CN106444701B - Leader-follower type multi-agent system finite time Robust Fault Diagnosis design method - Google Patents

Abstract

The invention discloses a limited-time robust fault diagnosis design method for a leader-follower multi-agent system. Firstly, a multi-agent system connection graph with a leader is constructed and expressed as a directed graph, and the Laplacian matrix of the follower is obtained. L and the adjacency matrix G of the leader; then establish the state equation and output equation of each node's flight control system, and augment the state vector and fault vector into a new vector; for each node, according to the constructed directed graph, Construct the distributed error equation and the global error equation based on the directed graph, and based on the finite-time robust control, construct the finite-time fault diagnosis observer of the flight control system, and perform the finite-time fault diagnosis of multi-agent actuator faults based on the directed graph Troubleshooting. The invention implements effective and accurate limited-time online diagnosis and fault estimation for any node failure or simultaneous failure of multiple nodes in the control system.

Description

Design of finite-time robust fault diagnosis for leader-follower multi-agent systems method

technical field

The invention belongs to the technical field of multi-agent systems, and in particular relates to a limited-time robust fault diagnosis design method for a leader-follower multi-agent system.

Background technique

For control systems, in the process of analysis or design, the stability of a system is a priority. This depends on the unstable system, and it cannot be applied in practice. In general, the stability we often say in the field of control, such as Lyapunov stability and BIBO (bounded-input-bounded-output) stability, are asymptotically stable. The essence of asymptotic stability is to observe whether the system state can be infinitely close to the equilibrium point when the time t approaches infinity after a system is disturbed in the initial state. It should be noted that the above-mentioned stability theory in the traditional sense focuses on the behavior of the system, which is discussed for an infinite time interval. The state of the system is not limited to a bound, as long as it is bounded. That is to say, these traditional stability theories describe only the steady-state performance of the system, and do not actually require the transient performance. This will cause, such as a system is asymptotically stable, but its transient performance is so poor that it cannot be used in engineering, and its infinitely long convergence time will also limit its rapid maneuvering control in actual engineering application in the case.

The finite-time stability mentioned in this patent is FTS (finite-time stability), which is different from the stability in the traditional sense and puts forward a stability concept that focuses on the transient performance and convergence performance of the system. FTS pre-determines a finite time interval and a specific limit, within this time interval, the state of the control system will always remain within this limit and can converge to stability within a finite time relative to an infinite time interval balance point. For finite-time stability, there are three elements, including (1) a finite time interval, (2) bounds on the initial conditions and (3) bounds on the desired state of the system.

With the development of flight control systems, situations that require multi-agents to complete tasks emerge in an endless stream, and the research based on MAS (Multi-Agent Systems) technology has also received more and more attention and research. However, due to the precise and complex characteristics of MAS, more attention should be paid to the theoretical research of its fault diagnosis. Fault diagnosis technology can be divided into three parts: fault detection, fault separation and fault estimation. Fault diagnosis technology is mainly used to improve the reliability of system operation and reduce the risk of system operation. It judges whether there is a fault by monitoring the system operating status, and at the same time determines the specific information of the fault, such as time, location and size. Since the multi-agent system, especially the formation flight of the flight control system, is a high-cost and high-investment technology, the fault diagnosis technology for it must be accurate and fast. This requires both the transient performance and the convergence performance of fault diagnosis. The finite-time robust fault diagnosis design method of the leader-follower multi-agent system proposed in this patent is just the research completed for this situation, which has very important theoretical research value and broad application prospects.

Contents of the invention

Purpose of the invention: The present invention is a finite-time robust fault diagnosis design method for a leader-follower multi-agent system provided to solve existing problems. The present invention designs a finite-time distributed fault diagnosis method through a finite-time robust control method. The diagnostic observer can theoretically suppress the influence of external time-varying interference on fault diagnosis, and can ensure the transient performance and convergence performance of fault diagnosis, that is, for the fault of any node in the control system or the simultaneous failure of multiple nodes Effective and accurate limited-time online diagnosis and fault estimation.

Technical scheme: the concrete technical scheme of the present invention is as follows:

A design method for finite-time robust fault diagnosis of a leader-follower multi-agent system, comprising the following specific steps:

The first step: Construct a multi-agent system connection graph with a leader and express it in a directed graph, and obtain the Laplacian matrix L of the follower and the adjacency matrix G of the leader;

The second step: establish the state equation and output equation of each node flight control system, and augment the state vector and fault vector into new vectors;

Step 3: For each node, according to the constructed directed graph, construct a distributed error equation and a global error equation based on the directed graph, and construct a finite-time fault diagnosis observer for the flight control system based on finite-time robust control ;

Step 4: Use the finite-time fault diagnosis observer obtained above to perform finite-time fault diagnosis on multi-agent actuator faults based on directed graphs.

Further, in the first step, the specific method of obtaining the Laplacian matrix L of the follower and the adjacency matrix G of the leader is as follows:

Assuming that a complete leader-follower directed graph is composed of several vertices ν and several edges ε, the vertex ν ₀ represents the leader 0; the vertex ν _i represents the i-th follower, i∈(1～N); Edge (ν _i , ν _j ) is used to indicate that follower j can receive information from follower i, and vice versa;

Definition A=[a _ij ]∈R ^n×n represents the weighted adjacency matrix of the directed graph, where a _ij represents the weight of each edge; if (ν _i ,ν _j )∈ε, then a _ij >0, otherwise a _ij = 0; a _ii = 0;

Define the adjacency matrix of the leader of the directed graph as G, where G=diag(g ₁ ,…,g _N ),

Define the Laplacian matrix L=G-A of the follower.

Further, the directed graph mentioned in the first step means that each edge in the multi-agent system connection graph has a connection direction.

Further, in the second step, the specific method is to establish a system model with faults for each follower node and augment:

Dynamic equation for leader 0:

The dynamic equation for follower i:

In the above equation, x _i (t) and y _i (t) are the state vector and output vector of each follower node respectively, u _i (t) is the control input vector of each follower node; A, B, C are respectively Be the state matrix, input matrix, output matrix of described flight control system, matrix H is fault distribution matrix, matrix D ₁ is the distribution matrix of the input disturbance of described every i follower node flight control system; f _i (t) is the system fault, ω _i (t) is the external time-varying disturbance vector, and for any ω(t), ω ^T (t)ω(t)≤d ₁ (d ₁ ≥0); is the differential of the fault, and for any Have (d ₂ ≥ 0), where d ₁ and d ₂ are two non-negative scalars;

For the augmented state equation, the new state vector is state matrix input perturbation matrix Fault Distribution Matrix

Further, the state equation and output equation of each node flight control system described in the second step are obtained by linearizing the online operating point of the nonlinear flight control system.

Further, in the third step, the finite-time fault diagnosis observer of the flight control system is constructed as follows:

in,

where y ₀ (t) and are the measured output vector and estimated output vector of the fault diagnosis observer of the leader node, respectively; is the measurement output vector of each follower node fault diagnosis observer;

observer matrix Wherein, the dimensionality matrices R and F are gain matrices of the described fault diagnosis observer;

The augmented observer state vector Send the collected output data of the flight control system of each node to the above-mentioned fault diagnosis observer, obtain the state vector of the observer, and obtain the fault estimation value of each node In this way, the faults of the actuators of the flight control system can be estimated online; is the state vector of each follower node fault diagnosis observer, is the actuator failure estimate for each follower node system.

Further, the specific design method of the dimensionality matrix R and F is as follows:

First, suppose Let the state estimation error fault estimation error output estimation error

Then for the i-th follower node, the local augmented state estimation error vector is:

Then the local augmented state estimation error equation of the i-th follower node is expressed as:

Secondly, let but:

Then, to convert the local error equation into a global error equation, first define the global variable:

The global augmented state estimation error vector is

The global output estimation error vector is

The global perturbation vector is

The global fault estimation error vector is

Based on the directed graph theory, the Kronecker product is introduced, and the obtained expression of the global error state space is:

Among them, IN is an _N ×N identity matrix.

Further, the global error dynamic system satisfies:

1) When v(t)=0, the system is stable in finite time, that is, for finite time parameters (c ₁ ,c ₂ ,T,R ₀ ,d ₁ ,d ₂ ), where c ₁ <c ₂ ,R ₀ > 0, c ₁ , c ₂ , d ₁ , d ₂ are all scalars, and R ₀ is a given matrix which can be taken as an identity matrix; the system satisfies Under conditions:

2) When v(t)≠0, for any ω(t) and There is ω ^T (t)ω(t)≤d ₁ , And take At this time, the system is bounded in finite time, and there is a scalar γ>0, T>0 so that the system satisfies:

Further, the finite-time robust fault diagnosis observer gain matrices R and F are obtained by solving the following linear matrix inequality:

For given finite time parameters (c ₁ ,c ₂ ,T,R ₀ =I,d ₁ ,d ₂ ) and scalars γ>0, α>0, λ ₁ >0, λ ₂ >0, λ ₃ > 0 and β>0 if there exists a symmetric positive definite matrix Q ₁ ∈ R ^(n+r)×(n+r) , a symmetric positive definite matrix Q ₂ ∈ R ^(n+r)×(n+r) , and the matrix Satisfy:

λ ₁ I < Q ₁ < I (17)

λ ₂ I < Q ₂ < λ ₃ I (18)

said formula translates into the following linear matrix inequality:

in

according to Gain matrices R and F of the fault diagnosis observer are obtained.

Beneficial effects: Compared with the prior art, the design method for the limited-time robust fault diagnosis of the leader-follower multi-agent system provided by the present invention has significant advantages in that:

One is that the present invention applies the finite time control technology to the fault diagnosis process of the multi-agent system, optimizes the transient performance of the diagnosis process, and defines a limit for the fault estimated by the observer, combined with the robust control used, in In the process of fault estimation, the time-varying interference and fault differential items received by the system when the actuator fault occurs have a good inhibitory effect, which improves the accuracy of fault diagnosis;

Second, the present invention adds e ^-αT in the solution process, the formula compared to It is easier to obtain, which can reduce the conservatism of the solution results, and for complex multi-agent systems, it is more likely to obtain a solution that satisfies the conditions;

The third is that the present invention applies the finite time control technology to the fault diagnosis process of the multi-agent system, which improves the convergence performance of the system, which is different from the convergence performance of the asymptotically stable performance in the infinite time interval, and can make the fault diagnosis observer in the On-line diagnosis and fault estimation of multi-agent system faults can be performed within a limited time.

The invention has important practical reference value for the real-time fault diagnosis and accurate monitoring of the formation flight control system of the flight control system.

Description of drawings

Fig. 1: Fig. 1 is the directed graph of the distributed flight control system with 1 leader and 4 follower nodes established by the example of the implementation verification of the present invention.

Fig. 2: Fig. 2-1 is when the 1st, 4th follower nodes (agent 1 and agent 4) of the embodiment 1 of the present invention are measured to break down at the same time, 4 follower nodes 2 (agent 1, 2 , 3 and 4) Schematic diagram of the fault estimation curve of the fault diagnosis observer; Fig. 2-2 is when the first and fourth follower nodes (agent 1 and agent 4) measured by embodiment 1 of the present invention all fail , a schematic diagram of the comparison curve between the estimated fault value and the real fault value measured by the fault diagnosis observer of the follower node 1 (agent 1); When both follower nodes (Agent 1 and Agent 4) fail, the comparison curve between the estimated fault value and the real fault value measured by the fault diagnosis observer of follower node 4 (Agent 4) is shown.

Fig. 3: Fig. 3-1 is when the 2nd, 3 follower nodes (agent 2 and agent 3) of embodiment 2 of the present invention are measured and break down simultaneously, 4 follower nodes 2 (agent 1, 2 , 3 and 4) Schematic diagram of the fault estimation curve of the fault diagnosis observer; Fig. 3-2 is when the second and third follower nodes (agent 2 and agent 3) measured by embodiment 2 of the present invention all fail , a schematic diagram of the comparison curve between the estimated fault value and the real fault value measured by the fault diagnosis observer of the follower node 2 (agent 2); Schematic diagram of the comparison curve between the estimated fault value measured by the fault diagnosis observer of the follower node 3 (Agent 3) and the fault real value when both the follower nodes (Agent 2 and Agent 3) fail.

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings.

According to the finite time robust fault diagnosis design method of the leader-follower multi-agent system proposed by the present invention, it comprises the following specific steps:

The first step: Construct a multi-agent system connection graph with a leader and express it in a directed graph, and obtain the Laplacian matrix L of the follower and the adjacency matrix G of the leader:

Suppose a complete leader-follower directed graph consists of several vertices ν and several edges ε. Vertex ν ₀ represents the leader 0; Vertex ν _i represents the i-th follower, i∈(1～N). Edge (ν _i , ν _j ) is used to indicate that follower j can receive information from follower i, but not vice versa, because there may be one-way communication between followers.

Definition A=[a _ij ]∈R ^n×n represents the weighted adjacency matrix of the directed graph, where a _ij represents the weight of each edge; if (ν _i ,ν _j )∈ε, then a _ij >0, otherwise a _ij =0. And for the directed graph used in the present invention, the connectivity of the nodes themselves, that is, a _ii =0, is not considered.

Define the adjacency matrix of the leader of the directed graph as G, where G=diag(g ₁ ,…,g _N ), Define the Laplacian matrix L=GA of the follower.

The second step: establish the state equation and output equation of each node flight control system, and augment the state vector and fault vector into a new vector:

Dynamic equation for leader 0:

The dynamic equation for follower i:

In the above equation, x _i (t) and y _i (t) are the state vector and output vector of each follower node respectively, u _i (t) is the control input vector of each follower node; A, B, C are respectively Be the state matrix, input matrix, output matrix of described flight control system, matrix H is fault distribution matrix, matrix D ₁ is the distribution matrix of the input disturbance of described every i follower node flight control system; f _i (t) is the system fault (the actuator additive fault is considered here), ω _i (t) is the external time-varying disturbance vector, and for any ω(t), ω ^T (t)ω(t)≤d ₁ (d ₁ ≥ 0); is the differential of the fault, and for any Have For the augmented state equation, the new state vector is state matrix output matrix input perturbation matrix Fault Distribution Matrix

Step 3: For each node, according to the constructed directed graph, construct the distributed error equation and the global error equation based on the directed graph, and based on the finite-time robust control, construct the following finite-time fault of the flight control system Diagnostic Observer:

In the above dynamic equation,

where y ₀ (t) and They are the measured output vector of the leader node (assuming that the full state of the leader is measurable), the estimated output vector of the leader node, and the augmented observer state vector Send the collected output data of the flight control system of each node to the above-mentioned fault diagnosis observer, obtain the state vector of the observer, and obtain the fault estimation value of each node In this way, the faults of the actuators of the flight control system can be estimated online.

is the output vector of the fault diagnosis observer of the leader node; and are the state vector and measurement output vector of each follower node fault diagnosis observer, respectively, is the actuator failure estimate for each follower node system.

observer matrix Dimensional matrix R and F are described fault diagnosis observer gain matrix, also are the unknown matrix that the key point of the present invention needs to design, and concrete design method is as follows:

Known from the second step, the present invention assumes that the full state of the leader node 0 is measurable, and it can be known that the estimated output vector of the leader is the original measured output vector, that is to say: Based on this assumption, let the state estimation error be The fault estimation error is The output estimate error is

Then for the i-th follower node, the local augmented state estimation error vector is:

Then the local augmented state estimation error equation of the i-th follower node can be expressed as:

make but:

To convert the local error equation into a global error equation, first define the global variables:

The global augmented state estimation error vector is

The global output estimation error vector is

The global perturbation vector is

The global fault estimation error vector is

Based on the directed graph theory, the Kronecker product is introduced (using Indicates), the obtained global error state space expression is:

Among them, IN is an _N ×N identity matrix.

In order to solve the dimension-appropriate unknown gain matrix that needs to be designed, that is, the finite-time robust fault diagnosis observer gain matrix R and F, the present invention requires the global error dynamic system to satisfy:

1) When v(t)=0, the system is stable in finite time, that is, for finite time parameters (c ₁ ,c ₂ ,T,R ₀ ,d ₁ ,d ₂ ), where

c ₁ <c ₂ , R ₀ >0, c ₁ , c ₂ , d ₁ , d ₂ are all scalars, R ₀ is a given matrix and can be taken as an identity matrix; the system satisfies Under conditions:

2) When v(t)≠0, for any ω(t) and There is ω ^T (t)ω(t)≤d ₁ , And take At this time, the system is bounded in finite time, and there is a scalar γ>0, T>0 so that the system satisfies:

in,

The gain matrices R and F of the finite-time robust fault diagnosis observer described in the third step of the present invention can be obtained by solving the following linear matrix inequality: for given finite-time parameters (c ₁ , c ₂ , T, R ₀ = I,d ₁ ,d ₂ ) and scalars γ＞0, α＞0, λ ₁ ＞0, λ ₂ ＞0, λ ₃ ＞0 and β＞0 if there is a symmetric positive definite matrix Q ₁ ∈ R ^{(n+r) ×(n+r)} , the symmetric positive definite matrix Q ₂ ∈R ^{(n +r)×(n+r)} , and the matrix Satisfy:

λ ₁ I < Q ₁ < I (37)

λ ₂ I < Q ₂ < λ ₃ I (38)

For ease of solution, the above formula translates into the following linear matrix inequality:

in according to Gain matrices R and F of the fault diagnosis observer are obtained; the above matrices all satisfy the operation rules of the matrix.

Using the distributed fault diagnosis observer obtained above, the finite-time fault diagnosis of multi-agent actuator fault based on directed graph is carried out.

The further preferred solution of the present invention is: the directed graph described in the first step of the present invention refers to that each edge in the multi-agent system connection graph has a connection direction, and the undirected graph refers to the multi-agent system communication topology connection Each edge in the graph does not have a connection direction. Undirected graphs are a special case of directed graphs, and directed graphs are more general.

The state equation and output equation of each node flight control system described in the second step of the present invention are obtained by linearizing the online operating point of the nonlinear flight control system.

The present invention can be better understood from the following examples. However, those skilled in the art will readily understand that the specific material ratios, process conditions and results described in the examples are only used to illustrate the present invention, and should not and will not limit the present invention described in detail in the claims .

Example

The present invention takes the following longitudinal motion equation of a certain type of civil aviation aircraft as the implementation object, and proposes a limited-time distributed fault diagnosis observer for actuator faults that occur during its formation flight. This fault diagnosis method can improve the transient state of fault diagnosis Performance and convergence performance;

Consider the following longitudinal motion equation of a civil aviation aircraft:

Among them, the state vector x(t) is pitch rate q(rad/s), true air speed V _tas (m/s), angle of attack α(rad) and pitch angle θ(rad). The control input u(t) is elevator deflection angle δ _e (rad) and thrust T(10 ⁵ N). Each matrix of the system is represented as follows:

Assume that the system has an actuator fault: in view of the fact that the actuator fault occurs in the part of the control input, the present invention has a fault distribution matrix H=B; it is assumed that the distribution matrix of the input disturbance of the system is D ₁ =0.1[1,1,1 ,1] ^T ; as shown in Figure 1, Agent 0 in Figure 1 represents the leader, Agent 1, Agent 2, Agent 3 and Agent 4 represent that the directed graph has 4 follower nodes, where Only node 1 can communicate with leader 0; from Figure 1, the Laplacian matrix L of the follower and the adjacency matrix G of the leader can be obtained:

The finite-time fault diagnosis of multi-agent actuator faults based on directed graph is carried out by using the distributed fault diagnosis observer obtained above.

Using the CVX toolbox in Matlab software, directly minimize c ₂ , λ ₃ and β, and solve the above-mentioned conditions: when c ₁ =1, T=1, c ₂ =129.0068 can be obtained, β=0.8590, so we can get The other distributed observer matrices obtained are as follows:

In order to verify the effect of the flight control system fault diagnosis method of the present invention, the following two simulation examples are used for verification. In the two examples, noise is added to the system model as a disturbance.

Example 1

Suppose the first and fourth follower nodes fail at the same time:

Failure of the first follower node

Failure of the 4th follower node

That is, the first follower node had an actuator failure at 20s, and the fourth follower node had a failure at 50s. The experimental simulation results are shown in Figure 2. Fig. 2-1 is when the 1st, 4th follower nodes (agent 1 and agent 4) of embodiment 1 of the present invention are measured to break down at the same time, 4 follower nodes 2 (agent 1, 2, 3 and 4) Schematic diagram of the fault estimation curve of the fault diagnosis observer; Fig. 2-2 is when the first and fourth follower nodes (agent 1 and agent 4) measured in embodiment 1 of the present invention all fail, the follower The comparison curve schematic diagram of the fault estimated value and the fault true value measured by the fault diagnosis observer of node 1 (agent 1); Fig. 2-3 is the 1st, the 4th follower node ( Schematic diagram of the comparison curve between the estimated fault value measured by the fault diagnosis observer of the follower node 4 (Agent 4) and the fault real value when both Agent 1 and Agent 4) are faulty.

Example 2

Suppose the second and third follower nodes fail at the same time:

Failure of the second follower node

Failure of the 3rd follower node

That is, the second follower node had an actuator failure at 10s, and the third follower node had an actuator failure at the collective distance at 40s. The experimental simulation results are shown in Figure 3.

Fig. 3-1 is when the 2nd, 3rd follower nodes (agent 2 and agent 3) of embodiment 2 of the present invention are measured to break down at the same time, 4 follower nodes 2 (agent 1, 2, 3 and 4) Schematic diagram of the fault estimation curve of the fault diagnosis observer; Fig. 3-2 is when the second and third follower nodes (agent 2 and agent 3) measured by embodiment 2 of the present invention all fail, the follower The comparison curve diagram of the fault estimated value and the fault true value measured by the fault diagnosis observer of node 2 (intelligent body 2); Fig. 3-3 is the 2nd, 3 follower nodes ( Schematic diagram of the comparison curve between the estimated fault value measured by the fault diagnosis observer of the follower node 3 (Agent 3) and the fault real value when both Agent 2 and Agent 3) are faulty.

As shown in the accompanying drawings, it can be seen from Figures 2-1 and 3-1 that when the system fails, the observer can diagnose in real time which agent the failure occurred on. It can be seen from Figures 2-2, 2-3, 3-2 and 3-3 that the fault estimated by this observer can simulate the real value of the fault within a limited time, and it can be seen from the small fluctuation of the curve that the observed The device has good robustness.

It can be drawn from the simulation results that when one or more follower nodes in the multi-agent system fail, the augmented finite-time fault diagnosis observer designed by the present invention can diagnose the faulty ones within a limited time. Nodal system, and estimate the size of the fault within a limited time, has better fault estimation performance, and has a good suppression effect on the added disturbance and fault differential terms. The invention has important practical reference value for the fault diagnosis and accurate monitoring of the formation flight control system of the flight control system within a limited time.

All descriptions that are not involved in the specific embodiments of the present invention belong to the known technology in the art and can be implemented with reference to the known technology.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (5)

1. A method for designing finite time robust fault diagnosis of a leader-follower type multi-agent system is characterized by comprising the following steps: the method comprises the following specific steps:

the first step is as follows: constructing a multi-agent system connection graph with a leader, and representing the multi-agent system connection graph by a directed graph to obtain a Laplacian matrix L of the follower and an adjacent matrix G of the leader; the specific method comprises the following steps:

setting a complete leader-follower directed graph consisting of a plurality of vertexes v and a plurality of edges epsilon, wherein the vertex v is₀Represents leader 0; vertex v_iIndicating the ith followingI belongs to (1-N); side (v)_i,ν_j) The information used for indicating that the follower j can receive the information of the follower i, and otherwise, the information cannot be received;

definition a ═ a_ij]∈R^n×nA weighted adjacency matrix representing the directed graph, wherein a_ijRepresenting the weight of each edge; if (v)_i,ν_j) E is epsilon, then a_ij> 0, otherwise a_ij＝0；a_ii＝0；

The adjacency matrix that defines the leader of the directed graph is G, where G ═ diag (G)₁,…,g_N),

Defining Laplacian matrix L of the follower as G-A;

the directed graph means that each edge in the multi-agent system connection graph has a connection direction.

The second step is that: establishing a state equation and an output equation of each node flight control system, and increasing a state vector and a fault vector into a new vector; the specific method is that for each follower node, a system model with faults is established and is expanded:

dynamic equations for the leader:

dynamic equation for follower i:

in the above equations (1) and (2), x_i(t) and y_i(t) are the state vector and output vector, u, of each follower node, respectively_i(t) is the control input vector for each follower node; A. b, C are respectively the state matrix, input matrix and output matrix of the flight control system, matrix H is fault distribution matrix and matrix D₁A distribution matrix of input disturbances for each i follower node flight control system; f. of_i(t) is a system fault, ω_i(t) is an external time-varying disturbance vector, and for any omega (t), there is omega^T(t)ω(t)≤d₁，d₁≥0；Is a differential of the fault and is arbitraryIs provided withd₂Not less than 0, wherein d₁、d₂Two non-negative scalars;

for the augmented equation of state, the new state vector isState matrix Input disturbance matrixFault distribution matrix

The third step: for each node, constructing a distributed error equation and a global error equation based on the directed graph according to the constructed directed graph, and constructing a finite time robust fault diagnosis observer of the flight control system based on finite time robust control; the finite time robust fault diagnosis observer for constructing the flight control system comprises the following steps:

wherein,

wherein y is₀(t) anda measurement output vector and an estimation output vector of the fault diagnosis observer which are the leader node respectively;is the measurement output vector of each follower node fault diagnosis observer;

observer matrixThe adaptive matrixes R and F are gain matrixes of the finite time robust fault diagnosis observer;

augmented observer state vectorSending the collected output data of the flight control system of each node to the fault diagnosis observer to obtain the state vector of the observer, thereby obtaining the fault estimation value of each nodeThus, the fault of the flight control system actuator is estimated on line; whereinIs the state vector of each follower node fault diagnosis observer,is an actuator of each follower node systemA barrier estimate value;

the fourth step: and carrying out finite time fault diagnosis on the fault of the multi-agent actuator based on the directed graph by using the obtained finite time robust fault diagnosis observer.

2. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: and the second step is that the state equation and the output equation of each node flight control system are obtained by linearizing the online working point of the nonlinear flight control system.

3. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: the specific design method of the dimension-adaptive matrixes R and F is as follows:

first, assume thatEstimate error of order stateError of fault estimationOutput estimation error

Then for the ith follower node, the local augmented state estimation error vector is:

then the local augmented state estimation error equation for the ith follower node is expressed as:

secondly, orderThen:

then, the local error equation is converted into a global error equation, and a global variable is defined:

the global augmented state estimates the error vector as

Global output estimation error vector of

The global disturbance vector is

The global fault estimation error vector is

Based on the directed graph theory, a kronecker product is introduced, and the obtained global error state space expression is as follows:

wherein I_NIs an N × N identity matrix.

4. The lead-follow multi-agent system time-limited robust troubleshooting design method of claim 3 characterized by: the global error dynamic system satisfies:

1) when v (t) is 0, the system is time-limited stable, i.e. for the time-limited parameter (c)₁,c₂,T,R₀,d₁,d₂) Wherein c is₁＜c₂,R₀＞0，c₁,c₂,d₁,d₂Are all scalar quantities, R₀For a given matrix, an identity matrix may be taken; the system is satisfyingUnder the conditions of (a):

2) when v (t) ≠ 0, it is determined by summing any ω (t)Has omega^T(t)ω(t)≤d₁， And getThe system is bounded in time at this point, and there is a scalar γ > 0, T > 0, which makes the system satisfy:

5. the lead-follow multi-agent system time-limited robust troubleshooting design method of claim 1 characterized by: the finite time robust fault diagnosis observer gain matrixes R and F are obtained by solving the following linear matrix inequality:

for a given finite time parameter c₁,c₂,T,R₀＝I,d₁,d₂And scalar gamma > 0, α > 0, lambda₁＞0，λ₂＞0，λ₃> 0 and β > 0 if a symmetric positive definite matrix Q exists₁∈R^(n+r)×(n+r)Symmetric positive definite matrix Q₂∈R^(n+r)×(n+r)A sum matrixSatisfies the following conditions:

λ₁I＜Q₁＜I (17)

λ₂I＜Q₂＜λ₃I (18)

said formulaThe following linear matrix inequalities are converted:

wherein

According toAnd obtaining gain matrixes R and F of the fault diagnosis observer.