A multi-agent fault-tolerant formation tracking control method with multiple leaders and switching topology

Abstract

The present invention relates to a multi-agent fault-tolerant formation tracking control method under multiple leaders and switching topologies. A fault model is added to a dynamic model of a follower, and a fault-tolerant time-varying formation tracking control protocol is constructed based on adjacent errors between agents. Feasibility conditions required for multiple agents to complete formation tracking are obtained. A multi-agent model for fault-tolerant time-varying formation tracking is designed, and parameters required in an adaptive update formula are given. A control model of the agent is constructed to realize fault-tolerant time-varying formation tracking control under multiple leaders and switching topologies.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system collaborative control, and in particular to a multi-agent fault-tolerant formation tracking control method under multi-leader and switching topology. Background Art

[0002] In recent years, the cooperative control of multi-agent systems has developed rapidly and attracted attention from various fields because of its extremely important applications in various fields. For example, micro-satellites, vehicle formation control, aircraft formation control, complex network synchronization, underwater robots, etc. have extremely important applications. Cooperative control can be divided into several branches, including formation control, consistency control, encirclement control, and formation encirclement control. Consistency control is to make all agents reach a consistent state under the designed control protocol. In the past few decades, there have been three typical control methods in the field of robot control, namely, behavior-based method, leader-follower method, and virtual structure method.

[0003] Currently, many studies on multi-agent formations do not consider actuator failures. However, as the scale of multi-agents expands, the probability of actuator failure in the agents will also increase. When an actuator fails, it will affect the continued execution of the task, thereby causing the task to fail. Summary of the invention

[0004] The object of the present invention is to provide a method for solving the time-varying fault-tolerant formation tracking control problem of a high-order linear multi-agent system with multiple leaders, where the control input of the leader is unknown and time-varying.

[0005] The present invention adopts the following technical solution:

[0006] A multi-agent fault-tolerant formation tracking control method under multi-leader and switching topology comprises the following steps:

[0007] (1) Determine leaders and followers based on the spatial distribution of agents;

[0008] (2) Determine the fault type based on the fault information obtained during the external switching topology, and add the fault model to the follower's dynamic model;

[0009] (3) construct the topological interaction structure between leaders and followers;

[0010] (4) Construct a fault-tolerant time-varying formation tracking control protocol based on the adjacent errors between agents;

[0011] (5) Obtain the feasibility conditions required for multi-agents to complete formation tracking;

[0012] (6) Based on the leader and follower model in multi-agent, the set X topological relationship, and the formation feasibility condition, a multi-agent model for fault-tolerant time-varying formation tracking is designed, and the parameters required in the adaptive update formula are given;

[0013] (7) Construct a control model of the intelligent agent to realize fault-tolerant time-varying formation tracking control under multiple leaders and switching topologies.

[0014] Furthermore, in step (1), all informed followers are well-informed followers, and the information exchange channel between followers is non-directional. For each uninformed follower, there is at least one well-informed follower connected to it.

[0015] Furthermore, in step (2), the fault types are divided into four cases:

[0016] Case 1: When ρ id (t)=1 and u bid (t) = 0 There is no fault in the system;

[0017] Case 2: When 0<ρ id (t)<1 and u bid When (t) = 0, only failure occurs;

[0018] Case 3: When ρ id (t)=1 and u bid When (t)≠0, the system only has a bias fault;

[0019] Case 4: When 0<ρ id (t)<1 and u bid When (t)≠0, the system has both failure fault and bias fault.

[0020] Furthermore, in step (4), the fault-tolerant time-varying formation tracking control protocol is:

[0021]

[0022] in, and

[0023] and is the adaptivity parameter, and represents the fault bound estimate, and P is a positive definite matrix.

[0024] Furthermore, in step (4), the positive definite matrix P is given by the linear inequality Find, where the linear inequality (A,B) is stable and

[0025] Furthermore, in step (5), the compensation input v of the feasibility condition of the formation i (t), through Solve, assuming that there is a compensation input v i (t) If the above formula is satisfied, the process can continue; otherwise, the formed formation is not feasible for the multi-agent system under the fault-tolerant protocol.

[0026] Furthermore, in step (6), the adaptive parameters include Calculated by the following formulas:

[0027]

[0028]

[0029]

[0030] Furthermore, the local formation tracking error ξ of the fault-tolerant control protocol i (t)i∈F is calculated by the following formula:

[0031]

[0032] Among them, the coordination variable θ i (t) is based on the expected time-varying formation h i (t) is defined, and the coordination variable of the formation is defined as θ i (t) = x i (t)-h i (t)i∈F;

[0033] During multi-agent operation, the time-varying formation offset vector h of the followers is i (t), the following conditions need to be satisfied: For any given bounded initial state, if there exists a positive constant a k (k∈E) satisfies Formation tracking control with multiple leaders can be achieved;

[0034]

[0035] Represents the formation reference function.

[0036] Furthermore, in step (7), the follower dynamics model with actuator failure is:

[0037]

[0038] The beneficial effects of the present invention are:

[0039] 1. When one or more agents in a multi-agent system have an actuator failure, not only can the desired time-varying formation be completed, but also the expected trajectory of the leader can be tracked. The existence of unknown time-varying control input in the leader makes the research more complicated. Compared with no leader or a single leader, the present invention studies the situation with multiple leaders, which is more complicated and more robust. The research results of a single leader cannot be directly applied to multiple leaders.

[0040] 2. The formation is time-varying, and each multi-agent is high-order. Compared with the time-invariant formation, the research on time-varying formation is more practical and more complex.

[0041] 3. The topology of the present invention is switched. Compared with the research on fixed topology, the switching topology studied in the present invention is more widely used and more robust, because when obstacles block or communication equipment link fails, the interactive topology of the multi-agent system may switch. In addition, the processing method of fixed topology cannot be directly applied to switching topology. The research on multi-agent system with switching topology is more complicated and more challenging than that of fixed topology.

[0042] This paper considers the formation control method, proposes a distributed formation control protocol to compensate for bias failure and unknown efficiency failure, and provides a feasible method for time-varying formation. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the process of the present invention.

[0044] Figure 2 In the calculation example, the multi-agent communication topology graph set X contains G 1 Spanning tree formation topology.

[0045] Figure 3 In the calculation example, the multi-agent communication topology graph set X contains G 2 Spanning tree formation topology.

[0046] Figure 4 This is a schematic diagram of the topology switching signal timing.

[0047] Figure 5 The error for the follower. DETAILED DESCRIPTION

[0048] Let G = {V, E, W} represent a weighted directed graph with M nodes, and V = {v 1 ,v 2 ,....,v M} to represent a node set, is an edge set, W=[wij ]∈R M×M represents w with non-negative weights ij The adjacency matrix of G is represented by e ij =(v i ,v j ) to indicate that v i Yes j Neighbors of. Weight w ij >0 if and only if e ji ∈E, and w ii =0(i=1,2,.....,M). N i = {v j ∈V:e ji ∈E} represents the set of all neighbors. Indicates v i The in-degree of in (v i ),i=1,2,......,M} to represent the in-degree matrix of graph G. The Laplacian matrix of graph G is represented as L=DW.

[0049] The present invention has N followers and MN leaders, with a total of M intelligent agents. F = [1, 2, ....., N] and E = [N+1, N+2, ....., M] are used to represent the set of followers and leaders respectively.

[0050] 1. Determining leaders and followers based on the spatial distribution of agents

[0051] Leaders and followers are defined as follows, if a multi-agent has no neighbors then it is called a leader, otherwise if the multi-agent has at least one neighbor then it is called a follower. If the follower's neighbor set includes a leader then it is called an informed leader, if it includes all leaders then it is called an informed follower, otherwise if its neighbor set does not include a leader then it is called an uninformed follower.

[0052] Assuming that all informed followers of the present invention are well-informed followers, the information exchange channel between followers is non-directional, and for each uninformed follower, there is at least one well-informed follower connected to it.

[0053] (ii) Determine the fault type based on the fault information obtained during the external switching topology and add the fault model to the follower's dynamic model

[0054] In order to solve the fault-tolerant time-varying formation problem, an actuator failure model is constructed. For follower i (i∈F), the actuator failure model is defined as follows:

[0055]

[0056] in, represents the output of the actuator, u i ∈R m represents the input of the actuator, u bi (t)∈R m represents the actuator bias fault, ρ i (t) = diag[ρ i1 (t),ρ i2 (t),.....,ρ im (t)] and 0<ρ id (t)≤1 represents an unknown efficiency fault of actuator channel d (d=1,2,.....,m). The present invention considers both bias fault and failure fault.

[0057] Actuator failure can be divided into the following four situations.

[0058] Case 1: When ρ id (t)=1 and u bid (t) = 0 There is no fault in the system.

[0059] Case 2: When 0<ρ id (t)<1 and u bid When (t) = 0, only failure faults exist.

[0060] Case 3: When ρ id (t)=1 and u bid When (t)≠0, the system only has a bias fault.

[0061] Case 4: When 0<ρ id (t)<1 and u bid When (t)≠0, the system has both failure fault and bias fault.

[0062] Follower System Model:

[0063]

[0064] Among them, use x i (t)∈R n to represent the state vector of follower i, u i (t)∈R m represents the control input of follower i, u bi (t)∈R m represents the bias failure of follower i, ρ i (t) represents the unknown failure of follower i, A∈R n×n With B∈R n×m is a known constant matrix.

[0065] Unknown failure faulti (t) and bias fault u bi (t) are all bounded, and there exists an unknown positive constant ρ id Make 0< ρ id ≤ρ id (t)≤1, i=1,2,......,N, d=1,2,......,m, there exists a positive constant m i , so that ||u bi ||≤m i

[0066]

[0067] Leader System Model:

[0068]

[0069] Among them, x k (t)∈R n Represents the state vector of leader k, r k (t)∈R m represents the control input of leader k, which is unknown and time-varying. n×n With B∈R n×m is a known constant matrix.

[0070] 3. Constructing the topological interaction structure between leaders and followers

[0071] The information interaction between the multi-agent system of the present invention uses graph theory to describe any communication chain topology graph G σ(t) The following assumptions are met: σ(t) The information interaction between followers is undirected, graph G σ(t) Multiple root nodes are leaders, and the rest of the nodes are followers.

[0072] (IV) Constructing a fault-tolerant time-varying formation tracking control protocol based on adjacent errors between agents

[0073] Fault-tolerant time-varying formation tracking control protocol:

[0074]

[0075] in, and

[0076] and is the adaptability parameter, and represents the fault limit estimate. P is a positive definite matrix. According to the linear inequality Find, where the linear inequality (A,B) is stable and

[0077] (V) Obtaining the feasibility conditions required for multi-agent formation tracking

[0078] Compensation input v to solve the feasibility condition of the formation i (t), through Assume that there is a compensation input v i (t) If the above formula is satisfied, the process can continue; otherwise, the formed formation is not feasible for the multi-agent system (formula (2)) under the fault-tolerant protocol (formula (4)).

[0079] (VI) Based on the leadership and follower model in multi-agents, the set X topological relationship, and the formation feasibility conditions, a multi-agent model for fault-tolerant time-varying formation tracking is designed, and the parameters required in the adaptive update formula are given.

[0080] The adaptability parameters are calculated by the following adaptivity law:

[0081]

[0082]

[0083]

[0084] The local formation tracking error ξ of the above fault-tolerant control protocol i (t)i∈F is calculated by the following formula:

[0085]

[0086] When i (t) = 0 means that the system has completed the formation tracking. i (t) is based on the expected time-varying formation h i (t) is defined, and the coordination variable of the formation is defined as θ i (t) = x i (t)-h i (t)i∈F.

[0087] Formula (8) can be rewritten as formula (9)

[0088]

[0089] in, and

[0090] During multi-agent operation, the time-varying formation offset vector h of the followers is i(t), the following conditions need to be satisfied. For any given bounded initial state, if there exists a positive constant a k (k∈E) satisfies Formation tracking control with multiple leaders can be achieved.

[0091]

[0092] Represents the formation reference function. When the formation tracking is completed, all followers need to pay attention to the formation reference function. While maintaining the time-varying offset h i (t), in order to make x i (t)-h i (t) reach agreement, h i (t) It will inevitably be introduced into the system, thus affecting the analysis and design, which makes the formation tracking problem more complicated.

[0093] (VII) Constructing the control model of intelligent agents to achieve fault-tolerant time-varying formation tracking control under multiple leaders and switching topologies

[0094] The communication topology of multi-agents can be switched. Set X represents the possible topology set of multi-agents, topology index O∈N represents the set of natural numbers, δ(t):[0,∞)→O is the communication topology switching signal at the topology switching time t, and its value represents the number of the communication topology corresponding to the multi-agent system at time t in set X. For example, δ(t 1 )=1,δ(t 2 )=2. 1 t 1 After time, we expect the agent to switch to the first spanning tree formation topology, G 2 t 2 After time, the agent is expected to switch to the second spanning tree formation topology.

[0095] The set X includes at least a first spanning tree formation topology and a second spanning tree formation topology, and these two topologies have a common leader. At time t, the multi-agent system receives a topology switching signal δ(t), which causes the agent group in the multi-agent system to switch from the first spanning tree formation topology to the second spanning tree formation topology. δ(t) Switch, t is the topology switching time, leader-follower topology structure, the topology switching at time t is represented by the Laplace matrix L δ(t) describe.

[0096]

[0097] L1δ(t) ∈R N×N The Laplace matrix representing the information interaction between followers,

[0098] L 2δ(t) ∈R N×(M-N) Laplacian matrix representing the information exchange between followers and leaders.

[0099] If the definitions and assumptions of the present invention for leaders and followers are met, then for each follower, there is at least one leader with a directed path pointing to it. δ(t) There is the following lemma.

[0100] L 1δ(t) All eigenvalues ​​have positive real parts. is non-negative, Each row is the same and sums to 1. There are the following forms:

[0101] Substituting the fault-tolerant protocol (Formula (4)) into the follower dynamics model (Formula (2)) yields

[0102]

[0103] Derivative of the follower's local error (Formula (8)) yields

[0104]

[0105] in, ρ(t)=diag{ρ 1 (t),ρ 2 (t),.....,ρ N (t)}

[0106]

[0107]

[0108]

[0109]

[0110] In order to eliminate the influence of external input from the leader, it is assumed that there exists a normal number d i , so that Established.

[0111] Calculation Example

[0112] In order to prove the effectiveness of the designed fault-tolerant control protocol, the present invention uses MATLAB to establish a multi-agent system. The multi-agent system consists of eight agents, divided into two leaders and six followers. The dynamic model x of each multi-agent is constructed according to formula (1) and formula (2): i (t) = [x i1 (t),x i2 (t),x i3 (t)] T , where x i1 (t),x i2 (t),x i3 (t) The intelligent agent represents the state of the X-axis, Y-axis, and Z-axis respectively. The control input of the six followers is u i (t)=[u i1 (t),u i2 (t)] T , the control inputs of the two leaders

[0113] r 7 =[0.1sin(t)+0.1,0.1sin(t+1)-0.1] T ,r 8 =[0.2sin(t)+0.2,0.2sin(t+1)-0.2] T .

[0114] The fault simulation model satisfies formula (1). For each agent, set r i =0.5,η i =0.5, μ i =0.5,σ i (t) = 10e -0.9t ,

[0115] The executor failure parameters of the followers are set to:

[0116] ρ 1 (t) = diag{1,1}, u b1 (t)=[-0.2sin(t),-0.2cos(t)], u b2 (t) = [0, 0], ρ 2 (t) = diag{1,1},

[0117] u b3 (t) = [0, 0], ρ 3 (t)=diag{0.8-0.2sin(t),0.5+0.2cos(t)},

[0118] u b4 (t)=[0,0],ρ 4(t) = diag{1,1}, ρ 5 (t) = diag{0.5 + 0.2e -0.2t ,0.5+0.1cos(t)},

[0119] u b5 (t) = [-0.2-0.2e -0.1t ,0.2cos(t)],ρ 6 (t) = diag{1,1}, u b6 (t)=[0,0].

[0120] The expected states of the follower agents are:

[0121]

[0122] The constant matrices A and B are,

[0123]

[0124] The multi-agent communication topology graph set X contains G 1 , G 2 The two spanning tree formation topologies correspond to Figure 2 and Figure 3 The connection weight between each agent is 0 or 1, 0 means no connection, 1 means connection, Figure 4 Indicates the switching topology signal, and the switching period is set to 10s. Figure 5 It can be seen that the error of the follower approaches 0. According to the feasibility condition of the formation, the compensation input v can be obtained i (t).

[0125]

[0126] The positive definite matrix P obtained by linear inequalities is.

[0127]

[0128] This invention studies the formation tracking control under actuator failure, and takes into account the bias failure and unknown failure of the actuator so that the multi-agent system can still form the expected formation and track the leader when the follower actuator fails.

[0129] The present invention considers that a multi-agent system with multiple leaders has stronger robustness than a single leader and is more complex to study. For example, taking an unmanned vehicle as an example, if the tracking target is a given unmanned vehicle, the failure of the unmanned vehicle will cause the collapse of the entire formation. However, in the case of multiple leaders, if some leader unmanned vehicles fail, the remaining leader unmanned vehicles can be regarded as new tracking targets and the mission can continue.

[0130] The multi-agent system of the present invention is a time-varying multi-agent of high order. Compared with the time-invariant system, the time-varying system is more robust and more complex to study. In the process of designing the fault-tolerant formation tracking control protocol, there is formation information and its derivative information, so the study of time-varying formations is more challenging.

[0131] The topology considered in the present invention is a switching topology, which is more robust than a fixed topology because the interactive topology of the multi-agent system may switch when there is an obstacle blocking or a communication device link failure.

[0132] The method adopted by the present invention is the leader-follower method. Compared with the formation control method, the leader-follower method can better control the center.

[0133] Those skilled in the art should understand that the above embodiments are only preferred embodiments of the present invention, and the detailed description is only to help readers better understand the spirit of the present invention, but not to limit the scope of protection of the present invention. On the contrary, any improvements or modifications based on the spirit of the present invention should fall within the scope of protection of the present invention.

Claims

1. A multi-agent fault-tolerant formation tracking control method under multiple leaders and switching topology, It is characterized in that It includes the following steps: (1) Determine leaders and followers based on the spatial distribution of agents; (2) Determine the fault type based on the fault information obtained during the external switching topology, and add the fault model to the follower's dynamic model; (3) construct the topological interaction structure between leaders and followers; (4) Construct a fault-tolerant time-varying formation tracking control protocol based on the adjacent errors between agents; The fault-tolerant time-varying formation tracking control protocol is: in, and is an adaptability parameter, P is a positive definite matrix; The positive definite matrix P is given by the linear inequality Find, where the linear inequality (A,B) is stable and (5) Obtain the feasibility conditions required for multi-agents to complete formation tracking; The compensation input v of the feasibility condition of the formation i (t), through Solve, assuming that there is a compensation input v i (t) If the above formula is satisfied, the process can continue. Otherwise, the formation formed is not feasible for the multi-agent system under the fault-tolerant protocol. (6) Based on the leader and follower model in multi-agents, the topological relationship of set X, and the feasibility conditions of the formation, a multi-agent model for fault-tolerant time-varying formation tracking is designed, and the parameters required in the adaptive update formula are given; set X represents the topological set that the multi-agents may form; The adaptive parameters include Calculated by the following formulas: The local formation tracking error ξ of the fault-tolerant control protocol is i (t) i∈F is calculated by the following formula: Among them, the coordination variable θ i (t) is based on the expected time-varying formation h i (t) is defined, and the coordination variable of the formation is defined as θ i (t) = x i (t)-h i (t) i∈F; M is the number of agents, N is the number of followers; F=[1,2,............,N] and E=[N+1,N+2,.........,M] represent the set of followers and leaders respectively; During multi-agent operation, the time-varying formation offset vector h of the followers is i (t), the following conditions need to be satisfied: For any given bounded initial state, if there exists a positive constant a k , k∈E satisfies Formation tracking control with multiple leaders can be achieved; represents the formation reference function; (7) Construct the control model of the intelligent agent to realize fault-tolerant time-varying formation tracking control under multiple leaders and switching topologies; follower dynamics model with actuator failure: ρ i (t) is an unknown failure, u bi (t) is bias fault; x i (t)∈R n represents the state vector of follower i, x k (t)∈R n Represents the state vector of leader k.

2. According to the multi-agent fault-tolerant formation tracking control method under multi-leader and switching topology according to claim 1, It is characterized in that In step (1), all informed followers are well-informed followers. The information exchange channel between followers is non-directional. For each uninformed follower, there is at least one well-informed follower connected to it. A multi-agent with no neighbors is called a leader. If the multi-agent has at least one neighbor, it is called a follower. If the follower's neighbor set contains a leader, it is called an informed follower. If it contains all leaders, it is called a well-informed follower. If its neighbor set does not include a leader, it is called an uninformed follower.

3. According to the multi-agent fault-tolerant formation tracking control method under multi-leader and switching topology described in claim 1, It is characterized in that In step (2), the actuator fault model is defined as follows: in, represents the output of the actuator, u i ∈R m represents the input of the actuator, u bi (t)∈R m represents the actuator bias fault, ρ i (t) = diag[ρ i1 (t),ρ i2 (t),.....,ρ im (t)] and 0<ρ id (t)≤1 represents unknown efficiency fault of actuator channel d (d=1,2,.....,m); The fault types are divided into four types: Case 1: When ρ id (t)=1 and u bid (t) = 0 There is no fault in the system; Case 2: When 0<ρ id (t)<1 and u bid When (t) = 0, only failure occurs; Case 3: When ρ id (t)=1 and u bid When (t)≠0, the system only has a bias fault; Case 4: When 0<ρ id (t)<1 and u bid When (t)≠0, the system has both failure fault and bias fault.

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