Cooperative formation control method based on distributed filtering synchronization estimator

Abstract

The invention discloses a collaborative formation control method based on a distributed filtering synchronous estimator. The method comprises the following steps: constructing a state-space equation according to a mathematical model of an intelligent agent; defining a global instruction system, and generating a global reference instruction; establishing a communication network of a multi-agent system, and modeling channel disturbance of a global reference instruction; constructing a distributed filtering synchronization estimator based on disturbed output for the global reference instruction influenced by channel disturbance; solving a regulator equation solution to obtain a feed-forward gain matrix for determining the equivalent output feedback controller; and designing and determining an equivalent output feedback controller to generate control input of the intelligent agent so as to realize an expected formation control effect. The distributed filtering synchronization estimator based on disturbed output is provided, a distributed determination equivalence controller is designed, the stability of a closed-loop system is achieved, the motion trail of the intelligent agent approaches to a set trail, and the distributed filtering synchronization estimator has wide 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 one of the core contents of current automation, robotics and artificial intelligence research. Multi-agent systems are usually composed of multiple agents that can act independently but can coordinate and cooperate with each other, such as drone formations, autonomous driving fleets, multi-robot collaborative operations, etc. In these systems, formation control is a crucial technology, which requires agents to maintain specific relative positions and postures according to predetermined formations or task requirements in order to complete complex collaborative tasks.

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

[0004] In order to overcome these challenges, a literature has proposed an improved particle filter (PF) algorithm to improve navigation accuracy in the case of poor master-slave UAV swarm collaborative navigation under time-varying non-Gaussian noise caused by external interference in complex environments (UAV formation collaborative navigation algorithm based on improved particle filter Jingxuan, Wang Hongru, Zhu Dongqin, ALEKSANDR Chupalov, School of Information and Communication Engineering, Harbin Engineering University). However, this method has limitations. The single-master structure is too dependent on the host and does not fully utilize the local observation information without fully 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 to provide a collaborative formation control method based on a distributed filtering synchronization estimator. It utilizes local observation information and, through communication and collaboration between intelligent agents, realizes accurate estimation of the global state of the system or specific targets, and solves the distributed formation control problem of a class of linear multi-agent systems under the influence of communication interference. It 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 by 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 command system and generate global reference commands;

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

[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, solving the regulator equation to obtain a 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 They represent the control input and measured position vector of the ith agent in the p-dimensional space, respectively. and They are 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 They represent the action on the position p of the i-th agent. i (t), speed v i (t) and the measured 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 ith agent in the p-dimensional space, and t represents the time;

[0018] The second-order system of the intelligent agent is transformed into 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 ith 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) the 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 ith agent, C mi is the measurement output matrix of the ith agent, D mi is the measurement transfer matrix of the ith agent, F mdi is the measurement interference matrix of the ith 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 as and denote the Kronecker product of matrices as

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

[0027]

[0028] \(d\) i (t)=\(\varphi\) di \(h\) di (t);

[0029] where denotes the state vector of the system interference model of the \(i\)-th agent, \(q\) di is a constant representing the dimension of the state vector of the system interference model of the \(i\)-th agent, \(\mathbb{R}\) represents the real number field, is the derivative of \(h\) di (t) with respect to time \(t\), \(\varPhi\) di is the modal matrix of the system interference model of the \(i\)-th agent, \(\varphi\) di is the output matrix of the system interference model of the \(i\)-th agent.

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

[0031]

[0032] \(y_0(t)=\psi_0g_0(t)\);

[0033] where \(g_0(t)\in\mathbb{R}\) q is the \(q\)-dimensional state vector of the global instruction system, is the derivative of \(g_0(t)\) with respect to time \(t\), \(y_0(t)\in\mathbb{R}\) p represents the \(p\)-dimensional output vector of the global instruction system, \(\varPsi_0\) is the modal matrix of the global instruction system, and \(\psi_0\) is the output matrix of the global instruction system; assume the minimal polynomial of the matrix \(\varPsi_0\) is:

[0034] \(\lambda\) l +\(\alpha\) 01 \(\lambda\) l-1 +…+\(\alpha\) 0(l-1) \(\lambda\)+\(\alpha\) 0l ;

[0035] where \(l\lt q\) represents the order of the minimal polynomial of \(\varPsi_0\), \(\alpha\) 01 ,..., \(\alpha\) 0llis the coefficient of the Ψ0 minimal polynomial, and the l-dimensional coefficient vector of the Ψ0 minimal polynomial is defined as 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 command system, q bi is a constant, representing the dimension of the state vector of the i-th agent offset command system, Yes bi The derivative of (t) with respect to time t, represents the p-dimensional offset command of the ith agent relative to the global command system output vector y0(t), Φ bi is the modal matrix of the offset command 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 regarded 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. Whenij >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, represents 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 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] Further, using the disturbed global reference instruction The first part of the distributed filtering synchronization estimator based on the disturbed output is designed to estimate 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, the algebraic Riccati equation:

[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 minimum polynomial. For each element k=1,...,l in the Ψ0 minimum polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator based on the disturbed output of the i-th agent 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 state matrix of the first part of the i-th intelligent estimator (1+2σ)×l dimensions; ρ ik (t)∈R 1+2σ is the matrix ρ i(t) column vector of the kth column; is i (t) 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; represents the i-th smart pair The estimate, represents the jth intelligent pair The estimate, 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 An estimate of , α0 is the l-dimensional coefficient vector of the minimum polynomial of the coefficient matrix Ψ0 of the global instruction system.

[0057] Further, 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 based on the disturbed output of the i-th agent is designed as:

[0064]

[0065] Where N represents the number of agents, represents the state matrix of the second part of the i-th 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 The estimate of ξ j (t)∈R 1×p represents the jth 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, representing the estimate of y0(t), where 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 ith agent, E di is the interference matrix of the ith agent, C i is the output matrix of the ith agent, Φ di is the modal matrix of the interference model of the ith 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 ith 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 command 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 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 the 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 i-th agent's response to the disturbance of the 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 Ψi (t) is the asymptotic state solution of the regulator equation associated with the global command system of the ith 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 k-th column of With the estimator status Column vector of the k-th column Related, satisfying I l is the l-th 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 then 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 A directed graph describing a multi-agent system communication network in an embodiment of the present invention;

[0085] Figure 2 is a position change diagram 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 A flowchart of a collaborative formation control method based on a distributed filtering synchronization estimator according to an embodiment of the present invention; DETAILED DESCRIPTION

[0089] 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.

[0090] like Figure 5 A collaborative 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 ith 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 They represent the control input and measured position vector of the ith agent in the p-dimensional space, respectively. and They are 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 the measured 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 ith agent in the p-dimensional space, and t represents the time;

[0096] The second-order system of the intelligent agent is transformed into 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 ith 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) the 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 ith agent, C mi is the measurement output matrix of the ith agent, D mi is the measurement transfer matrix of the ith agent, F mdi is the measurement interference matrix of the ith 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 a system interference model. 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 is 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 desired 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 command system, q bi is a constant, representing the dimension of the state vector of the i-th agent offset command system, Yes bi The derivative of (t) with respect to time t, represents the p-dimensional offset command of the ith agent relative to the global command system output vector y0(t), Φ bi is the modal matrix of the offset command system, φ bi is the output matrix of the offset command 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 perturbation of the global reference command;

[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 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, the channel perturbation of the global reference instruction is modeled:

[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, represents 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 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] Using the disturbed global reference instruction The first part of the distributed filtering synchronization estimator based on the disturbed output is designed to estimate 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, the algebraic Riccati equation:

[0132] The only positive solution of ρ , I 1+2ρ is a 1+2σ-dimensional identity matrix. 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 minimum polynomial. For each element k=1,...,l in the Ψ0 minimum polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator based on the disturbed output of the i-th agent 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 state matrix of the first part of the i-th intelligent estimator (1+2σ)×l dimensions; ρ ik (t)∈R 1+2σ is the matrix ρ i (t) column vector of the kth column; is i (t) 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; represents the i-th smart pair The estimate, represents the jth intelligent pair The estimate, 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 An estimate of , α0 is the l-dimensional coefficient vector of the minimum polynomial of the coefficient matrix Ψ0 of the global instruction system.

[0136] 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 . 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 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 based on the disturbed output of the i-th agent is designed as:

[0142]

[0143] Where N represents the number of agents, represents the state matrix of the second part of the i-th 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 The estimate of ξ j (t)∈R 1×p represents the jth 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, representing the estimate of y0(t), where y0(t) represents the output vector of the global command system.

[0144] Step 5, solving the regulator equation to obtain a 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 ith agent, E di is the interference matrix of the ith agent, C i is the output matrix of the ith agent, Φ di is the modal matrix of the interference model of the ith 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 ith 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 command 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 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 the 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 of the 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 ith 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 minimum 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 status Column vector of the kth column Related, satisfying I l is the l-th order identity matrix.

[0160] As an embodiment, in this embodiment, Matlab is used to simulate a multi-agent system containing 4 agents. In the specific implementation, the interference vector ζ is set 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 and form 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 global command system output vector be y0(t)=col(0,t,10), and the coefficient matrix and initial state value in the global command system be:

[0162]

[0163] The coefficient vector of the Ψ0 minimum 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=30rad / s. Design feedback gain K xi Make A i +B i K xi The poles 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 The estimated error curve of the global reference instruction y0(t) is shown as Figure 3 As shown in Figure 2, 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 2. Figure 4 As shown, the formation mission was successfully completed. So far, the digital simulation of the present invention has been completed and its effectiveness has been verified.

[0166] 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 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 command system and generate global reference commands; Step 3: Establish a communication network for the multi-agent system and model the channel perturbation of the global reference command; 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, solving the regulator equation to obtain a feedforward gain matrix of the equivalent output feedback controller; 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.

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: Where i = 1,...,N, N represents the number of agents, u i (t), y mi (t)∈R p They represent the control input and measured position vector of the ith agent in the p-dimensional space, respectively. and They are p i (t) and v i The derivative of (t) with respect to time t, They represent the action on the position p of the i-th agent. i (t), speed v i (t) and the measured 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 ith agent in the p-dimensional space, and t represents the time; The second-order system of the intelligent agent is transformed into 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 ith agent, y i (t) = p i (t) represents the position of the ith agent, represents the interference vector acting on the i-th agent model, is x i (t) the 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 ith agent, C mi is the measurement output matrix of the ith agent, D mi is the measurement transfer matrix of the ith agent, F mdi is the measurement interference matrix of the ith 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), construct the system interference model. The system interference model of the i-th agent is described as: d i (t)=φ di h di (t); Among them, h di (t)∈R qdi represents the state vector of the interference model of the ith agent system, q di is a constant, representing the dimension of the state vector of the interference model of the ith agent system, R represents the real number domain, Yes di (t) The derivative with respect to time t, Φ di is the modal matrix of the interference model of the ith agent system, φ di The output matrix of the interference model of the ith 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 expected path of each agent are defined, and 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 command system output vector, Ψ0 is the modal matrix of the global command system, and ψ0 is the output matrix of the global command system; assuming 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 \(\alpha\) 01 , \(\cdots\), \(\alpha\) 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: Among them, h bi (t)∈R qbi is the state vector of the offset command system, q ii is a constant, representing the dimension of the state vector of the i-th agent offset command system, Yes bi The derivative of (t) with respect to time t, represents the p-dimensional offset command of the ith agent relative to the global command system output vector y0(t), Φ bi is the modal matrix of the offset command 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 regarded 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 h-th agent, The jth (i≠j)th agent is called the neighbor of the uth agent, i≠h; 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 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, the channel perturbation of the global reference instruction is modeled: 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, represents 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 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 The first part of the distributed filtering synchronization estimator based on the disturbed output is designed to estimate The truth value of is defined as: c ρ =[1 1 0 … 1 0]∈R 1×(1+2σ) ; X ρ =[1 0 0 … 0 0]∈R 1x(1+2σ) ; 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 N×(1+2σ) represents a 1×(1+2σ)-dimensional real row vector, because (γ ρ ,Λ ρ ) can be observed as follows, the algebraic Riccati equation: The only positive solution of is P 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 minimum polynomial. For each element k=1,...,l in the Ψ0 minimum polynomial coefficient vector α0, the first part of the distributed filtering synchronization estimator based on the disturbed output of the i-th agent 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 state matrix of the first part of the i-th intelligent estimator (1+2σ)×l dimensions; ρ ik (t)∈R 1+2σ is the matrix ρ i (t) column vector of the kth column; is i (t) 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; represents the i-th smart pair The estimate, represents the jth intelligent pair The estimate, 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 An estimate of , 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: 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: 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×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; Defining the estimator gain in is the algebraic Riccati equation: The positive solution of 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 based on the disturbed output of the i-th agent is designed as: Where N represents the number of agents, represents the state matrix of the second part of the i-th 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, α 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 The estimate of ξ j (t)∈R 1×p represents the jth 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, representing the estimate of y0(t), where y0(t) represents the output vector of the global command system.

9. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 1, characterized in that: In step 5, 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: 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 u-th agent, E di is the interference matrix of the ith agent, C i is the output matrix of the ith agent, Φ di is the modal matrix of the interference model of the ith 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 ith 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 command 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 .

10. The method for cooperative formation control based on distributed filtering synchronization estimator according to claim 9, characterized in that: In step 6, an equivalent output feedback controller is designed to generate the control input of the 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 the 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 i-th agent's response to the disturbance of the 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 Ψi (t) is the asymptotic state solution of the regulator equation associated with the global command system of the ith 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 minimal 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 k-th column of With the estimator status Column vector of the k-th column Related, satisfying I l is the unit matrix of order l.

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