A cooperative formation control method based on distributed filtering synchronization estimator

Abstract

The present invention discloses a collaborative formation control method based on a distributed filtering synchronization estimator, comprising the following steps: constructing the state space equation of an intelligent agent according to its mathematical model; defining a global instruction system and generating a global reference instruction; establishing a communication network for a multi-agent system and modeling the channel perturbation of the global reference instruction; constructing a distributed filtering synchronization estimator based on a disturbed output for the global reference instruction affected by the channel perturbation; solving the regulator equation to obtain a feedforward gain matrix of a deterministic equivalent output feedback controller; designing a deterministic equivalent output feedback controller to generate the control input of the intelligent agent, thereby achieving the desired formation control effect. The present invention proposes a type of distributed filtering synchronization estimator based on a disturbed output and designs a distributed deterministic equivalent controller to achieve closed-loop system stability and the intelligent agent motion trajectory approaches the set trajectory, which has broad application prospects.

Description

Technical Field

[0001] The present invention relates to the field of flight control technology, and in particular to a collaborative formation control method based on a distributed filtering synchronization estimator. Background Art

[0002] With the rapid development of science and technology, multi-agent systems have become a core area of ​​research in automation, robotics, and artificial intelligence. These systems typically consist of multiple agents that can act independently yet coordinate with each other, such as drone formations, autonomous vehicle fleets, and multi-robot collaborative operations. Formation control is a crucial technology in these systems, requiring the agents to maintain specific relative positions and postures according to predetermined formations or mission requirements in order to complete complex collaborative tasks.

[0003] However, formation control in multi-agent systems faces numerous challenges. First, ensuring formation stability and accuracy is challenging given the uncertainty of each agent's state information and the influence of multiple factors such as communication interference. Second, as the number of agents increases, the system's complexity and computational burden rise dramatically, making traditional centralized control methods difficult to meet real-time and scalability requirements.

[0004] To overcome these challenges, a paper (UAV Formation Collaborative Navigation Algorithm Based on Improved Particle Filter, Jing Xuan, Wang Hongru, Zhu Dongqin, Aleksandr Chupalov, School of Information and Communication Engineering, Harbin Engineering University) proposed an improved particle filter (PF) algorithm to improve navigation accuracy, addressing the problem of poor performance of master-slave UAV collaborative navigation in complex environments due to time-varying non-Gaussian noise generated by external interference. However, this approach has limitations. The single-master architecture is overly dependent on the host and does not fully utilize local observation information while eliminating the influence of channel disturbances. Summary of the Invention

[0005] The purpose of the present invention is to solve the above-mentioned defects in the prior art and provide a collaborative formation control method based on a distributed filtering synchronization estimator. It utilizes local observation information and realizes accurate estimation of the global state or specific target of the system through communication and collaboration between intelligent agents. It solves the distributed formation control problem of a class of linear multi-agent systems under the influence of communication interference, which not only improves the robustness and fault tolerance of the system, but also improves the performance and reliability of the multi-agent system in a dynamic environment, and provides a new solution for the formation control of the multi-agent system.

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

[0007] A coordinated formation control method based on a distributed filtering synchronization estimator comprises the following steps:

[0008] Step 1: Construct the state space equation of the intelligent agent based on its mathematical model;

[0009] Step 2: Define the global instruction system and generate global reference instructions;

[0010] Step 3: Establish a communication network for the multi-agent system and model the channel perturbations of the global reference instructions;

[0011] Step 4: For the global reference instruction affected by the channel disturbance, a distributed filtering synchronization estimator based on the disturbed output is constructed;

[0012] Step 5: Solve the regulator equation to obtain the feedforward gain matrix of the equivalent output feedback controller;

[0013] Step 6: Design and determine the equivalent output feedback controller to generate the control input of the intelligent agent, thereby achieving the desired formation control effect.

[0014] Furthermore, in step 1, the mathematical model of the i-th agent is described by the following second-order system:

[0015]

[0016] y mi (t) = p i (t)+ζ i3 (t);

[0017] Where i=1,...,N, N represents the number of agents, u i (t), y mi (t)∈R p Represent the control input and measurement position vector of the i-th agent in the p-dimensional space, and p i (t) and v i (t) The derivative with respect to time t, ζ i1 (t),ζ i2 (t),ζ i3 (t)∈R p Respectively represent the action on the position p of the i-th agent i (t), speed v i (t) and measurement position y mi (t), R represents the real number domain; p i (t), v i (t)∈R p They represent the position and speed of the i-th agent in the p-dimensional space, and t represents time;

[0018] The second-order system of the intelligent agent is transformed into the form of a general linear system, and its state space equation is:

[0019]

[0020] y mi (t) = C mi x i (t)+D mi u i (t)+F mdi d i (t);

[0021] y i (t) = C i x i (t);

[0022] Among them, x i (t)=[p i (t) T v i (t) T ] T represents the state of the i-th agent, y i (t) = p i (t) represents the position of the i-th agent, d i (t) = [ζ i1 (t) T ζ i2 (t) T ζ i2 (t) T ] T represents the interference vector acting on the i-th agent model, is x i (t) derivative with respect to time t; A i is the modal matrix of the u-th agent, B i is the input matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i is the output matrix of the ith agent, satisfying:

[0023]

[0024] D mi =0,

[0025] Ip Denote the p - order identity matrix, Denote the Kronecker product of matrices.

[0026] Furthermore, for the interference vector d i (t) acting on the i - th agent model, construct the system interference model. The system interference model of the i - th agent is described as:

[0027]

[0028] d i (t)=φ di h di (t);

[0029] where, Denote the state vector of the i - th agent system interference model, q di is a constant, denoting the dimension of the state vector of the i - th agent system interference model, R denotes the real number field, is the derivative of h di (t) with respect to time t, Φ di is the modal matrix of the i - th agent system interference model, φ di is the output matrix of the i - th agent system interference model.

[0030] Furthermore, in step 2, define the global instruction system, generate the global reference instruction, define the offset instruction system and the desired travel path of each agent. The global instruction system is defined as follows:

[0031]

[0032] y0(t)=ψ0g0(t);

[0033] where, g0(t)∈R q is the q - dimensional state vector of the global instruction system, is the derivative of g0(t) with respect to time t, y0(t)∈R p denotes the p - dimensional global instruction system output vector, Ψ0 is the modal matrix of the global instruction system, ψ0 is the output matrix of the global instruction system; Assume the minimal polynomial of the matrix Ψ0 is:

[0034] λ l +α 01 λ l-1 +…+α 0(l-1) λ+α 0l ;

[0035] where, l < q represents the order of the minimal polynomial of Ψ0, α 01 ,...,α 0llThe coefficients of the Ψ0 minimal polynomial are defined as the l-dimensional coefficient vector α0=[α 01 ,...,α 0l ] T ∈R l , the global reference instruction χ0(t) is defined as χ0(t) = [α0 T y0(t) T ] T ∈R l+p ;

[0036] The offset command system of the i-th agent is:

[0037]

[0038] in, is the state vector of the offset instruction system, q bi is a constant representing the dimension of the state vector of the i-th agent offset command system, It is h bi The derivative of (t) with respect to time t, represents the p-dimensional offset instruction of the ith agent relative to the global instruction system output vector y0(t), Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset command system, and the expected path vector y of the i-th agent ri (t)∈R p Described as: The trajectory error e of the i-th agent i (t)∈R p Described as: i (t) = y i (t)-y ri (t).

[0039] Furthermore, in step 3, the global command system and the multi-agent system are considered as an augmented system, and the communication network is represented by a directed graph. Represents a node set Where N represents the number of agents, node 0 represents the global command system, node i, i=1,…,N represents the i-th agent, and edge set When the i-th agent obtains the information of the j-th agent, The jth (i≠j) agent is called the neighbor of the i-th agent, i≠j; let Represents the set of all neighbors of the ith agent, with a directed graph The weighted adjacency matrix of a ij Represents the communication weight coefficient between node i and node j. When aij >0, otherwise a ij =0, directed graph Contains a directed spanning tree with the global command system as the root node.

[0040] Furthermore, the channel perturbation acting on the global reference instruction is modeled as follows:

[0041]

[0042] in, represents the l+p-dimensional channel perturbation vector acting on the global reference instruction χ0(t), R represents the real number field, represents the channel perturbation vector acting on α0, Denotes the channel perturbation vector acting on y0(t), let represents the modal information in the disturbed global reference instructions that the agent can receive, represents the output information in the disturbed global reference instruction that the agent can receive, and satisfy:

[0043]

[0044] For τ=1,...,l+p, the channel perturbation vector Each element has the same form:

[0045]

[0046] in, represents the channel perturbation vector The τth element of the channel perturbation vector Contains σ different channel perturbation frequencies; Indicates the The frequency of the channel disturbance, The channel disturbance frequencies are all known; is the unknown disturbance amplitude, is the unknown initial phase of the disturbance; for m=ω1,...,ω σ , a two-dimensional square matrix Define the channel perturbation frequency vector Ω=[ω1...ω σ ] T ∈R σ , define the channel perturbation matrix

[0047] Furthermore, using the disturbed global reference instruction Design the first part of the distributed filtering synchronization estimator based on the disturbed output, estimating The truth value of is defined as:

[0048]

[0049] γ ρ =[1 1 0…1 0]∈R 1×(1+2σ) ;

[0050] Ξ ρ =[1 0 0…0 0]∈R 1x(1+2σ) ;

[0051] Among them, Λ ρ is the modal matrix of the first part of the estimator, is the channel perturbation matrix, γ ρ is the simulated perturbation matrix of the first part of the estimator, Ξ ρ is the output matrix of the first part of the estimator, σ is the number of channel perturbation frequencies, R (1 +2σ)×(1+2σ) represents a (1+2σ)×(1+2σ) dimensional real matrix, R 1×(1+2σ) Represents a 1×(1+2σ)-dimensional real row vector, because (γ ρ ,Λ ρ ) can be observed, as follows:

[0052]

[0053] The only positive solution of ρ , I 1+2σ is the identity matrix of 1+2σ dimensions. According to the solution of the algebraic Riccati equation P ρ , further design the gain matrix of the first part of the estimator μ α >0 is the gain coefficient of the estimator; l is the order of the Ψ0 minimal polynomial. For each element k=1,...,l in the Ψ0 minimal polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as:

[0054]

[0055] α i (t) = Ξ ρ ρ i (t);

[0056] Where N represents the number of agents, ρ i (t)∈R (1+2σ)×l represents the (1+2σ)×l-dimensional state matrix of the first part of the i-th intelligent estimator; ρ ik (t)∈R 1+2σ is the matrix ρ i(t) column vector of the kth column; is ρ i (t) derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; Represents the i-th smart pair Estimates, represents the jth smart pair Estimates, represents the modal information in the disturbed global reference instructions that the agent can receive, express The kth element of Yes The estimate of the kth element in ; α i (t)∈R 1×l is the output of the first part of the estimator, which represents the T , α0 is the l-dimensional coefficient vector of the minimum polynomial of the coefficient matrix Ψ0 of the global instruction system.

[0057] Furthermore, using the disturbed global reference instruction and the estimated value α i (t), design the second part of the distributed filtering synchronization estimator based on the disturbed output, and estimate The truth value of is defined as:

[0058]

[0059] Among them, Θ i (t) is the simulation equivalent matrix of Ψ0; α i1 (t),…,α il (t) are the output of the first part of the estimator α i The first,…,lth element of (t); l is the order of the Ψ0 minimal polynomial; θ is the simulation equivalent matrix of ψ0; is the modal matrix of the second part of the estimator; is the channel perturbation matrix; is the simulated disturbed matrix of the second part of the estimator; is the output matrix of the second part of the estimator; R l×l Represents an l×l dimensional real matrix, R 1×l represents a 1×l-dimensional real row vector, R (l+2σ)×(l+2σ) represents a (l+2σ)×(l+2σ)-dimensional real matrix, σ is the number of channel perturbation frequencies, R 1×(l+2σ) represents a 1×(l+2σ)-dimensional real row vector;

[0060] Defining the estimator gain in is the algebraic Riccati equation:

[0061]

[0062] The positive solution of I l+2σ is the identity matrix of dimension l+2σ, is the gain coefficient of the estimator;

[0063] In the p-dimensional space, for each dimension ε = 1, ..., p, the second part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as:

[0064]

[0065] Where N represents the number of agents, represents the state matrix of the second part of the ith agent estimator (l+2σ)×p dimensions; is a matrix The column vector of the ε-th column; yes The derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; ξ i (t)∈R 1×p Represents the i-th agent pair Estimate of ξ j (t)∈R 1×p Represents the j-th agent pair estimates; represents the output information in the disturbed global reference instruction that the agent can receive; ξ iε (t) represents ξ i The εth element of (t), ξ iε (t) is correct The estimate of the εth element in ; is the output of the second part of the estimator, which represents the estimate of y0(t), and y0(t) represents the output vector of the global command system.

[0066] Furthermore, the regulator equation is solved to obtain the feedforward gain matrix of the deterministic equivalent output feedback controller. The regulator equation related to the disturbance model of the i-th agent system is:

[0067] X di Φ di =A i X di +B i U di +Edi φ di ;

[0068] 0=C i X di ;

[0069] Among them, A i is the modal matrix of the ith agent, B i is the input matrix of the i-th agent, E di is the interference matrix of the i-th agent, C i is the output matrix of the i-th agent, Φ di is the modal matrix of the interference model of the i-th agent system, φ di The output matrix of the interference model of the i-th agent system, X di is the state solution of the regulator equation associated with the disturbance model of the i-th agent system, U di Enter the solution to the regulator equation associated with the disturbance model of the ith agent system. The regulator equation associated with the ith agent offset command system is:

[0070] X bi Φ bi =A i X bi +B i U bi ;

[0071] 0=C i X bi -φ bi ;

[0072] Among them, Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset instruction system, X bi is the state solution of the regulator equation associated with the offset command system of the i-th agent, U bi Input the solution to the regulator equation associated with the i-th agent offset command system and design the controller feedforward gain matrix K associated with the system disturbance model di =U di -K xi X di , the controller feedforward gain matrix K associated with the offset command system bi =U bi -K xi X bi .

[0073] Furthermore, an equivalent output feedback controller is designed to generate the control input of the intelligent agent, thereby achieving the desired formation control effect:

[0074] Define the related operator symbols col, vec and M:

[0075] Suppose there are m column vectors β1,…,β m , define the operator col(β1,…,β m )=[β1 T ,…,β m T ] T , β1 T ,…,β m T denote β1,…,β m The transpose of

[0076] Suppose there is an m×n dimensional matrix Υ, and the operator vec(Υ)=col(γ1,…,γ n ),γ1,…,γ n are the 1st,…,nth columns of the matrix Y respectively;

[0077] Suppose there is an mn-dimensional column vector Defining operators in are all n-dimensional column vectors and satisfy column vector

[0078] Select feedback gain K xi Make A i +B i K xi is the Hurwitz matrix, and the observer gain matrix L is selected i Make is the Hurwitz matrix, the i-th intelligent deterministic equivalent output feedback controller u i (t) is:

[0079]

[0080] in is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the perturbation of the system state ω by the i-th agent di The estimated value of (t), for The derivative with respect to time t; K zi =[K xi ,K di ]; is the state vector of the feedforward compensator, is the gain coefficient of the feedforward compensator, the coefficient matrix represents the Kronecker product of matrices, the coefficient vector I p is the p-order identity matrix, Θ i (t) is the simulation equivalent matrix of Ψ0, θ is the simulation equivalent matrix of ψ0, I pl is the pl-order unit matrix, X Ψi (t) is the asymptotic state solution of the regulator equation associated with the global command system of the i-th agent, U Ψi (t) is the asymptotic input solution of the regulator equation associated with the global command system of the ith agent, is the operator, p is the dimension of the agent's motion space, l is the order of the Ψ0 minimum polynomial, and the controller feedforward gain matrix related to the global command system is Equivalent state of the global command system For κ=1,..,p, for The κth column of With the estimator state κth column vector Relevant, satisfying I l is the l-order identity matrix.

[0081] In summary, the present invention has the following advantages and beneficial effects over the prior art:

[0082] (1) A distributed filtering synchronization estimator based on the disturbed output is designed. By estimating the effective information and the disturbance information as a whole, the mixed signal can be decomposed and separated at the disturbance frequency point, and the true value of the effective information can be obtained.

[0083] (2) A distributed controller based on a communication network is designed for the multi-agent system, so that the closed-loop system can be stable for any system initial value and the system motion trajectory error approaches zero. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 is a directed graph describing a multi-agent system communication network in an embodiment of the present invention;

[0085] Figure 2 A diagram showing position changes of four agents in an embodiment of the present invention;

[0086] Figure 3 is an estimated error curve diagram of the global reference instruction y0(t) in an embodiment of the present invention;

[0087] Figure 4 is a trajectory error curve diagram of each intelligent agent in an embodiment of the present invention;

[0088] Figure 5 This is a flow chart of a cooperative formation control method based on a distributed filtering synchronization estimator according to an embodiment of the present invention; DETAILED DESCRIPTION

[0089] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the specific implementation of the present invention will be clearly and completely described below in conjunction 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 making creative efforts are within the scope of protection of the present invention.

[0090] like Figure 5 A cooperative formation control method based on a distributed filtering synchronization estimator is shown, comprising the following steps:

[0091] Step 1: Construct the state space equation of the intelligent agent based on its mathematical model;

[0092] The mathematical model of the i-th agent is described by the following second-order system:

[0093]

[0094] y mi (t) = p i (t)+ζ i3 (t);

[0095] Where i=1,...,N, N represents the number of agents, u i (t), y mi (t)∈R p Represent the control input and measurement position vector of the i-th agent in the p-dimensional space, and p i (t) and v i (t) The derivative with respect to time t, ζ i1 (t),ζ i2 (t),ζ i3 (t)∈R p Respectively represent the action on the position of the i-th agent [ i (t), speed v i (t) and measurement position y mi (t), R represents the real number domain; p i (t), v i (t)∈R p They represent the position and speed of the i-th agent in the p-dimensional space, and t represents time;

[0096] The second-order system of the intelligent agent is transformed into the form of a general linear system, and its state space equation is:

[0097]

[0098] y mi (t) = C mi x i (t)+D mi u i (t)+F mdi d i (t);

[0099] y i (t) = C i x i (t);

[0100] Among them, x i (t)=[p i (t) T v i (t) T ] T represents the state of the i-th agent, y i (t) = p i (t) represents the position of the i-th agent, d i (t) = [ζ ii (t) T ζ i2 (t) T ζ i2 (t) T ] T represents the interference vector acting on the i-th agent model, is x i (t) derivative with respect to time t; A i is the modal matrix of the ith agent, B i is the input matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i is the output matrix of the ith agent, satisfying:

[0101]

[0102] D mi =0,

[0103] I pDenote the p - order identity matrix, represent the Kronecker product of matrices.

[0104] For the interference vector d i (t) acting on the i - th agent model, construct the system interference model, and the interference model of the i - th agent system is described as:

[0105]

[0106] d i (t)=φ di h di (t);

[0107] Where, denote the state vector of the interference model of the i - th agent system, q di is a constant, representing the dimension of the state vector of the interference model of the i - th agent system, R represents the real number field, is the derivative of h di (r) with respect to time r, Φ di is the modal matrix of the interference model of the i - th agent system, φ di the output matrix of the interference model of the i - th agent system.

[0108] Step 2: Define the global instruction system, generate the global reference instruction, define the offset instruction system and the expected travel path of each agent. The global instruction system is defined as follows:

[0109]

[0110] y0(t)=ψ0g0(t);

[0111] Where, g0(t)∈R q is the q - dimensional state vector of the global instruction system, is the derivative of g0(t) with respect to time t, y0(t)∈R p represents the p - dimensional output vector of the global instruction system, Ψ0 is the modal matrix of the global instruction system, ψ0 is the output matrix of the global instruction system; Assume the minimal polynomial of the matrix Ψ0 is:

[0112] λ l +α 01 λ l-1 +…+α 0(l-1) λ+α 0l ;

[0113] Where, l < q represents the order of the minimal polynomial of Ψ0, α 01 ,...,α 0l are the coefficients of the minimal polynomial of Ψ0, define the l - dimensional coefficient vector α0 = [α01 ,...,α 0l ] T ∈R l , the global reference instruction χ0(t) is defined as χ0(t) = [α0 T y0(t) T ] T ∈R l+p ;

[0114] The offset command system of the i-th agent is:

[0115]

[0116] Among them, h bi (t)∈R qbi is the state vector of the offset instruction system, q bi is a constant representing the dimension of the state vector of the i-th agent offset command system, It is h bi The derivative of (t) with respect to time t, represents the p-dimensional offset instruction of the ith agent relative to the global instruction system output vector y0(t), Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset instruction system. At this time, the expected path vector y of the i-th agent ri (t)∈R p Described as: The trajectory error e of the i-th agent i (t)∈R p Described as: i (t) = y i (t)-y ri (t).

[0117] Step 3: Establish a communication network for the multi-agent system and model the channel perturbations of the global reference instructions;

[0118] The global command system and multi-agent system are regarded as an augmented system, and the communication network is represented by a directed graph. Represents a node set {0,1,…,N}, where N represents the number of agents, node 0 represents the global command system, node i, i=1,…,N represents the i-th agent, and edge set When the i-th agent obtains the information of the j-th agent, The jth (i≠j) agent is called the neighbor of the i-th agent, i≠j; let Represents the set of all neighbors of the ith agent, with a directed graph The weighted adjacency matrix of aij Represents the communication weight coefficient between node i and node j. When a ij >0, otherwise a ij =0, directed graph Contains a directed spanning tree with the global command system as the root node.

[0119] For the channel perturbation acting on the global reference instruction, model the channel perturbation of the global reference instruction:

[0120]

[0121] in, represents the l+p-dimensional channel perturbation vector acting on the global reference instruction χ0(t), R represents the real number field, represents the channel perturbation vector acting on α0, Denotes the channel perturbation vector acting on y0(t), let represents the modal information in the disturbed global reference instructions that the agent can receive, represents the output information in the disturbed global reference instruction that the agent can receive, and satisfy:

[0122]

[0123] For τ=1,...,l+p, the channel perturbation vector Each element has the same form:

[0124]

[0125] in, represents the channel perturbation vector The τth element of the channel perturbation vector Contains σ different channel perturbation frequencies; Indicates the The frequency of the channel disturbance, The channel disturbance frequencies are all known; is the unknown disturbance amplitude, is the unknown initial phase of the disturbance; for m=ω1,...,ω σ , a two-dimensional square matrix Define the channel perturbation frequency vector Ω=[ω1...ω σ ] T ∈R σ , define the channel perturbation matrix

[0126] Step 4: For the global reference instruction affected by the channel disturbance, a distributed filtering synchronization estimator based on the disturbed output is constructed;

[0127] Exploiting the disturbed global reference instruction Design the first part of the distributed filtering synchronization estimator based on the disturbed output, estimating The truth value of . Definition:

[0128]

[0129] γ ρ =[1 1 0…1 0]∈R 1×(1+2σ) ;

[0130] Ξ ρ =[1 0 0…0 0]∈R 1x(1+2σ) ;

[0131] Among them, Λ ρ is the modal matrix of the first part of the estimator, is the channel perturbation matrix, γ ρ is the simulated perturbation matrix of the first part of the estimator, Ξ ρ is the output matrix of the first part of the estimator, σ is the number of channel perturbation frequencies, R (1 +2σ)×(1+2σ) represents a (1+2σ)×(1+2σ) dimensional real matrix, R 1×(1+2σ) represents a 1×(1+2σ)-dimensional real row vector. ρ ,Λ ρ ) can be observed, as follows:

[0132] The only positive solution of ρ , I 1+2ρ is the identity matrix of 1+2σ dimensions. According to the solution of the algebraic Riccati equation P ρ , further design the gain matrix of the first part of the estimator is the gain coefficient of the estimator; l is the order of the Ψ0 minimal polynomial. For each element k=1,...,l in the Ψ0 minimal polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as:

[0133]

[0134] α i (t) = Ξ ρ ρ i (t);

[0135] Where N represents the number of agents, ρ i (t)∈R(1+2σ)×l represents the (1+2σ)×l-dimensional state matrix of the first part of the i-th intelligent estimator; ρ ik (t)∈R 1+2σ is the matrix ρ i (t) column vector of the kth column; is ρ i (t) derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; Represents the i-th smart pair Estimates, represents the jth smart pair Estimates, represents the modal information in the disturbed global reference instructions that the agent can receive, express The kth element of Yes The estimate of the kth element in ; α i (t)∈R 1×l is the output of the first part of the estimator, which represents the T , α0 is the l-dimensional coefficient vector of the minimum polynomial of the coefficient matrix Ψ0 of the global instruction system.

[0136] Exploiting the disturbed global reference instruction and the estimated value α i (t), design the second part of the distributed filtering synchronization estimator based on the disturbed output, and estimate The truth value of . Definition:

[0137]

[0138] Among them, Θ i (t) is the simulation equivalent matrix of Ψ0; α i1 (t),…,α il (t) are the output of the first part of the estimator α i The first,…,lth element of (r); l is the order of the Ψ0 minimal polynomial; θ is the simulation equivalent matrix of ψ0; is the modal matrix of the second part of the estimator; is the channel perturbation matrix; is the simulated disturbed matrix of the second part of the estimator; is the output matrix of the second part of the estimator; R l×l Represents an l×l dimensional real matrix, R 1×l represents a 1×l-dimensional real row vector, R (l+2ε)×(l+2ε)represents a (l+2σ)×(l+2σ)-dimensional real matrix, σ is the number of channel perturbation frequencies, R 1×(l+2σ) represents a 1×(l+2σ)-dimensional real row vector.

[0139] Defining the estimator gain in is the algebraic Riccati equation:

[0140] The positive solution of I l+2σ is the identity matrix of dimension l+2σ, is the gain coefficient of the estimator;

[0141] In the p-dimensional space, for each dimension ε = 1, ..., p, the second part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as:

[0142]

[0143] Where N represents the number of agents, represents the state matrix of the second part of the ith agent estimator (l+2σ)×p dimensions; is a matrix The column vector of the ε-th column; yes The derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; ξ i (t)∈R 1×p Represents the i-th agent pair Estimate of ξ j (t)∈R 1×p Represents the j-th agent pair estimates; represents the output information in the disturbed global reference instruction that the agent can receive; ξ iε (t) represents ξ i The εth element of (t), ξ iε (t) is correct The estimate of the εth element in ; is the output of the second part of the estimator, which represents the estimate of y0(t), and y0(t) represents the output vector of the global command system.

[0144] Step 5: Solve the regulator equation to obtain the feedforward gain matrix of the equivalent output feedback controller;

[0145] The regulator equation associated with the disturbance model of the ith agent system is:

[0146] X di Φ di =A i X di +B i U di +E di φ di ;

[0147] 0=C i X di ;

[0148] Among them, A i is the modal matrix of the ith agent, B i is the input matrix of the i-th agent, E di is the interference matrix of the i-th agent, C i is the output matrix of the i-th agent, Φ di is the modal matrix of the interference model of the i-th agent system, φ di The output matrix of the interference model of the i-th agent system, X di is the state solution of the regulator equation associated with the disturbance model of the i-th agent system, U di Enter the solution for the regulator equation associated with the disturbance model of the ith agent system. The regulator equation associated with the ith agent offset command system is:

[0149] X bi Φ bi =A i X bi +B i U bi ;

[0150] 0=C i X bi -φ bi ;

[0151] Among them, Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset instruction system, X bi is the state solution of the regulator equation associated with the offset command system of the i-th agent, U bi Enter the solution for the regulator equation associated with the i-th agent's offset command system. Design the controller feedforward gain matrix K associated with the system disturbance model. di =U di -K xi X di , the controller feedforward gain matrix K associated with the offset command system bi =U bi -K xi X bi .

[0152] Step 6: Design and determine the equivalent output feedback controller to generate the control input of the intelligent agent, thereby achieving the desired formation control effect.

[0153] Define the related operator symbols col, vec and M:

[0154] Suppose there are m column vectors β1,…,β m , define the operator col(β1,…,β m )=[β1 T ,…,β m T ] T , β1 T ,…,β m T denote β1,…,β m The transpose of

[0155] Suppose there is an m×n dimensional matrix Υ, and the operator vec(Υ)=col(γ1,…,γ n ),γ1,…,γ n are the 1st,…,nth columns of the matrix Y respectively;

[0156] Suppose there is an mn-dimensional column vector Defining operators in Are all n-dimensional column vectors and satisfy column vector

[0157] Select feedback gain K xi Make A i +B i K xi is the Hurwitz matrix, and the observer gain matrix L is selected i Make is the Hurwitz matrix, the i-th intelligent deterministic equivalent output feedback controller u i (t) is:

[0158]

[0159] in is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the i-th agent's response to the disturbance system state ω di The estimated value of (t), for The derivative with respect to time t; K zi=[K xi ,K di ]; is the state vector of the feedforward compensator, is the gain coefficient of the feedforward compensator, the coefficient matrix represents the Kronecker product of matrices, the coefficient vector I p is the p-order identity matrix, Θ i (t) is the simulation equivalent matrix of Ψ0, θ is the simulation equivalent matrix of ψ0, I pl is the pl-order unit matrix, X wi (t) is the asymptotic state solution of the regulator equation associated with the global command system of the i-th agent, U Ψi (t) is the asymptotic input solution of the regulator equation associated with the global command system of the ith agent, is the operator, p is the dimension of the agent's motion space, and l is the order of the Ψ0 minimal polynomial. The controller feedforward gain matrix related to the global command system is Equivalent state of the global command system For k=1,..,p, for The kth column of With the estimator state column vector of the kth column Relevant, satisfying I l is the l-order identity matrix.

[0160] As an embodiment, in this embodiment, Matlab is used to simulate a multi-agent system containing 4 agents. i1 (t),ζ i2 (t),ζ i3 Each element in (t) is a sinusoidal signal with an amplitude of 1 and a frequency between 10 rad / s and 13 rad / s.

[0161] In p=3-dimensional space, let the multi-agent system move uniformly along the y-axis while forming a square formation on the xOz plane. The distance between each agent and the center of the square formation is 5m. The communication directed graph of the multi-agent system is as follows: Figure 1 As shown. Let the output vector of the global instruction system be y0(t)=col(0,t,10), and the coefficient matrix and initial state value in the global instruction system are:

[0162]

[0163] The coefficient vector of the Ψ0 minimal polynomial is α0=col(0,0). Let the offset instruction be The coefficient matrix and initial state value in the offset instruction system are: li =0 3×3 ,φ di =I3,h b1 (0) = col(0,0,5), h b2 (0)=col(0,0,-5),h b3 (0)=col(5,0,0),h b4 (0) = col(-5,0,0).

[0164] The channel interference frequency of the global reference instruction χ0(t) during transmission is ω1 = 30 rad / s. Design feedback gain K xi Make A i +B i K xi The extreme points are: -1, -1.2, -1.4, -1.6, -1.8, -2. Design L i make The poles are: -7, -7.1, -7.2, -7.3, -7.4, -7.5, -7.6, -7.7. The gain coefficient μ of the estimator is α =50, Gain coefficient of feedforward compensator

[0165] The position changes of the four agents are as follows Figure 2 As shown in the figure. The estimated error curve of the global reference instruction y0(t) is as follows Figure 3 As shown in the figure, the distributed filtering synchronization estimator based on the disturbed output can quickly estimate the true value of the disturbed signal. The trajectory error curve of each agent is shown in Figure 4 As shown in FIG, the formation mission was successfully completed. Thus, the digital simulation of the present invention was completed and its effectiveness was verified.

[0166] The above examples are preferred implementations of the present invention, but the implementation of the present invention is 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 considered equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A collaborative formation control method based on a distributed filtering synchronization estimator, characterized in that: The following steps are involved: Step 1: Construct the state space equation of the intelligent agent based on its mathematical model; Step 2: Define the global instruction system and generate global reference instructions; Step 3: Establish a communication network for the multi-agent system and model the channel perturbations of the global reference instructions; Step 4: For the global reference instruction affected by the channel disturbance, a distributed filtering synchronization estimator based on the disturbed output is constructed; Step 5: Solve the regulator equation to obtain the feedforward gain matrix of the deterministic equivalent output feedback controller. Solve the regulator equation to obtain the feedforward gain matrix of the deterministic equivalent output feedback controller. The regulator equation related to the interference model of the i-th agent system is: X di F di =A i X di +B i U di +E di f di ; 0=c i X di ; Among them, A i is the modal matrix of the ith agent, B i is the input matrix of the ith agent, E di is the interference matrix of the i-th agent, C i is the output matrix of the i-th agent, Φ di is the modal matrix of the interference model of the i-th agent system, φ di The output matrix of the interference model of the i-th agent system, X di is the state solution of the regulator equation associated with the disturbance model of the i-th agent system, U di Enter the solution to the regulator equation associated with the disturbance model of the ith agent system. The regulator equation associated with the ith agent offset command system is: X bi Φ bi =A i X bi +B i U bi ; 0=C i X bi -f bi ; Among them, Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset instruction system, X bi is the state solution of the regulator equation associated with the offset command system of the i-th agent, U bi Input the solution to the regulator equation associated with the i-th agent offset command system and design the controller feedforward gain matrix K associated with the system disturbance model di =U di -K xi X di , the controller feedforward gain matrix K associated with the offset command system bi =U bi -K xi X bi ; Step 6: Design and determine the equivalent output feedback controller to generate the control input of the intelligent agent, thereby achieving the desired formation control effect: Define the related operator symbols col, vec and M: Suppose there are m column vectors β1,…,β m , define the operator col(β1,…,β m )=[β1 T ,…,β m T ] T , β1 T ,…,β m T denote β1,…,β m The transpose of Suppose there is an m×n dimensional matrix Υ, and the operator vec(Υ)=col(γ1,…,γ n ),γ1,…,γ n are the 1st,…,nth columns of the matrix Y respectively; Suppose there is an mn-dimensional column vector Defining operators in are all n-dimensional column vectors and satisfy column vector Select feedback gain K xi Make A i +B i K xi is the Hurwitz matrix, and the observer gain matrix L is selected i Make is the Hurwitz matrix, the i-th intelligent deterministic equivalent output feedback controller u i (t) is: in is the state vector of the Lumberg observer, satisfying is the i-th agent's response to the system state x i The estimated value of (t), is the perturbation of the system state ω by the i-th agent di The estimated value of (t), for The derivative with respect to time t; K zi =[K xi ,K di ]; is the state vector of the feedforward compensator, is the gain coefficient of the feedforward compensator, the coefficient matrix represents the Kronecker product of matrices, the coefficient vector I p is the p-order identity matrix, Θ i (t) is the simulation equivalent matrix of Ψ0, θ is the simulation equivalent matrix of ψ0, I pl is the pl-order unit matrix, X Ψi (t) is the asymptotic state solution of the regulator equation associated with the global command system of the i-th agent, U Ψi (t) is the asymptotic input solution of the regulator equation associated with the global command system of the ith agent, is the operator, p is the dimension of the agent's motion space, l is the order of the Ψ0 minimum polynomial, and the controller feedforward gain matrix related to the global command system is Equivalent state of the global command system For κ=1,..,p, for The κth column of With the estimator state κth column vector Relevant, satisfying I l is the l-th order identity matrix.

2. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 1, characterized in that: In step 1, the mathematical model of the i-th agent is described by the following second-order system: y mi (t)=p i (t)+ζ i3 (t); Where i=1,...,N, N represents the number of agents, u i (t), y mi (t)∈R p Represent the control input and measurement position vector of the i-th agent in the p-dimensional space, and p i (t) and v i (t) The derivative with respect to time t, ζ i1 (t),ζ i2 (t),ζ i3 (t)∈R p Respectively represent the action on the position p of the i-th agent i (t), speed v i (t) and measurement position y mi (t), R represents the real number domain; p i (t), v i (t)∈R p They represent the position and speed of the i-th agent in the p-dimensional space, and t represents time; The second-order system of the intelligent agent is transformed into the form of a general linear system, and its state space equation is: y mi (t)=C mi x i (t)+D mi u i (t)+F mdi d i (t); y i (t)=C i x i (t); Among them, x i (t)=[p i (t) T v i (t) T ] T represents the state of the i-th agent, y i (t) = p i (t) represents the position of the i-th agent, d i (t) = [ζ i1 (t) T ζ i2 (t) T ζ i2 (t) T ] T represents the interference vector acting on the i-th agent model, is x i (t) derivative with respect to time t; A i is the modal matrix of the ith agent, B i is the input matrix of the ith agent, E di is the interference matrix of the i-th agent, C mi is the measurement output matrix of the i-th agent, D mi is the measurement transfer matrix of the i-th agent, F mdi is the measurement interference matrix of the i-th agent, C i is the output matrix of the ith agent, satisfying: I p represents the p-order identity matrix, Represents the Kronecker product of matrices.

3. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 2, characterized in that: For the interference vector d acting on the i-th agent model i (t), build a system interference model. The system interference model of the i-th agent is described as: d i (t)=φ di h di (t); in, represents the state vector of the interference model of the i-th agent system, q di is a constant, representing the dimension of the state vector of the interference model of the i-th agent system, R represents the real number field, It is h di (t) The derivative with respect to time t, Φ di is the modal matrix of the interference model of the i-th agent system, φ di The output matrix of the interference model of the i-th agent system.

4. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 1, characterized in that: In step 2, a global command system is defined, a global reference command is generated, an offset command system and the desired path of each agent are defined. The global command system is defined as follows: y0(t)=ψ0g0(t); Where g0(t)∈R q is the q-dimensional state vector of the global command system, is the derivative of g0(t) with respect to time t, y0(t)∈R p represents the p-dimensional global instruction system output vector, Ψ0 is the modal matrix of the global instruction system, and ψ0 is the output matrix of the global instruction system. Assume that the minimum polynomial of the matrix Ψ0 is: l l +a 01 l l-1 +…+a 0(l-1) λ+a 0l ; where \(l < q\) represents the order of the minimal polynomial of \(\varPsi_0\), and \(\alpha\) 0i , \(\cdots\), \(\alpha\) 0l are the coefficients of the minimal polynomial of \(\varPsi_0\). Define the \(l\)-dimensional coefficient vector \(\alpha_0 = [\alpha\) 01 , \(\cdots\), \(\alpha\) 0l T \(\in \mathbb{R}\) l . The global reference instruction \(\chi_0(t)\) is defined as \(\chi_0(t) = [\alpha_0\) T \ y_0(t) T T \(\in \mathbb{R}\) l+p ;​​ The offset command system of the i-th agent is: in, is the state vector of the offset instruction system, q bi is a constant representing the dimension of the state vector of the i-th agent offset command system, It is h bi The derivative of (t) with respect to time t, represents the p-dimensional offset instruction of the ith agent relative to the global instruction system output vector y0(t), Φ bi is the modal matrix of the offset instruction system, φ bi is the output matrix of the offset command system, and the expected path vector y of the i-th agent ri (t)∈R p Described as: The trajectory error e of the i-th agent i (t)∈R p Described as: i (t) = y i (t)-y ri (t).

5. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 1, characterized in that: In step 3, the global command system and the multi-agent system are considered as an augmented system, and the communication network is represented by a directed graph. Represents a node set Where N represents the number of agents, node 0 represents the global command system, node i, i=1,…,N represents the i-th agent, and edge set When the i-th agent obtains the information of the j-th agent, The jth (i≠j) agent is called the neighbor of the i-th agent, i≠j; let Represents the set of all neighbors of the ith agent, with a directed graph The weighted adjacency matrix of a ij Represents the communication weight coefficient between node i and node j. When a ij >0, otherwise a ij =0, directed graph Contains a directed spanning tree with the global command system as the root node.

6. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 5, characterized in that: For the channel perturbation acting on the global reference instruction, model the channel perturbation of the global reference instruction: in, represents the l+p-dimensional channel perturbation vector acting on the global reference instruction χ0(t), R represents the real number field, represents the channel perturbation vector acting on α0, Denotes the channel perturbation vector acting on y0(t), let represents the modal information in the disturbed global reference instructions that the agent can receive, represents the output information in the disturbed global reference instruction that the agent can receive, and satisfy: For τ=1,...,l+p, the channel perturbation vector Each element has the same form: in, represents the channel perturbation vector The τth element of the channel perturbation vector Contains σ different channel perturbation frequencies; Indicates the The frequency of the channel disturbance, The channel disturbance frequencies are all known; is the unknown disturbance amplitude, is the unknown initial phase of the disturbance; for m=ω1,...,ω σ , a two-dimensional square matrix Define the channel perturbation frequency vector Ω=[ω1...ω σ ] T ∈R σ , define the channel perturbation matrix 7. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 1, characterized in that: In step 4, using the disturbed global reference instruction Design the first part of the distributed filtering synchronization estimator based on the disturbed output, estimating The truth value of is defined as: c ρ =[1 1 0…1 0]∈R 1×(1+wσ) ; X ρ =[1 0 0…0 0]∈R 1x(1+2σ) ; Among them, Λ σ is the modal matrix of the first part of the estimator, is the channel perturbation matrix, γ σ is the simulated perturbation matrix of the first part of the estimator, Ξ ρ is the output matrix of the first part of the estimator, σ is the number of channel perturbation frequencies, R (1+2σ)×(1+2σ) represents a (1+2σ)×(1+2σ) dimensional real matrix, R 1×(1+2σ) Represents a 1×(1+2σ)-dimensional real row vector, because (γ ρ ,Λ ρ ) can be observed, as follows: The only positive solution of ρ , I 1+2σ is the identity matrix of 1+2σ dimensions. According to the solution of the algebraic Riccati equation P ρ , further design the gain matrix of the first part of the estimator μ α >0 is the gain coefficient of the estimator; l is the order of the Ψ0 minimal polynomial. For each element k=1,...,l in the Ψ0 minimal polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as: a i (t)=Ξ ρ r i (t); Where N represents the number of agents, ρ i (t)∈R (1+2σ)×l represents the (1+2σ)×l-dimensional state matrix of the first part of the i-th intelligent estimator; ρ ik (t)∈R 1+2σ is the matrix ρ i (t) column vector of the kth column; is ρ i (t) derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; Represents the i-th smart pair Estimates, represents the jth smart pair Estimates, represents the modal information in the disturbed global reference instructions that the agent can receive, express The kth element of Yes The estimate of the kth element in ; α i (t)∈R 1×l is the output of the first part of the estimator, which represents the T , α0 is the l-dimensional coefficient vector of the minimum polynomial of the coefficient matrix Ψ0 of the global instruction system.

8. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 7, characterized in that: Exploiting the disturbed global reference instruction and the estimated value α i (t), design the second part of the distributed filtering synchronization estimator based on the disturbed output, and estimate The truth value of is defined as: θ=[1 0…0]∈R 1×l ; Among them, Θ i (t) is the simulation equivalent matrix of Ψ0; α i1 (t),…,α il (t) are the output of the first part of the estimator α i The first,…,lth element of (t); l is the order of the Ψ0 minimal polynomial; θ is the simulation equivalent matrix of ψ0; is the modal matrix of the second part of the estimator; is the channel perturbation matrix; is the simulated disturbed matrix of the second part of the estimator; is the output matrix of the second part of the estimator; R l×l Represents an l×l dimensional real matrix, R 1×l represents a 1×e-dimensional real row vector, R (l+2σ)×(e+2σ) represents a (e+2σ)×(l+2σ) dimensional real matrix, σ is the number of channel perturbation frequencies, R 1×(l+2σ) represents a 1×(l+2σ)-dimensional real row vector; Defining the estimator gain in is the algebraic Riccati equation: The positive solution of I l+2σ is the identity matrix of dimension l+2σ, is the gain coefficient of the estimator; In the p-dimensional space, for each dimension ε = 1, ..., p, the second part of the distributed filtering synchronization estimator of the i-th agent based on the disturbed output is designed as: Where N represents the number of agents, represents the state matrix of the second part of the ith agent estimator (l+2σ)×p dimensions; is a matrix The column vector of the ε-th column; yes The derivative with respect to time t; a ij represents the communication weight coefficient between agent i and agent j, a i0 represents the communication weight coefficient between agent i and the global command system; ξ i (t)∈R 1×p Represents the i-th agent pair Estimate of ξ j (t)∈R 1×p Represents the j-th agent pair estimates; represents the output information in the disturbed global reference instruction that the agent can receive; ξ iε (t) represents ξ i The εth element of (t), ξ iε (t) is correct An estimate of the εth element in ; is the output of the second part of the estimator, which represents the estimate of y0(t), and y0(t) represents the output vector of the global command system.

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