Multi-agent system fault diagnosis and estimation method based on fuzzy observer

Abstract

The invention discloses a multi-agent system fault diagnosis and estimation method based on a fuzzy observer, and aims to solve the problem of fault detection and estimation of a multi-agent system in a complex environment. The method comprises the following steps: firstly, establishing a system state space model containing a plurality of factors, then approaching a nonlinear term by applying a fuzzy logic system, constructing a global model, and then designing a fault observer. And finally, estimating an actuator fault by setting a network topology, calculating a gain matrix, setting a fault function and by means of MATLAB simulation. According to the method, the accuracy of fault diagnosis of the multi-agent system can be effectively improved, and stable operation of the system in a complex and uncertain environment is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection of multi-agent systems, and in particular to a multi-agent fault diagnosis and estimation method based on fuzzy observers. Background Art

[0002] The research background of multi-agent fault diagnosis stems from the growing demand for collaboration and reliability in modern complex systems. Multi-agent systems (MAS) are distributed systems composed of multiple agents with autonomy, collaboration and distributed decision-making capabilities. They are widely used in drone formations, intelligent robots, traffic management systems, smart grids and other fields. Such systems can cope with task processing and dynamic decision-making in complex environments due to their distributed structure and task allocation advantages. However, due to their complexity and diversity, multi-agent systems are more susceptible to failures, interference and uncertainty factors during operation.

[0003] The occurrence of faults not only affects the performance of a single agent, but also threatens the coordination, stability and reliability of the entire system. Therefore, how to detect, estimate and take countermeasures in time when a fault occurs is a key issue to ensure the normal operation of multi-agent systems. Traditional fault detection methods often have difficulty in achieving fast and accurate detection and estimation in the face of high complexity and environmental noise, which has prompted researchers to develop new, more intelligent and robust technologies.

[0004] Fault diagnosis can be performed by taking advantage of the advantages of fuzzy observers, such as the ability to handle uncertainty and fuzzy data, so that multi-agent systems can perform more accurate fault diagnosis and estimation when dealing with complex and uncertain environments, providing technical support for the stable operation of the system and promoting the continued development of this field. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a method for multi-agent fault diagnosis and estimation based on fuzzy observer, which can enable the multi-agent system to perform more accurate fault diagnosis and fault prediction and estimation when dealing with complex and uncertain environments.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The multi-agent system fault diagnosis and estimation method based on fuzzy observer includes the following steps:

[0008] S1: Establish a state space model of a multi-agent system with nonlinear terms, disturbances, and actuator failures;

[0009] S2: Construct a fuzzy logic system to approximate the nonlinear terms of the multi-agent system;

[0010] S3: Construct a global state space model of the multi-agent system;

[0011] S4: Construct a multi-agent fault observer based on fuzzy logic;

[0012] S5: Estimation of actuator failures in multi-agent systems.

[0013] Furthermore, a state space model of a multi-agent system with nonlinear terms, interference, and actuator failure is established in S1:

[0014]

[0015] in, is the state vector, is the input vector, It is an actuator failure. is the external disturbance of the system and is bounded, is a nonlinear term. A~E are system real matrices, and C and E are full-rank matrices.

[0016] Fuzzy logic systems can be used to approximate unknown smooth functions on compact sets. The IF-THEN rule is defined as

[0017]

[0018] Then the fuzzy logic system can be expressed as follows:

[0019]

[0020] Fuzzy basis function ξ j (x) can be expressed as:

[0021]

[0022] Let ξ(x)=[ξ1(x),ξ2(x),...,ξ M (x)] T and So formula (2) can be rewritten as

[0023] y=θ T ξ(x) (4)

[0024] Assume g(x) is in the compact set U∈R n For the continuous function defined above, for any constant ε, there exists a fuzzy logic system such that the following inequality holds:

[0025] sup|f(x)-g(x)|<ε (5)

[0026] The optimal parameter vector θ* The definition is as follows:

[0027]

[0028] The minimum fuzzy approximation error is:

[0029]

[0030] Furthermore, the fuzzy logic system constructed in S1 approximates the nonlinear terms of the multi-agent system:

[0031] Nonlinear functions is unknown, the following fuzzy logic system is used to approximate the unknown nonlinear function:

[0032]

[0033] From fuzzy reasoning, we know that there is a vector θ * , so that equation (3) holds true, where ε i Represents the fuzzy approximation error.

[0034]

[0035] The augmented vector and augmented matrix are defined as follows:

[0036]

[0037] Substituting these expressions into (1) we obtain:

[0038]

[0039] Next, define the global vector:

[0040]

[0041]

[0042] So the global state equation can be written as:

[0043]

[0044] in represents the Kronecker inner product, I N Represents the identity matrix of appropriate dimension.

[0045] For a given H ∞ The performance index γ is given by the existence of positive definite matrices P, Q and F such that equations (6)(7)(8) hold.

[0046]

[0047] in, Then the global dynamic system meets the performance index Therefore the system is asymptotically stable.

[0048] Furthermore, in S4, a multi-agent fault observer based on fuzzy logic is constructed to complete fault diagnosis:

[0049]

[0050] In order to obtain the global fault observer of the nonlinear multi-agent system, the following global vector is defined

[0051]

[0052]

[0053] Therefore, the global fault observer can be expressed as

[0054]

[0055] Furthermore, in S3, the actuator failure occurring in the multi-agent system is estimated:

[0056] First, the network topology of the multi-agent system is set, and then the LMI tool of MATLAB is used to calculate the gain matrix of formula (8). Then, the corresponding fault function is set, and finally the fault diagnosis is verified through MATLAB simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0058] Figure 1 It is the overall flow chart of the present invention;

[0059] Figure 2 is a communication topology diagram of the multi-agent system in the present invention; DETAILED DESCRIPTION

[0060] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0061] The present invention first establishes a state space model of a multi-agent system with nonlinear terms, interference, and actuator failures, then constructs a fuzzy logic system to approximate the nonlinear terms of the multi-agent system, based on which a multi-agent fault observer is constructed, and finally the actuator failures occurring in the multi-agent system are diagnosed. Figure 1 As shown, Figure 1 The overall flow chart of the present invention is as follows:

[0062] Step 1: Establish a global state-space model of the multi-agent system with nonlinear terms, disturbances, and actuator failures;

[0063]

[0064] in, is the state vector, is the input vector, It is an actuator failure. is the external disturbance of the system and is bounded, is a nonlinear term. A~E are system real matrices, and C and E are full-rank matrices.

[0065] Fuzzy logic systems can be used to approximate unknown smooth functions on compact sets. The IF-THEN rule is defined as

[0066]

[0067] Then the fuzzy logic system can be expressed as follows:

[0068]

[0069] Fuzzy basis function ξ j (x) can be expressed as:

[0070]

[0071] Let ξ(x)=[ξ1(x),ξ2(x),...,ξ M (x)] T and So formula (2) can be rewritten as

[0072] y=θ T ξ(x) (20)

[0073] Assume g(x) is in the compact set U∈R n For the continuous function defined above, for any constant ε, there exists a fuzzy logic system such that the following inequality holds:

[0074] sup|f(x)-g(x)|<ε (21)

[0075] The optimal parameter vector θ * The definition is as follows:

[0076]

[0077] The minimum fuzzy approximation error is:

[0078]

[0079] Nonlinear functions is unknown, the following fuzzy logic system is used to approximate the unknown nonlinear function:

[0080]

[0081] From fuzzy reasoning, we know that there is a vector θ * , so that equation (25) holds, where ε i Represents the fuzzy approximation error.

[0082]

[0083] The augmented vector and augmented matrix are defined as follows:

[0084]

[0085] Substituting these expressions into (1) we obtain:

[0086]

[0087] Next, define the global vector:

[0088]

[0089] So the global state equation can be written as:

[0090]

[0091] Step 2: Construct a multi-agent fault observer based on fuzzy logic

[0092] Since all agents are connected through a directed communication topology such as Figure 2 As shown in Figure 2, when designing a fault diagnosis sliding mode observer, it is necessary to consider the information interaction between agents. By transferring information between adjacent agents, the fault diagnosis of system (1) is realized, and the relative output estimation error variable ζ is introduced. i (t), which is defined as follows:

[0093]

[0094] in and i (t) represent the estimated measurement value and actual value of the subsystem in the multi-agent system, respectively, and a ij and g i Represent the elements in the adjacency matrix and Laplacian matrix of the communication topology graph respectively. If the node has no ring, then g i =0.

[0095] According to system (11) and formula (12), the fault observer of the multi-agent subsystem can be expressed as follows:

[0096]

[0097] Where c>0 is the coupling gain, is the observer gain matrix, u c is an adaptive robust structure, which is expressed as follows:

[0098]

[0099] In order to obtain the global fault diagnosis observer for nonlinear multi-agent systems, the following global vector is defined:

[0100]

[0101] Therefore, the global fault observer can be expressed as:

[0102]

[0103] According to equations (8) and (9), we define and So we get:

[0104]

[0105] Next we define the agent's error vector: and the global error vector

[0106]

[0107] Finally, we get the global error system state equation:

[0108]

[0109] For a given H ∞ The performance index γ is given by the existence of positive definite matrices P, Q and F such that equations (34)(35)(36) hold.

[0110]

[0111] in, Then the global dynamic system meets the performance index

[0112] Choose an appropriate Lyapunov function:

[0113]

[0114] By taking the derivative of this equation and substituting (33) into it, we can obtain:

[0115]

[0116] After sorting, substituting (14) into the equation, we can obtain:

[0117]

[0118] Among them, Z i (t) = Fe yi (t).

[0119] After simplification, we can get

[0120]

[0121] Since the matrix Q is a positive definite matrix, It is semi-negative definite. definition:

[0122]

[0123] Integrating both sides of the equation yields:

[0124]

[0125] because Bounded, It is not monotonically increasing, so:

[0126]

[0127] Therefore, the system is asymptotically stable.

[0128] Step 3 estimates the actuator failures that occur in the multi-agent system.

[0129] The parameters in system (1) and the communication topology used in Figure (2) are set as follows:

[0130]

[0131] Assume that the unknown nonlinear function of the multi-agent is g i (x i (t)) = 2sin(x i (t)), select the coupling gain function c = 0.2, and use the linear matrix inequality to calculate the gain matrix And the performance index γ = 1.3867. The observer gain matrix And the matrix F is as follows:

[0132]

[0133] In order to verify the effectiveness of the designed full-frequency domain fault sliding mode observer, it is assumed that the actuator fault signals of the four subsystems of the multi-agent system are expressed as follows:

[0134]

[0135] f4(t)=00≤t≤100

[0136] Select the following fuzzy membership function:

[0137] μ N =exp(-(x i +2) 2 )

[0138] μ Z =exp(-x i 2 )

[0139] μ p =exp(-(x i -2) 2 )

[0140] Finally, according to S5, the actuator failure occurring in the multi-agent is estimated or predicted.

Claims

1. A multi-agent system fault diagnosis and estimation method based on fuzzy observer, characterized by: The method comprises the following steps: S1: Establish a state space model of a multi-agent system with nonlinear terms, disturbances, and actuator failures; S2: Construct a fuzzy logic system to approximate the nonlinear terms of the multi-agent system; S3: Construct a global state space model of the multi-agent system; S4: Construct a multi-agent fault observer based on fuzzy logic; S5: Estimation of actuator failures in multi-agent systems. The multi-agent fault diagnosis method based on fuzzy observer is characterized by: In S1, the state space model of the multi-agent system is: in, is the state vector, is the input vector, It is an actuator failure. is the external disturbance of the system and is bounded, is a nonlinear term. A~E are system real matrices, and C and E are full-rank matrices. The multi-agent fault diagnosis and estimation method based on fuzzy observer is characterized by: In S2, a fuzzy logic system is constructed to approximate a nonlinear function: is unknown, the following fuzzy logic system is used to approximate the unknown nonlinear function: From fuzzy reasoning, we know that there is a vector θ * , so that equation (3) holds true, where ε i Represents the fuzzy approximation error. The multi-agent fault diagnosis and estimation method based on fuzzy observer is characterized in that: in S3, a global multi-agent system state space model is constructed: The augmented vector and augmented matrix are defined as follows: Substituting these expressions into (1) we obtain: Next, define the global vector: So the global state equation can be written as: in represents the Kronecker inner product, I N Represents the identity matrix of appropriate dimension. For a given H ∞ The performance index γ is given by the existence of positive definite matrices P, Q and F such that equations (6)(7)(8) hold. in, Then the global dynamic system meets the performance index Therefore the system is asymptotically stable.

2. The multi-agent fault diagnosis and estimation method based on fuzzy observer according to claim 1 is characterized in that: In S4, a multi-agent fault observer based on fuzzy logic is constructed: In order to obtain the global fault observer of the nonlinear multi-agent system, the following global vector is defined Therefore, the global fault observer can be expressed as at last According to claim 1, S5 estimates the actuator failure occurring in the multi-agent system.

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