Optimal cooperative fault-tolerant control of heterogeneous multi-agent system

Abstract

The invention discloses optimal cooperative fault-tolerant control of a heterogeneous multi-agent system, and relates to the technical field of multi-agent system control, and the method comprises the steps: writing an unmanned plane system and an unmanned vehicle system into a state-space equation through a Kronecker product, and introducing a distributed formation control protocol; based on a formation control protocol, combining the optimal fault-tolerant control law with the formation control protocol to obtain a heterogeneous multi-agent system with distributed optimal fault-tolerant formation control; according to the optimal cooperative fault-tolerant control of the heterogeneous multi-agent system provided by the invention, the unmanned aerial vehicle system and the unmanned vehicle system are integrated into a unified state space equation by using a Kronecker product, and a distributed formation control protocol is introduced, so that effective cooperation of the heterogeneous multi-agent system is realized, the flexibility and expandability of the system are improved, and the fault-tolerant control efficiency of the heterogeneous multi-agent system is improved. The intelligent agents of different types can work cooperatively under a unified framework, and the system has remarkable advantages in the aspects of improving the flexibility, expandability, reliability and robustness of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system control, and in particular to optimal collaborative fault-tolerant control of heterogeneous multi-agent systems. Background Art

[0002] In the field of multi-agent system control technology, the cooperative control of heterogeneous multi-agent systems is an important and complex issue. Heterogeneous multi-agent systems are composed of different types of agents, such as drones and unmanned vehicles. These agents have differences in functions, performance and dynamic characteristics. In practical applications, heterogeneous multi-agent systems need to perform various complex tasks, such as cooperative search, target tracking and formation flying. However, due to environmental uncertainty, communication limitations between agents and actuator failures, achieving optimal cooperative control of heterogeneous multi-agent systems faces huge challenges.

[0003] Traditional collaborative control methods for multi-agent systems are mostly targeted at homogeneous systems, that is, the agents in the system have the same dynamic characteristics and functions. The application of these methods in heterogeneous multi-agent systems is limited because there are significant differences between the agents in the heterogeneous system, making it difficult to directly apply traditional control strategies. In addition, actuator failure is a common problem in heterogeneous multi-agent systems, which may lead to system performance degradation or even loss of control. Therefore, it is of great significance to study the optimal collaborative fault-tolerant control of heterogeneous multi-agent systems.

[0004] At present, the research on cooperative control of heterogeneous multi-agent systems has made some progress, but there are still some problems, such as how to effectively integrate different types of agents into a unified control framework, how to achieve information exchange and collaborative decision-making between agents, and how to maintain the stability and performance of the system when actuators fail. These problems limit the application and development of heterogeneous multi-agent systems in complex tasks. In this regard, we propose the optimal cooperative fault-tolerant control of heterogeneous multi-agent systems. Summary of the invention

[0005] In order to solve the above technical problems and provide optimal collaborative fault-tolerant control for heterogeneous multi-agent systems, this technical solution solves the above problems.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] Optimal coordinated fault-tolerant control of heterogeneous multi-agent systems, including:

[0008] Use Kronecker product to write the UAV system and the unmanned vehicle system into the state space equation and introduce the distributed formation control protocol;

[0009] Based on the formation control protocol, the optimal fault-tolerant control law and the formation control protocol are combined to obtain a heterogeneous multi-agent system with distributed optimal fault-tolerant formation control.

[0010] The optimal cooperative fault-tolerant control is applied to UAVs and unmanned vehicles, and the optimal fault-tolerant cooperative control law of UAVs and unmanned vehicles is obtained.

[0011] Preferably, the system uses Kronecker product to write drones and unmanned vehicles into the state space to form a heterogeneous system, establishes an actuator fault model, and brings the fault model into the heterogeneous state space to obtain a heterogeneous multi-agent system fault model, introduces a distributed formation protocol, and uses graph theory to prove that the control protocol can complete the formation task.

[0012] Preferably, the drone motion model is:

[0013] Among them, the single drone motion model is:

[0014]

[0015]

[0016]

[0017]

[0018] gθ=M θ / I y

[0019]

[0020] In the formula, g represents the acceleration due to gravity, p x 、p y 、p z They represent the positions of the UAV in the three coordinate systems, φ, θ, ψ represent the roll angle, pitch angle and yaw angle of the UAV, respectively, and f z represents the total lift of the four propellers, M φ / I x 、M θ / I y 、M ψ / I z They represent the control inputs for controlling the drone to rotate around three coordinate axes;

[0021] Assuming there are l drones, convert the formula into state:

[0022]

[0023] in,

[0024]

[0025] In the formula, represents the Kronecker product, A a , B a Represent the state matrix and output matrix of the UAV respectively;

[0026] The expected formation of multiple UAV systems is: That is, the system formation error can be obtained as

[0027] Therefore, when the multi-UAV system meets the following conditions when an actuator failure occurs, the formation is considered to be completed:

[0028] lim t→∞ ∥δ ai -δ aj ∥=0

[0029] lim t→∞ ∥v ai ∥=0

[0030] lim t→∞ ∥Ω i ∥=0

[0031]

[0032] Preferably, the unmanned vehicle motion model is:

[0033] Among them, the motion model of a single unmanned vehicle is:

[0034]

[0035] in represents the position in ground space, Indicates direction p gi The speed of represents the input of agent i;

[0036] Assuming there are m unmanned vehicles, convert the formula into state:

[0037]

[0038] Among them, x Gi =(p i ,v i ) T ,

[0039] In the formula, represents the Kronecker product, A g , B gRepresent the state matrix and output matrix of the unmanned vehicle respectively; the expected formation is That is, the system formation error can be obtained as

[0040] Therefore, when the multi-unmanned vehicle system meets the following conditions when an actuator failure occurs, the formation is considered to be completed:

[0041] lim t→∞ ∥δ gi -δ gj ∥=0

[0042] lim t→∞ ∥v gi ∥=0.

[0043] Preferably, the fault model is brought into the heterogeneous state space to obtain the heterogeneous multi-agent system fault model, which specifically includes:

[0044] Establish fault models based on drones and unmanned vehicles, and construct state space expressions for heterogeneous multi-agent systems by merging state variables;

[0045] Among them, the fault model expression is:

[0046]

[0047] Where P i represents the actuator failure coefficient. The actuator failure of the UAV is expressed as: P Ai =diag(ρ ix ,ρ iy ,ρ iz )∈R 3 , the actuator failure of the unmanned vehicle is expressed as: P Gi =diag(ρ ix ,ρ iy )∈R 2 , and P Ai ,P Gi ∈(0,1);

[0048] According to the fault model expression, the system state model after the actuator failure is obtained as follows:

[0049]

[0050] The heterogeneous multi-agent state space model is defined as:

[0051]

[0052]

[0053] in

[0054] X G =(P G ,V G ) T ,U=(U A ,U G ) T

[0055] P A =(p1,p2,...,p l ) T ,

[0056] V A =(v1,v2,...,v l ) T ,

[0057] Ω A =(Ω1,Ω2,...,Ω l ) T ,

[0058]

[0059]

[0060] P G =(p l+1 ,p l+2 ,...,p l+m ) T ,

[0061] V G =(v l+1 ,v l+2 ,...,v l+m ) T ,

[0062]

[0063]

[0064]

[0065] Perform a simple linear transformation on the Laplace matrix of the system. When there are unmanned vehicles and unmanned aerial vehicles in the system, the corresponding Laplace matrix L is as follows:

[0066]

[0067] Where, L AA Represents the communication relationship between multiple drones, L AG Represents the communication relationship between the UAV and the unmanned vehicle, L GA Represents the communication relationship between the unmanned vehicle and the drone, L GG Represents the communication relationship between multiple unmanned vehicles;

[0068] The expected formation for a heterogeneous multi-agent system is expressed as That is, the formation error of the heterogeneous multi-agent system is

[0069] When all agent states satisfy the following equation, the multi-agent system completes the formation:

[0070] lim t→∞ ∥δ i -δ j ∥=0

[0071] lim t→∞ ∥v i ∥=0

[0072] lim t→∞ ∥Ω i ∥=0

[0073]

[0074] Preferably, using graph theory to prove that the control protocol can complete the formation task specifically includes:

[0075] The weighted undirected graph G = (V, E, A) is used to describe the communication topology of the multi-agent system;

[0076] Assume that G consists of n vertices, where V = (v1, v2, ... v n ) represents the set of all vertices in an undirected graph, and each vertex represents an agent;

[0077] represents the edge set between vertices, e ij =(v i ,v j ) represents the i To the vertex v j The edge of

[0078] The edge connection between two vertices indicates that there is information exchange between the two vertices;

[0079] If bidirectional communication is allowed, the graph is undirected; otherwise, it is directed;

[0080] A=[a ij ]n×n Represents the adjacency matrix of the relationship between the following agents, where a ij It is edge ij =(v i ,v j ) weight coefficient, if e ij ∈E, then a ij >0, otherwise a ij =0;

[0081] In the communication topology, D = diag{d1,d2,...d n}D=diag{d1,d2,...d n} is used to represent the degree matrix of the multi-agent system, where Represents the degree of each agent, that is, the number of neighbor nodes. Therefore, we can define the Laplacian matrix of a graph G as L = DA.

[0082] Preferably, the formation control protocol specifically includes:

[0083] Among them, the UAV formation control protocol is expressed as:

[0084]

[0085] Among them, the unmanned vehicle formation control law protocol is expressed as:

[0086]

[0087] Preferably, the optimal fault-tolerant control law specifically includes:

[0088] For a single UAV and unmanned vehicle, the state vector is defined as:

[0089]

[0090] The integral performance index function consisting of the error variable and the control variable is constructed respectively, where the integral performance index function expression is:

[0091]

[0092]

[0093] Since the dimension of the state vector of the UAV is different from that of the state vector of the unmanned vehicle, the weight coefficient of the UAV is set as:

[0094] Q=q * I 12 ,R=r*I3

[0095] Where q>0,r>0;

[0096] The weight coefficient of the unmanned vehicle is set as:

[0097] T=λ*I6,γ=μ*I3

[0098] Where λ>0,μ>0;

[0099] For heterogeneous multi-agent systems, the optimal control law that satisfies the performance index It is expressed as follows:

[0100]

[0101]

[0102] Where P Ai and P Ai is the solution of the Riccati equation:

[0103]

[0104]

[0105] Preferably, the optimal collaborative fault-tolerant control law specifically includes:

[0106] Based on the application of optimal cooperative fault-tolerant control on UAVs and unmanned vehicles, the optimal fault-tolerant controller for a single agent is obtained;

[0107] The control parameters of a single agent are defined as:

[0108]

[0109] Let Q i =q i I 12 ,R i =r i I3;

[0110] Among them, the drone expression is:

[0111]

[0112] Among them, the expression of unmanned vehicle is:

[0113]

[0114] Preferably, the distributed optimal cooperative fault-tolerant control protocol of the system is obtained by replacing only the gain parameters, and the optimal fault-tolerant formation control protocol based on the formation control protocol is obtained as follows:

[0115]

[0116]

[0117] Combining the Laplacian matrices, the control protocol and can be rewritten as:

[0118]

[0119] in

[0120]

[0121] The heterogeneous multi-agent system is rewritten as:

[0122]

[0123] Compared with the prior art, the present invention has the following beneficial effects:

[0124] The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems proposed in the present invention integrates the drone system and the unmanned vehicle system into a unified state-space equation by using the Kronecker product, and introduces a distributed formation control protocol, thereby achieving effective collaboration of heterogeneous multi-agent systems and improving the flexibility and scalability of the system, so that different types of agents can work together under a unified framework, and when the system faces uncertain factors such as actuator failures, it can still maintain stable formations and collaborative work, thereby improving the reliability and robustness of the system. It has significant advantages in improving the flexibility, scalability, reliability and robustness of the system, and provides a new solution for the collaborative control of heterogeneous multi-agent systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 is a flow chart of the method of the present invention;

[0126] Figure 2 It is the communication topology diagram of heterogeneous multi-agent system;

[0127] Figure 3 It is the position state and speed state diagram of UAV and UGV under the distributed formation protocol;

[0128] Figure 4 It is the state diagram of attitude angle and angular velocity of UAV under distributed formation protocol;

[0129] Figure 5 This is the state diagram of multiple unmanned vehicle formations at different times under the distributed formation protocol;

[0130] Figure 6 This is the state diagram of multiple UAV formations at different times under the distributed formation protocol;

[0131] Figure 7 It is the formation trajectory diagram of heterogeneous multi-agent system under distributed formation protocol;

[0132] Figure 8 It is the position state and speed state diagram of the UAV and the unmanned vehicle under the optimal fault-tolerant formation control protocol;

[0133] Fig. 9 It is the state diagram of the attitude angle and angular velocity of the UAV under the optimal fault-tolerant control protocol;

[0134] Fig.10 This is the state diagram of multiple unmanned vehicle formations at different times under the optimal fault-tolerant control protocol;

[0135] Fig.11 This is the state diagram of multi-UAV formation at different times under the optimal fault-tolerant control protocol;

[0136] Fig.12 This is the formation trajectory diagram of the heterogeneous multi-agent system under the optimal fault-tolerant formation control protocol. DETAILED DESCRIPTION

[0137] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are only examples, and those skilled in the art may think of other obvious variations.

[0138] Reference Figure 1 As shown in Figure 1, the optimal collaborative fault-tolerant control of heterogeneous multi-agent systems includes:

[0139] Use Kronecker product to write the UAV system and the unmanned vehicle system into the state space equation and introduce the distributed formation control protocol;

[0140] Based on the formation control protocol, the optimal fault-tolerant control law and the formation control protocol are combined to obtain a heterogeneous multi-agent system with distributed optimal fault-tolerant formation control.

[0141] The optimal cooperative fault-tolerant control is applied to UAVs and unmanned vehicles, and the optimal fault-tolerant cooperative control law of UAVs and unmanned vehicles is obtained.

[0142] The system uses Kronecker product to write drones and unmanned vehicles into the state space to form a heterogeneous system, establishes an actuator fault model, and brings the fault model into the heterogeneous state space to obtain a heterogeneous multi-agent system fault model. The distributed formation protocol is introduced, and graph theory is used to prove that the control protocol can complete the formation task.

[0143] The feasibility of the fault-tolerant formation algorithm is verified through the designed experiment. A heterogeneous multi-agent system consisting of three drones and three unmanned vehicles is considered for the experiment. The communication relationship is as follows Figure 2 As shown;

[0144] according to Figure 2 The communication topology relationship, the corresponding Laplace matrix is:

[0145]

[0146] Assume that UAV2 and UAV3 do not fail, UGV2 does not fail, and the remaining agents have different degrees of actuator partial failure. The specific degree of failure is given by the following formula:

[0147]

[0148] The initial state of the UAVs system and the stable state after the formation is completed are given in Table 1, and the initial state of the UGVs system and the stable state after the formation is completed are given in Table 2.

[0149]

[0150] Table 1 UAVs system initial state and stable state

[0151]

[0152]

[0153] Table 2 Initial state and stable state of UGVs system

[0154] The experimental platform used in this section is Matlab2017a. The experimental content mainly includes two parts. One part is to verify the effectiveness of the distributed formation control algorithm (13) and (14) when the actuator does not fail, and use this as a reference. The other part is to verify the feasibility of the proposed algorithm (34) (35) when the actuator fails. The parameters of the distributed formation control algorithm are α=0.2, β=1.5, γ1=5, γ2=2.

[0155] The optimal fault-tolerant formation control parameters corresponding to the UAVs system and UGVs system are shown below.

[0156] UA1 parameters are:

[0157]

[0158] UAV2 and UAV3 have the same parameters, both are k α1 =2.23,k α2 =6.20,k α3 =7.48,k α4 =4.47,

[0159] UGV1 parameters are

[0160] The parameters of UGV2 are g1=1.73, g2=2.54,

[0161] UGV3 parameters are

[0162] Figure 3 - Figure 7 is the simulation result of the distributed formation control law, Figure 3 and Figure 4 The state changes of multi-UAV and multi-UAV heterogeneous systems under the formation control protocol are shown. Figure 3 It can be seen that the position states of the drone and the unmanned vehicle eventually tend to a stable value. The positions of the X, Y, and Z axes are consistent at time t=30s. The X axis is stable at two values, and the Y axis is stable at three values, completing the triangular formation. The speeds in the three directions eventually tend to 0. Figure 4 The changes in attitude angle and angular velocity of the UAV during the formation process are shown.

[0163] Figure 5 and Figure 6 The figure shows the formation status of the unmanned vehicle and the unmanned aerial vehicle at t = 10s, t = 30s, and t = 50s respectively under the distributed formation control protocol. Figure 5 We can see that under the distributed formation control protocol, the UGVs finally complete the triangle formation and reach stability at t = 30s. Figure 6 We can see that the UAVs complete the formation at t=30s and reach a stable state.

[0164] Figure 7 The formation trajectory diagram of the heterogeneous multi-agent system under the distributed formation control protocol is shown. From the figure, we can see that the UAVs and UGVs finally converge to the desired position and complete the formation task. The three drones and three unmanned vehicles converge to the same position. The drone altitude is stable at 80m.

[0165] Figure 8 - Fig.11 is the simulation result under the optimal fault-tolerant formation control protocol, Figure 8 The position and speed states of the UAVs and UGVs on the X, Y, and Z axes are shown under the condition of partial actuator failure. It can be seen from the figure that the X, Y axis speed and position states of the UAVs and UGVs tend to be stable at t = 30s. Fig. 9 The attitude angle and angular velocity states of the UAVs during the formation process when a partial actuator failure occurs are shown. It can be seen that the attitude angle of the UAVs tends to 0° at t=40s, and the pitch angle eventually tends to 0°, that is, the UAVs finally reach stability.

[0166] Fig.10 and Fig.11 The formation states of UAVs and UGVs using the optimal fault-tolerant formation control law at t = 10s, t = 30s, and t = 50s are shown respectively. Fig.10 It can be seen that the UGVs system completed the triangle formation at t = 30s under the condition of actuator failure. Fig.11 It shows that the UAVs system completed the triangle formation at t = 30s when the actuators suffered partial efficiency failure.

[0167] Fig.12 The formation trajectory diagram of the UAVs and UGVs system in three-dimensional space using the optimal fault-tolerant formation control protocol is shown. It can be seen from the figure that the UAVs and UGVs finally converge to the desired position and complete the triangular formation when some failures occur during execution. The three drones and three unmanned vehicles converge to the same corresponding position, and the drones finally stabilize at a height of 80m.

[0168] The use process of the present invention is as follows: the UAV system and the unmanned vehicle system are written into the state space equation using the Kronecker product, and a distributed formation control protocol is introduced; based on the formation control protocol, the optimal fault-tolerant control law and the formation control protocol are combined to obtain a heterogeneous multi-agent system with distributed optimal fault-tolerant formation control; the optimal collaborative fault-tolerant control is applied to the UAV and the unmanned vehicle to obtain the optimal fault-tolerant collaborative control law of the UAV and the unmanned vehicle.

[0169] To sum up, the advantages of the present invention are: by using Kronecker products to integrate drone and unmanned vehicle systems into a unified state space equation, introducing a distributed formation control protocol, achieving effective collaboration, improving system flexibility and scalability, and enabling different types of intelligent agents to work together under a unified framework. In the face of uncertain factors such as actuator failures, they can still maintain stable formations and collaborative work, thereby improving system reliability and robustness, and providing a new solution for the collaborative control of heterogeneous multi-agent systems.

[0170] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. Optimal collaborative fault-tolerant control of heterogeneous multi-agent systems, characterized by: include: Use Kronecker product to write the UAV system and the unmanned vehicle system into the state space equation and introduce the distributed formation control protocol; Based on the formation control protocol, the optimal fault-tolerant control law and the formation control protocol are combined to obtain a heterogeneous multi-agent system with distributed optimal fault-tolerant formation control. The optimal cooperative fault-tolerant control is applied to UAVs and unmanned vehicles, and the optimal fault-tolerant cooperative control law of UAVs and unmanned vehicles is obtained.

2. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 1, characterized in that: The system uses Kronecker product to write drones and unmanned vehicles into the state space to form a heterogeneous system, establishes an actuator fault model, and brings the fault model into the heterogeneous state space to obtain a heterogeneous multi-agent system fault model. The distributed formation protocol is introduced, and graph theory is used to prove that the control protocol can complete the formation task.

3. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 2, characterized in that: The UAV motion model is: Among them, the single drone motion model is: gθ=M θ / I y In the formula, g represents the acceleration due to gravity, p x 、p y 、p z They represent the positions of the UAV in the three coordinate systems, φ, θ, ψ represent the roll angle, pitch angle and yaw angle of the UAV, respectively, and f z represents the total lift of the four propellers, M φ / I x 、M θ / I y 、M ψ / I z They represent the control inputs for controlling the drone to rotate around three coordinate axes; Assuming there are l drones, convert the formula into state: in, i=1,2,...,l, In the formula, represents the Kronecker product, A a , B a Represent the state matrix and output matrix of the UAV respectively; The expected formation of multiple UAV systems is: That is, the system formation error can be obtained as Therefore, when the multi-UAV system meets the following conditions when an actuator failure occurs, the formation is considered to be completed: lim t→∞ ∥δ ai -δ aj ∥=0 lim t→∞ ∥v ai ∥=0 lim t→∞ ∥Ω i ∥=0 4. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 2, characterized in that: The motion model of the unmanned vehicle is: Among them, the motion model of a single unmanned vehicle is: in represents the position in ground space, Indicates direction p gi The speed of represents the input of agent i; Assuming there are m unmanned vehicles, convert the formula into state: Among them, x Gi =(p i ,v i ) T , i=1,2,...,m, In the formula, represents the Kronecker product, A g , B g Represent the state matrix and output matrix of the unmanned vehicle respectively; The expected formation is That is, the system formation error can be obtained as Therefore, when the multi-unmanned vehicle system meets the following conditions when an actuator failure occurs, the formation is considered to be completed: lim t→∞ ∥δ gi -δ gj ∥=0 lim t→∞ ∥v gi ∥=0。 5. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 3, characterized in that: Bringing the fault model into the heterogeneous state space, the fault model of the heterogeneous multi-agent system is obtained, which specifically includes: Establish fault models based on drones and unmanned vehicles, and construct state space expressions for heterogeneous multi-agent systems by merging state variables; Among them, the fault model expression is: Where P i represents the actuator failure coefficient. The actuator failure of the UAV is expressed as: P Ai =diag(ρ ix ,ρ iy ,ρ iz )∈R 3 , the actuator failure of the unmanned vehicle is expressed as: P Gi =diag(ρ ix ,ρ iy )∈R 2 , and P Ai ,P Gi ∈(0,1); According to the fault model expression, the system state model after the actuator failure is obtained as follows: The heterogeneous multi-agent state space model is defined as: in X G =(P G ,V G ) T ,U=(U A ,U G ) T P A =(p1,p2,...,p l ) T , V A =(v1,v2,...,v l ) T , Oh A =(Ω1,Ω2,...,Ω l ) T , P G =(p l+1 ,p l+2 ,...,p l+m ) T , V G =(v l+1 ,v l+2 ,...,v l+m ) T , Perform a simple linear transformation on the Laplace matrix of the system. When there are unmanned vehicles and unmanned aerial vehicles in the system, the corresponding Laplace matrix L is as follows: Where, L AA Represents the communication relationship between multiple drones, L AG Represents the communication relationship between the UAV and the unmanned vehicle, L GA Represents the communication relationship between the unmanned vehicle and the drone, L GG Represents the communication relationship between multiple unmanned vehicles; The expected formation for a heterogeneous multi-agent system is expressed as That is, the formation error of the heterogeneous multi-agent system is When all agent states satisfy the following equation, the multi-agent system completes the formation: lim t→∞ ∥δ i -δ j ∥=0 lim t→∞ ∥v i ∥=0 lim t→∞ ∥Ω i ∥=0 6. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 3, characterized in that: Using graph theory to prove that the control protocol can complete the formation task includes: The weighted undirected graph G = (V, E, A) is used to describe the communication topology of the multi-agent system; Assume that G consists of n vertices, where V = (v1, v2, ... v n ) represents the set of all vertices in an undirected graph, and each vertex represents an agent; represents the edge set between vertices, e ij =(v i ,v j ) represents the i To the vertex v j The edge of The edge connection between two vertices indicates that there is information exchange between the two vertices; If bidirectional communication is allowed, the graph is undirected; otherwise, it is directed; A=[a ij ] n×n Represents the adjacency matrix of the relationship between the following agents, where a ij It is edge ij =(v i ,v j ) weight coefficient, if e ij ∈E, then a ij >0, otherwise a ij =0; In the communication topology, D = diag{d1,d2,…d n }D=diag{d1,d2,...d n } is used to represent the degree matrix of the multi-agent system, where Represents the degree of each agent, that is, the number of neighbor nodes. Therefore, we can define the Laplacian matrix of a graph G as L = DA.

7. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 1, characterized in that: Formation Control Protocol Details include: Among them, the UAV formation control protocol is expressed as: Among them, the unmanned vehicle formation control law protocol is expressed as:

8. The optimal cooperative fault-tolerant control of heterogeneous multi-agent systems according to claim 1, characterized in that: The optimal fault-tolerant control law specifically includes: For a single UAV and unmanned vehicle, the state vector is defined as: The integral performance index function consisting of the error variable and the control variable is constructed respectively, where the integral performance index function expression is: Since the dimension of the state vector of the UAV is different from that of the state vector of the unmanned vehicle, the weight coefficient of the UAV is set as: Q=q * I 12 ,R=r*I3 Where q>0,r>0; The weight coefficient of the unmanned vehicle is set as: T=λ*I6,γ=μ*I3 Where λ>0,μ>0; For heterogeneous multi-agent systems, the optimal control law that satisfies the performance index i=1,2,...,m+l is expressed as follows: Where P Ai and P Ai is the solution of the Riccati equation:

9. The optimal collaborative fault-tolerant control of heterogeneous multi-agent systems according to claim 1, characterized in that: The optimal collaborative fault-tolerant control law specifically includes: Based on the application of optimal cooperative fault-tolerant control on UAVs and unmanned vehicles, the optimal fault-tolerant controller for a single agent is obtained; The control parameters of a single agent are defined as: Let Q i = q i ·I 12 , R i = r i ·I3; Among them, the drone expression is: Among them, the expression of unmanned vehicle is:

10. The optimal cooperative fault-tolerant control of heterogeneous multi-agent systems according to claim 1, characterized in that: By replacing only the gain parameters, the distributed optimal cooperative fault-tolerant control protocol of the system is obtained, and the optimal fault-tolerant formation control protocol based on the formation control protocol is obtained as follows: Combining the Laplacian matrices, the control protocol and can be rewritten as: in The heterogeneous multi-agent system is rewritten as:

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