Distributed robust control method based on semi-quasi position feedback

Abstract

The invention discloses a distributed robust control method based on semi-quasi position feedback. The method comprises the following steps: establishing a state-space equation of a multi-agent system; establishing a polynomial path to describe a reference path of the multi-agent system, and constructing a virtual leader system; establishing a switching communication network of the multi-agent system and the virtual leader system; constructing an output-based distributed observer, and estimating a polynomial path by using neighbor agent information; establishing a semi-quasi position estimator to generate a semi-quasi position for each agent; defining a new equivalent error of the intelligent agent; and according to the estimated polynomial path and the semi-quasi position, establishing a multiple internal model and robust internal model controller to realize control tracking of a reference trajectory. According to the method, the robustness of the system is ensured, the formation task is effectively completed, the adaptability and recovery capability of the multi-agent system in an unstable communication environment are enhanced, the space positioning capability of the system is optimized, and the performance and reliability of the multi-agent system in a dynamic environment are improved.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent systems, and in particular to a distributed robust control method based on semi-quasi-position feedback. Background Art

[0002] In the past two decades, the field of cooperative control of multi-agent systems has received extensive attention and achieved remarkable research results. These results have been widely applied in many fields, including unmanned aerial vehicles and unmanned mobile robots in collaborative search, escort, positioning and mapping tasks. In particular, the formation motion of multi-agent systems is crucial for performing many tasks, which requires each individual in the system to not only cooperate with each other, but also maintain an ideal relative position or orientation with each other while following a common reference path.

[0003] At present, the existing control methods for dealing with formation problems can be divided into three main categories: the first category is behavior-based methods, which are applicable to four basic formations such as straight lines, columns, wedges and diamonds, and achieve guidance and formation by designing and weighting different motion schemas; the second category is the "leader-follower" method, which constructs a global formation through a series of pre-defined "leader-follower" tracking problems; the third category is the virtual structure method, which forms a formation by defining the static or dynamic relative position / orientation of each agent relative to the virtual leader. With the application of graph theory in the control of multi-agent systems, the virtual structure method has become a popular strategy for achieving distributed formation control over sparse and fragile communication networks.

[0004] In the prior art, there are documents that aim at the problem of formation control of multiple AUVs in complex underwater environments (Multi-AUV formation control based on blind zone concept to reduce communication volume Zhou Tian, ​​Kang Fengju, School of Navigation, Northwestern Polytechnical University, National Laboratory for Underwater Information Processing and Control, Northwestern Polytechnical University), and design a distributed collaborative control method for multiple AUVs using artificial potential fields and virtual navigators and introducing blind zone design. However, this method has limitations, and does not consider the situation where the absolute position is difficult to obtain in a satellite denial environment, and lacks consideration of system robustness in the case of unstable communication networks. Summary of the invention

[0005] The purpose of the present invention is to solve the distributed polynomial path tracking control problem of a multi-agent system composed of N agents, and to provide a distributed robust control method based on semi-quasi-position feedback. Through distributed observers and semi-quasi-position estimators, when the communication network is unstable and the absolute position information cannot be obtained, the polynomial path of the multi-agent system can still be effectively restored, and the global position of each agent can be estimated. In addition, a robust internal model controller is proposed to enhance the adaptability of the system in an unstable communication environment and improve the performance and reliability of the multi-agent system in a dynamic environment. The present invention not only solves the reliable communication dependence existing in the prior art, but also significantly improves the robustness and practicality of the system, and provides a new solution for the formation control of the multi-agent system. The method of the present invention can effectively deal with the problem of robust formation tracking control of a multi-agent system in an unreliable communication network where the absolute position information cannot be obtained.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A distributed robust control method based on semi-quasi-position feedback comprises the following steps:

[0008] S1. Establish the state space equation of the multi-agent system;

[0009] S2, establish a polynomial path to describe the reference path of the multi-agent system and build a virtual leader system;

[0010] S3, establish a switching communication network between the multi-agent system and the virtual leader system;

[0011] S4. Construct an output-based distributed observer to estimate polynomial paths using neighboring agent information;

[0012] S5, establish a semi-quasi-position estimator to generate a semi-quasi-position for each agent;

[0013] S6. Define a new equivalent error for the agent;

[0014] S7. Based on the estimated polynomial path and semi-quasi-position, multiple internal models and robust internal model controllers are established to achieve control tracking of the reference trajectory.

[0015] Furthermore, in step S1, a mathematical model is established for the multi-agent system. Considering a multi-agent system containing N agents, the kinematic equation of the i-th agent is described as:

[0016]

[0017] where p i (t), v i (t),u i (t)∈Rn They represent the position, velocity and control input of the ith agent in n-dimensional space, i = 1, ..., N, R represents the real number domain, For p i The derivative of (t), v i The derivative of (t), γ i1 , γ i2 , γ i3 ∈R are the unknown system parameters related to the position, speed, and control input of the ith agent, satisfying and Δγ ij They are γ ij The determined part and the uncertain part, j=1, 2, 3.

[0018] Furthermore, the state space equation of the multi-agent system moving in n-dimensional space is established, and the state x of the i-th agent is i (t) is defined as x i (t) = [p i (t) T v i (t) T ] T According to formula (1), the state space equation is as follows:

[0019]

[0020] in, For x i The derivative of (t), A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, C i is the output matrix of the ith agent, which satisfies the following in the real number field R:

[0021]

[0022] I n Represents an n-dimensional identity matrix, let is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part of the

[0023]

[0024] Furthermore, in step S2, a polynomial path is established to describe the reference path of the multi-agent system, and a virtual leader system is constructed. For time t, in the n-dimensional real number field R, the polynomial path r0(t)∈R n The description is as follows:

[0025] r0(t)=a m t m +a m-1 t m-1 +···+a1t+a0 (3);

[0026] Where m is a non-negative integer, indicating the order of the polynomial path; t m is the mth power of time t, a0,...,a m ∈R n is a constant vector of corresponding order, and the polynomial path r0(t) is generated by the following virtual leader system:

[0027]

[0028] Where Ξ is the modal matrix of the virtual leader system, ∏ is the output matrix of the virtual leader system, and I n represents an n-dimensional identity matrix. In the real number field R,

[0029]

[0030] π=[1 0 0…0 0]∈R 1×(m+1) ;

[0031] ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, represents the Kronecker product of the matrix, l0(t) represents the internal state of the virtual leader system, is the derivative of l0(t); in the n-dimensional real number field R, the local formation command of the i-th agent is r fi ∈R n , to describe the relative position relationship between the ith agent and the polynomial path r0(t).

[0032] Furthermore, in step S3, a switching communication network between the multi-agent system and the virtual leader system is established: a function σ(t) is defined that maps from time t∈[0,+∞) to a finite positive integer set M={1,…,m}, where m is the largest integer in the set and σ(t) is regarded as a piecewise constant switching signal; the multi-agent system includes N agents, and its communication network is represented by a switching graph Represents a node set Edge Set Node 0 is associated with the virtual leader, node i is associated with the i-th agent, i = 1,...,N; If and only if the jth agent can receive the information of the i-th agent at time t; let Representation switching diagram The weighted adjacency matrix of ij (t) is a matrix The element in the i+1th row and j+1th column represents the communication weight between node i and node j. Define the subgraph G of the switching graph σ(t) =(V,E σ(t) ), where the subgraph node set V = {1,.,N}, the subgraph edge set E σ(t) ={(i,j),i,j∈V,i≠j}, let there be a subsequence in the switching time series {t0,t1,t2,...} is the time label θ k The corresponding time satisfies the initial time label θ0 = 0, and any two adjacent time labels θ k+1 and θ k The corresponding time interval is less than β, β is the upper limit of the sub-sequence time interval; the joint graph The joint graph is composed of the union of switching graphs under multiple time series. Contains a directed spanning tree with node 0 as the root, let the subgraph G σ(t) is an undirected graph.

[0033] Furthermore, in step S4, an output-based distributed observer is constructed to estimate the polynomial path r0(t) using the information of neighboring agents, including:

[0034] According to the following algebraic Riccati equation, find its positive definite solution χ:

[0035] χξ T +ξχ-χπ T πχ+I m+1 =0 (5);

[0036] Among them, ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, ξ T is the transpose of the matrix ξ, I m+1 represents an m+1-dimensional identity matrix; let the observer gain matrix I n represents an n-dimensional identity matrix, i represents the i-th agent, N represents the total number of agents, i=1,...N, and the i-th agent's output-based distributed observer is:

[0037]

[0038] in, is the estimated value of l0(t) by the ith agent, express The derivative of , Ξ is the modal matrix of the virtual leader system, Π is the output matrix of the virtual leader system, a ij(t) represents the communication weight between the ith agent and the jth agent, r i (t) and r j (t) represent the estimated values ​​of the polynomial path r0(t) by agent i and agent j respectively, is the gain coefficient of the observer.

[0039] Furthermore, in step S5, the semi-quasi position estimator of the i-th agent is:

[0040]

[0041] in, and denote the semi-quasi positions of agent i and agent j respectively, express The derivative of i (t) and p j (t) represent the positions of agent i and agent j respectively, p ji (t) represents the relative position between agent i and agent j, v i (t) represents the speed of the ith agent, a ij (t) represents the communication weight between the ith agent and the jth agent, represents the estimator gain coefficient.

[0042] Furthermore, in step S6, the equivalent error of the i-th agent is Defined as:

[0043]

[0044] where r fi ∈R n is the local formation instruction of the ith agent, r i (t) represents the estimated value of the polynomial path r0(t) by agent i.

[0045] Furthermore, in step S7, multiple internal models are designed according to the estimated polynomial path and semi-quasi-position:

[0046] In the real number field R, let the matrix ξ is the one-dimensional modal matrix of the virtual leader system, and the vector The internal model designed for the virtual leader system is make Get multiple internal models (G1, G2), I n Represents an n-dimensional identity matrix.

[0047] Furthermore, a robust internal model controller is established based on the estimated polynomial path, semi-quasi-position and multiple internal models, as follows:

[0048]

[0049] in, is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part, C i is the output matrix of the ith agent, is the parameter matrix that combines the multiple internal models with the nominal part of the agent modal matrix, is the parameter matrix combining the multiple internal models with the nominal part of the agent control matrix;

[0050] Select the controller gain matrix K i =[K i1 K i2 ], for the system Perform pole placement so that the matrix The eigenvalues ​​of K all have negative real parts. i1 is the feedback matrix, K i2 is the feedforward matrix. Using the estimated information of the semi-quasi-position estimator Let the equivalent system state The robust internal model controller u of the i-th agent i (t) is:

[0051]

[0052] Among them, x i (t) is the state of the dynamic compensator, For x i The derivative of (t), v i (t),u i (t)∈R n Respectively represent the position and speed of the ith agent in n-dimensional space, is the equivalent error of the ith agent.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] Compared with the existing technology, the present invention comprehensively considers the problems of unreliable communication, inability to obtain absolute position information, and uncertainty in system model parameters, decouples the system dynamics, communication network, and control objectives, and proposes an efficient distributed robust control scheme, which effectively enhances the robustness of the multi-agent system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 A switching diagram of a communication network of an embodiment;

[0056] Figure 2 The performance diagram of the distributed observer in the embodiment under the unreliable communication network;

[0057] Figure 3 is a performance diagram of a semi-quasi-position estimator of an embodiment;

[0058] Figure 4 is the absolute tracking error graph of all agents in the embodiment;

[0059] Figure 5 A three-dimensional trajectory diagram of all agents in the embodiment;

[0060] Figure 6 The present invention is a flow chart of a distributed robust control method based on semi-quasi-position feedback according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the specific implementation of the present invention will be clearly and completely described below in combination with the embodiments and drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] like Figure 6 As shown, a distributed robust control method based on semi-quasi-position feedback comprises the following steps:

[0063] S1. Establish the state space equation of the multi-agent system and establish a mathematical model for the multi-agent system. Consider a multi-agent system containing N agents. The kinematic equation of the i-th, i=1,…,N agents is described as:

[0064]

[0065] where p i (t), v i (t),u i (t)∈R n They represent the position, velocity and control input of the ith agent in n-dimensional space, R represents the real number domain, For p i The derivative of (t), v i The derivative of (t), γ i1 , γ i2 , γ i3∈R are the unknown system parameters related to the position, speed, and control input of the ith agent, satisfying and Δγ ij They are γ ij The determined part and the uncertain part, j=1, 2, 3.

[0066] Establish the state space equation of the multi-agent system moving in n-dimensional space, and transform the state x of the i-th agent into i (t) is defined as x i (t) = [p i (t) T v i (t) T ] T According to formula (1), the state space equation is as follows:

[0067]

[0068] in, For x i The derivative of (t), A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, C i is the output matrix of the ith agent, which satisfies the following in the real number field R:

[0069]

[0070] I n Represents an n-dimensional identity matrix, let is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part of the

[0071]

[0072] S2. Establish a polynomial path to describe the reference path of the multi-agent system and build a virtual leader system. For time t, in the n-dimensional real number field R, the polynomial path r0(t)∈R n The description is as follows:

[0073] r0(t)=a m t m +a m-1 t m-1 +···+a1t+a0 (3);

[0074] Where m is a non-negative integer, indicating the order of the polynomial path; t m is the mth power of time t, a0,...,am ∈R n is a constant vector of corresponding order, and the polynomial path r0(t) is generated by the following virtual leader system:

[0075]

[0076] Where Ξ is the modal matrix of the virtual leader system, Π is the output matrix of the virtual leader system, and I n represents an n-dimensional identity matrix. In the real number field R,

[0077]

[0078] π=[1 0 0…0 0]∈R 1×(m+1) ;

[0079] ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, represents the Kronecker product of the matrix, l0(t) represents the internal state of the virtual leader system, is the derivative of l0(t); in the n-dimensional real number field R, the local formation command of the i-th agent is r fi ∈R n , to describe the relative position relationship between the ith agent and the polynomial path r0(t). The tracking error of the ith agent can be described as: e i (t) = p i (t)-r i (t)-r fi .

[0080] S3. Establish a switching communication network between the multi-agent system and the virtual leader system: define a function σ(t) that maps from time t∈[0,+∞) to a finite positive integer set M={1,…,m}, where m is the largest integer in the set and σ(t) is regarded as a piecewise constant switching signal; the multi-agent system contains N agents, and its communication network is represented by a switching graph Represents a node set Edge Set Node 0 is associated with the virtual leader, node i is associated with the i-th agent, i = 1,...,N; If and only if the jth agent can receive the information of the i-th agent at time t; let Representation switching diagram The weighted adjacency matrix of ij (t) is a matrix The element in row i+1 and column j+1 defines the subgraph G of the switching graph. σ(t) =(V,E σ(t)), where the subgraph node set V = {1,.,N}, the subgraph edge set E σ(t) ={(i,j),i,j∈V,i≠j}, let there be a subsequence in the switching time series {t0,t1,t2,...} is the time label θ k The corresponding time satisfies the initial time label θ0 = 0, and any two adjacent time labels θ k+1 and θ k The corresponding time interval is less than β, β is the upper limit of the sub-sequence time interval; the joint graph The joint graph is composed of the union of switching graphs under multiple time series. Contains a directed spanning tree with node 0 as the root, let the subgraph G σ(t) is an undirected graph.

[0081] S4. Construct an output-based distributed observer to estimate the polynomial path using neighboring agent information, including:

[0082] According to the following algebraic Riccati equation:

[0083] χξ T +ξχ-χπ T πχ+I m+1 =0 (5);

[0084] Find its positive solution χ. Where ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, ξ T is the transpose of the matrix ξ, I m+1 represents an m+1-dimensional identity matrix; let the observer gain matrix I n represents an n-dimensional identity matrix, i represents the i-th agent, N represents the total number of agents, I n Represents an n-dimensional identity matrix, and the distributed observer based on the output of the i-th agent is:

[0085]

[0086] in, is the estimated value of l0(t) by the ith agent, express The derivative of , Ξ is the modal matrix of the virtual leader system, Π is the output matrix of the virtual leader system, a ij (t) represents the communication weight between the ith agent and the jth agent, r i (t) and r j (t) represent the estimated values ​​of the polynomial path r0(t) by agent i and agent j respectively, is the gain coefficient of the observer.

[0087] S5. Establish a semi-quasi-position estimator to generate a semi-quasi-position for each agent. The semi-quasi-position estimator of the i-th agent is:

[0088]

[0089] in, and denote the semi-quasi positions of agent i and agent j respectively, express The derivative of i (t) and p j (t) represent the positions of agent i and agent j respectively, p ji (t) represents the relative position between agent i and agent j, v i (t) represents the speed of the ith agent, a ij (t) represents the communication weight between the ith agent and the jth agent, represents the estimator gain coefficient.

[0090] S6. Define the new equivalent error of the agent, the equivalent error of the i-th agent Defined as:

[0091]

[0092] where r fi ∈R n is the local formation instruction of the ith agent, r i (t) represents the estimated value of the polynomial path r0(t) by agent i.

[0093] S7. Based on the estimated polynomial path and semi-quasi-position, establish multiple internal models and robust internal model controllers to achieve reference trajectory tracking; design n-fold internal models:

[0094] In the real number field R, let the matrix ξ is the one-dimensional modal matrix of the virtual leader system, and the vector The internal model designed for the virtual leader system is make Get multiple internal models (G1, G2), I n Represents an n-dimensional identity matrix.

[0095] According to the estimated polynomial path, semi-quasi-position and multiple internal models, a robust internal model controller is established:

[0096]

[0097] in, is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part, C i is the output matrix of the ith agent, is the parameter matrix that combines the multiple internal models with the nominal part of the agent modal matrix, is the parameter matrix that combines the multiple internal models with the nominal part of the agent's control matrix.

[0098] Select the controller gain matrix K i =[K i1 K i2 ], for the system Perform pole placement so that the matrix The eigenvalues ​​of K all have negative real parts. i1 is the feedback matrix, K i2 is the feedforward matrix. Using the estimated information of the semi-quasi-position estimator Let the equivalent system state The robust internal model controller u of the i-th agent i (t) is:

[0099]

[0100] Among them, z i (t) is the state of the dynamic compensator, For z i The derivative of (t), v i (t),u i (t)∈R n Respectively represent the position and speed of the ith agent in n-dimensional space, is the equivalent error of the ith agent.

[0101] As a specific embodiment, in this embodiment, Matlab is used to simulate a cluster system composed of 4 intelligent agents.

[0102] Consider a multi-agent system consisting of N = 4 agents moving in n = 3-dimensional space. Set the parameters in the dynamic form of equation (1) to Δγ i1 ∈[-1, 1], Δγ i2 ∈[-2, 2], Δγ i3 ∈[-1, 1]. Set the initial position and velocity of each agent to p1(0)=[5 5 0] T , p2(0)=[5 -5 0] T, p3(0) = [-5 5 0] T , p4(0) = [-5 -5 0] T and v1(0) = [0 0.6 -0.6] T , v2(0)=[0.5 0 -0.2] T , v3(0) = [0.2 0.3 -0.1] T , v4(0) = [-0.1 -0.5 -0.4] T . Let the order of the polynomial path be m = 1, r0(t) = [-2t + 6 3t - 15 t] T , the matrix in formula (4) π=[1 0]. The local formation command of each agent in formula (5) is r f1 =[0 0 0] T , r f2 =[0 0 5] T , r f3 =[5 0 -3] T , r f4 =[-5 0 -3] T As an embodiment, the time interval for switching the communication network is 0.1s.

[0103] Solving the Riccati equation χξ T +ξχ-χπ T πχ+Ι m+1 = 0, the positive solution is make Select the gain μ in the output-based distributed observer (6) l = 10, select the gain in the semi-quasi-position estimator (7) Select K so that the poles of A+BK are configured to {-5, -5.5, -6, -6.5, -7, -7.5, -8, -8.5, -9, -9.5, -10, -10.5P, then

[0104]

[0105] The initial value of the control strategy, i.e. and z i Each component of (0) takes a random value from the interval [0,0.5].

[0106] The simulation results are as follows Figure 2-5 The estimated errors of the output-based distributed observer in the x-axis, y-axis, and z-axis directions are shown as follows: Figure 2 As shown in (a), (b) and (c), each agent can quickly estimate the polynomial path. The estimation errors of the semi-quasi-position estimator in the x-axis, y-axis and z-axis directions are respectively Figure 3 As shown in (a), (b) and (c) in Figure 1, the difference between the actual position and the semi-precise position of all agents will converge to a common constant vector. In this case, the constant vector is very close to zero. The absolute tracking errors of all agents in the x-axis, y-axis and z-axis directions are respectively Figure 4 As shown in (a), (b) and (c) in Figure 1, it can be seen that the absolute tracking error of each agent also converges to a common constant vector. Finally, Figure 5 The three-dimensional trajectories of all agents are drawn in the figure, and the multi-agent system achieves the desired formation control effect.

[0107] The above examples are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above examples. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A distributed robust control method based on semi-quasi-position feedback, characterized in that: The following steps are involved: S1. Establish the state space equation of the multi-agent system; S2, establish a polynomial path to describe the reference path of the multi-agent system and build a virtual leader system; S3, establish a switching communication network between the multi-agent system and the virtual leader system; S4. Construct an output-based distributed observer to estimate polynomial paths using neighboring agent information; S5, establish a semi-quasi-position estimator to generate a semi-quasi-position for each agent; S6. Define a new equivalent error for the agent; S7. Based on the estimated polynomial path and semi-quasi-position, multiple internal models and robust internal model controllers are established to achieve control tracking of the reference trajectory.

2. A distributed robust control method based on semi-quasi-position feedback according to claim 1, characterized in that: In step S1, a mathematical model is established for the multi-agent system. Consider a multi-agent system containing N agents. The kinematic equation of the i-th agent is described as: where p i (t), v i (t),u i (t)∈R n They represent the position, velocity and control input of the ith agent in n-dimensional space, i=1,...,N, R represents the real number domain, For p i The derivative of (t), v i The derivative of (t), γ i1 , γ i2 , γ i3 ∈R are the unknown system parameters related to the position, speed, and control input of the ith agent, satisfying and Δγ ij They are γ ij The determined part and the uncertain part, j=1, 2, 3.

3. A distributed robust control method based on semi-quasi-position feedback according to claim 2, characterized in that: Establish the state space equation of the multi-agent system moving in n-dimensional space, and transform the state x of the i-th agent into i (t) is defined as x i (t) = [p i (t) T v i (t) T ] T According to formula (1), the state space equation is as follows: in, For x i The derivative of (t), A i is the modal matrix of the ith agent, B i is the control matrix of the ith agent, C i is the output matrix of the ith agent, which satisfies the following in the real number field R: I n Represents an n-dimensional identity matrix, let is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part of the 4. A distributed robust control method based on semi-quasi-position feedback according to claim 1, characterized in that: In step S2, a polynomial path is established to describe the reference path of the multi-agent system and a virtual leader system is constructed. For time t, in the n-dimensional real number field R, the polynomial path r0(t)∈R n The description is as follows: r0(t)=a m t m +a m-1 t m-1 +···+a1t+a0 (3); Where m is a non-negative integer, indicating the order of the polynomial path; t m is the mth power of time t, a0,...,a m ∈R n is a constant vector of corresponding order, and the polynomial path r0(t) is generated by the following virtual leader system: Among them, Ξ is the modal matrix of the virtual leader system, Π is the output matrix of the virtual leader system, In represents an n-dimensional identity matrix, in the real number field R, π＝[1 0 0 … 0 0]∈R 1×(m+1) ； ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, represents the Kronecker product of the matrix, l0(t) represents the internal state of the virtual leader system, is the derivative of l0(t); in the n-dimensional real number field R, the local formation command of the i-th agent is r fi ∈R n , to describe the relative position relationship between the ith agent and the polynomial path r0(t).

5. The distributed robust control method based on semi-quasi-position feedback according to claim 1, characterized in that: In step S3, a switching communication network between the multi-agent system and the virtual leader system is established: a function σ(t) is defined that maps from time t∈[0, +∞) to a finite positive integer set M={1, ..., m}, where m is the largest integer in the set and σ(t) is regarded as a piecewise constant switching signal; the multi-agent system contains N agents, and its communication network is represented by a switching graph Represents a node set Edge Set Node 0 is associated with the virtual leader, node i is associated with the i-th agent, i=1,...,N; If and only if the jth agent can receive the information of the i-th agent at time t; let Representation switching diagram The weighted adjacency matrix of ij (t) is a matrix The element in row i+1 and column j+1 represents the communication weight between node i and node j, defining the subgraph G of the switching graph. σ(t) =(V, E σ(t) ), where the subgraph node set V = {1, ., N}, the subgraph edge set E σ(t) ={(i, j), i, j∈V, i≠j}, let there be a subsequence in the switching time sequence {t0, t1, t2, ...} is the time label θ k The corresponding time satisfies the initial time label θ0 = 0, and any two adjacent time labels θ k+1 and θ k The corresponding time interval is less than β, β is the upper limit of the sub-sequence time interval; the joint graph The joint graph is composed of the union of switching graphs under multiple time series. Contains a directed spanning tree with node 0 as the root, let the subgraph G σ(t) is an undirected graph.

6. A distributed robust control method based on semi-quasi-position feedback according to claim 5, characterized in that: In step S4, an output-based distributed observer is constructed to estimate the polynomial path r0(t) using the information of neighboring agents, including: According to the following algebraic Riccati equation, find its positive definite solution χ: xx T +xx-xp T eg+I m+1 =0 (5); Among them, ξ is the one-dimensional modal matrix of the virtual leader system, π is the one-dimensional output matrix of the virtual leader system, ξ T is the transpose of matrix ξ, Im + 1 represents an m+1-dimensional identity matrix; let the observer gain matrix In represents an n-dimensional identity matrix, i represents the i-th agent, N represents the total number of agents, i=1,...N, and the i-th agent's output-based distributed observer is: in, is the estimated value of l0(t) by the ith agent, express The derivative of , Ξ is the modal matrix of the virtual leader system, Π is the output matrix of the virtual leader system, a ij (t) represents the communication weight between the ith agent and the jth agent, r i (t) and r j (t) represent the estimated values ​​of the polynomial path r0(t) by agent i and agent j, respectively, μ l >0 is the gain coefficient of the observer.

7. A distributed robust control method based on semi-quasi-position feedback according to claim 6, characterized in that: In step S5, the semi-quasi position estimator of the i-th agent is: in, and denote the semi-quasi positions of agent i and agent , respectively, express The derivative of i (t) and p j (t) represent the positions of agent i and agent j respectively, p ji (t) represents the relative position between agent i and agent j, v i (t) represents the speed of the ith agent, a ij (t) represents the communication weight between the ith agent and the jth agent, represents the estimator gain coefficient.

8. A distributed robust control method based on semi-quasi-position feedback according to claim 7, characterized in that: In step S6, the equivalent error of the i-th agent is Defined as: where r fi ∈R n is the local formation instruction of the ith agent, r i (t) represents the estimated value of the polynomial path r0(t) by agent i.

9. The distributed robust control method based on semi-quasi-position feedback according to claim 1, characterized in that: In step S7, multiple internal models are designed based on the estimated polynomial path and semi-quasi-position: In the real number field R, let the matrix ξ is the one-dimensional modal matrix of the virtual leader system, and the vector The internal model designed for the virtual leader system is make Get multiple internal models (G1, G2), I n Represents an n-dimensional identity matrix.

10. A distributed robust control method based on semi-quasi-position feedback according to claim 9, characterized in that: According to the estimated polynomial path, semi-quasi-position and multiple internal models, a robust internal model controller is established: in, is the modal matrix A of the ith agent i The nominal part of is the control matrix B of the ith agent i The nominal part, C i is the output matrix of the ith agent, is the parameter matrix that combines the multiple internal models with the nominal part of the agent modal matrix, is the parameter matrix combining the multiple internal models with the nominal part of the agent control matrix; Select the controller gain matrix K i =[K i1 K i2 ], for the system Perform pole placement so that the matrix The eigenvalues ​​of K all have negative real parts. i1 is the feedback matrix, K i2 is the feedforward matrix, using the estimated information of the semi-quasi-position estimator Let the equivalent system state The robust internal model controller u of the i-th agent i (t) is: Among them, z i (t) is the state of the dynamic compensator, For z i The derivative of (t), v i (t),u i (t)∈R n Respectively represent the position and speed of the ith agent in n-dimensional space, is the equivalent error of the ith agent.

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