used to determine the controller based on the state of the state observer and the combined measurement variables.

[0152] The solution module is used to solve linear matrix inequalities based on the state observer and the controller using robust control theory to obtain the controller gain matrix and the observer gain matrix.

[0153] The output vector determination module is used to determine the output vector based on the controller gain matrix, the controller, and the system state model.

[0154] The output vector estimation module is used to determine the output vector estimate based on the observer gain matrix and the state observer.

[0155] The residual evaluation function determination module is used to determine the residual evaluation function based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

[0156] As an optional implementation, the solution module specifically includes:

[0157] An acquisition unit is used to acquire the closed-loop system of the multiple intelligent agents.

[0158] The order reduction unit is used to reduce the order of the closed-loop system based on the Laplace matrix and the closed-loop system of the multiple agents, so as to obtain the reduced-order closed-loop system.

[0159] The transformation unit is used to transform the target problem of the reduced-order closed-loop system to obtain the optimization problem.

[0160] A linear matrix inequality determination unit is used to determine linear matrix inequalities based on the Lyapunov function according to the optimization problem.

[0161] The solution unit is used to determine the controller gain matrix and the observer gain matrix based on the linear matrix inequality, the state observer, and the controller.

[0162] As an optional implementation, the expression for the controller is:

[0163]

[0164] Among them, u i (t) represents the controller, and K is the controller gain matrix. For combined measurement variables, t is Let i be the most recent trigger time. Let k be the next trigger time for agent i, k be the number of times agent i's event is triggered, and i be the i-th agent.

[0165] As an optional implementation, the expression for the combined measurement variables is:

[0166]

[0167] Where, q i (t) represents the combined measurement variable, N is the number of agents, j is the neighboring agent of agent i, and a ij Let i be the connection weight between agent i and agent j. Let i be the state of the observer of agent i. Let be the state of the observers of the neighboring intelligent agents of agent i.

[0168] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0169] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A fault detection method for a nonlinear multi-agent system, characterized in that, include: Construct a Lipschitz nonlinear system model for each agent; The Lipschitz nonlinear system model includes a system state model and a system output model; The state observer is determined based on the system state model and the system output model; The controller is determined based on the state of the state observer and the combined measured variables; Based on the state observer and the controller, the linear matrix inequality is solved using robust control theory to obtain the controller gain matrix and the observer gain matrix. The output vector is determined based on the controller gain matrix, the controller, and the system state model. The output vector estimate is determined based on the observer gain matrix and the state observer. The residual evaluation function is determined based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

2. The fault detection method for a nonlinear multi-agent system according to claim 1, characterized in that, The step of solving linear matrix inequalities using robust control theory based on the state observer and the controller to obtain the controller gain matrix and the observer gain matrix specifically includes: Obtain a closed-loop system of multiple intelligent agents; Based on the Laplace matrix and the closed-loop system of the multiple agents, the order is reduced to obtain the reduced-order closed-loop system. The objective problem of the reduced-order closed-loop system is transformed into an optimization problem; Based on the Lyapunov function, determine the linear matrix inequalities according to the optimization problem; The controller gain matrix and the observer gain matrix are determined based on the linear matrix inequality, the state observer, and the controller.

3. The fault detection method for a nonlinear multi-agent system according to claim 1, characterized in that, The expression for the controller is: Among them, u i (t) represents the controller, and K is the controller gain matrix. For combined measurement variables, t is the time of the continuous system. Let k be the trigger time of agent i. Let k be the (k+1)th trigger time of agent i, where k is the number of times agent i is triggered, and i is the i-th agent.

4. The fault detection method for a nonlinear multi-agent system according to claim 3, characterized in that, The expression for the combined measurement variables is: Where, q i (t) represents the combined measurement variable, N is the number of agents, j is the neighboring agent of agent i, and a ij Let i be the connection weight between agent i and agent j. Let i be the state of the observer of agent i. Let be the state of the observers of the neighboring intelligent agents of agent i.

5. A fault detection system for a nonlinear multi-agent system, characterized in that, include: The building block is used to construct a Lipschitz nonlinear system model for each agent; The Lipschitz nonlinear system model includes a system state model and a system output model; A state observer determination module is used to determine a state observer based on the system state model and the system output model; A controller determination module is used to determine the controller based on the state of the state observer and the combined measurement variables; The solution module is used to solve linear matrix inequalities based on the state observer and the controller using robust control theory to obtain the controller gain matrix and the observer gain matrix. An output vector determination module is used to determine the output vector based on the controller gain matrix, the controller, and the system state model. An output vector estimate determination module is used to determine the output vector estimate based on the observer gain matrix and the state observer; The residual evaluation function determination module is used to determine the residual evaluation function based on the output vector estimate and the output vector; the residual evaluation function is used to detect system faults.

6. The fault detection system for a nonlinear multi-agent system according to claim 5, characterized in that, The solution module specifically includes: The acquisition unit is used to acquire the closed-loop system of the multiple intelligent agents; The order reduction unit is used to reduce the order of the closed-loop system based on the Laplace matrix and the closed-loop system of the multiple agents to obtain the reduced-order closed-loop system. The transformation unit is used to transform the target problem of the reduced-order closed-loop system to obtain the optimization problem; A linear matrix inequality determination unit is used to determine linear matrix inequalities based on the Lyapunov function according to the optimization problem. The solution unit is used to determine the controller gain matrix and the observer gain matrix based on the linear matrix inequality, the state observer, and the controller.

7. The fault detection system for a nonlinear multi-agent system according to claim 5, characterized in that, The expression for the controller is: Among them, u i (t) represents the controller, and K is the controller gain matrix. For combined measurement variables, t is the time of the continuous system. Let k be the trigger time of agent i. Let k be the (k+1)th trigger time of agent i, where k is the number of times agent i is triggered, and i is the i-th agent.

8. The fault detection system for a nonlinear multi-agent system according to claim 5, characterized in that, The expression for the combined measurement variables is: Where, q i (t) represents the combined measurement variable, N is the number of agents, j is the neighboring agent of agent i, and a ij Let i be the connection weight between agent i and agent j. Let i be the state of the observer of agent i. Let be the state of the observers of the neighboring intelligent agents of agent i.

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