Disturbance-resistant multi-agent discrete continuous hybrid specified time state estimation method

Abstract

The invention discloses an anti-disturbance multi-agent discrete continuous hybrid specified time state estimation method, which belongs to the field of distributed state estimation of a multi-agent system, and comprises the following steps: S1, considering the state dynamic state of the multi-agent system and the external disturbance influence, and constructing a multi-agent system dynamic equation; s2, based on the dynamic equation of the multi-agent system, constructing an augmented state estimation error equation and an extended state observer of the multi-agent system; s3, constructing an estimation error dynamic equation of a discrete time domain, and analyzing the convergence of an augmented state estimation error; and S4, a discrete sampling interval is designed, so that the augmented state estimation error is converged to zero within specified time. By adopting the anti-disturbance multi-agent discrete continuous hybrid specified time state estimation method, external disturbance can be effectively dealt with, discrete and continuous time advantages are fused, rapidness, accuracy and robustness are achieved, and it is ensured that multi-agent system state estimation is efficient and reliable.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed state estimation of multi-agent systems, and in particular to a method for anti-disturbance multi-agent discrete-continuous hybrid specified time state estimation. Background Art

[0002] In recent years, unmanned swarm systems have been widely used in agriculture, logistics, military, and other fields, leveraging the advantages of multi-agent collaboration. Accurate state estimation is the core foundation for mission execution. However, external disturbances, communication limitations, and convergence requirements in complex environments pose severe challenges to traditional state estimation methods.

[0003] Existing distributed state estimation methods are mainly divided into two categories: Kalman filter-based and observer-based. Kalman filter-based methods utilize local information for estimation, but when there are uncertainties such as unmodeled dynamics and external disturbances in the system, the estimation convergence cannot achieve mean square optimality. Furthermore, they rely on information exchange between nodes, which can lead to reduced real-time performance due to communication delays.

[0004] Observer-based methods estimate the overall system state through local observers. However, existing designs often rely on relative output vectors or neighbor node information, resulting in the following key drawbacks:

[0005] 1. Strong communication dependency: Nodes need to obtain neighbor or global information and are susceptible to communication channel transmission delays and network attacks. For example, the state estimation accuracy of existing distributed adaptive protocols drops significantly when communication is interrupted or attacked.

[0006] 2. Uncontrollable convergence time: Traditional observers mostly achieve asymptotic convergence and cannot meet the strict requirements of completing accurate state estimation within a specified time in tasks such as drone formation coordination and unmanned vehicle cluster obstacle avoidance. In addition, they are not robust enough to external disturbances such as sinusoidal disturbances of different frequencies and phases on the imaginary axis and bounded constant signals, resulting in limited consistency control accuracy.

[0007] To address the above issues, the existing technology has not yet proposed a state estimation method that combines localized communication, specified time convergence and strong robustness. Summary of the Invention

[0008] The purpose of the present invention is to provide a disturbance-resistant multi-agent discrete-continuous hybrid specified time state estimation method to solve the above technical problems.

[0009] To achieve the above object, the present invention provides a disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method, comprising the following steps:

[0010] S1. Consider the state dynamics of the multi-agent system and the influence of external disturbances, and construct the dynamic equation of the multi-agent system;

[0011] S2. Based on the dynamic equation of the multi-agent system constructed in step S1, construct an augmented state estimation error equation and an extended state observer of the multi-agent system;

[0012] S3. By constructing the estimation error dynamic equation in the discrete time domain and combining Lyapunov stability theory and Schur stability conditions, the convergence of the augmented state estimation error is analyzed;

[0013] S4. Design a discrete sampling interval so that the augmented state estimation error converges to zero within a specified time.

[0014] Preferably, step S1 specifically includes the following steps:

[0015] S11. Assuming that the dynamic equation of the multi-agent system is a linear steady-state equation, introduce external disturbances and establish the continuous-time dynamic equation of a single agent:

[0016]

[0017] Where x i 、y i 、u i d i denote the state variable, output vector, control input and external disturbance of node i respectively, and n, m, p, q all represent the dimensions of the matrix, and p, q<m<n; represents the time derivative of the state variable; N represents the number of nodes in the multi-agent system; A, B, C, and D represent the parameters of the system matrix, control input matrix, output matrix, and unknown input matrix, respectively, and Respectively represent the system matrix set, control input matrix set, output matrix and external disturbance matrix set;

[0018] S12. Assume that the external disturbance is generated by a linear dynamic system, whose eigenvalues ​​are distributed at different positions on the imaginary axis, and construct the external disturbance d i The dynamic equation of:

[0019]

[0020] Where, represents the external disturbance d i The derivative of ; G represents the perturbation matrix, and

[0021] Preferably, step S2 specifically includes the following steps:

[0022] S21. Combine the agent state with the external disturbance to construct the augmented state variable;

[0023] S22, based on augmented state variables, combining the continuous-time dynamic equations of a single agent and the external disturbance d i Dynamic equation of the state estimation error equation is constructed;

[0024] S23. Construct an extended state observer based on the augmented state variable;

[0025] S24. Design a consistency control protocol based on the estimated value of the extended state observer.

[0026] Preferably, the augmented state variable constructed in step S21 is

[0027] The augmented state estimation error equation constructed in step S22 is expressed as follows:

[0028]

[0029] Where, represents the augmented state variable η i The derivative of denote the augmented system matrix, input matrix, and output matrix respectively, and

[0030] The extended state observer constructed in step S23 The expression is as follows:

[0031]

[0032] Where, represents the augmented state estimate The derivative of ; F represents the feedback gain matrix, and P is a positive definite matrix that satisfies the linear matrix inequality The solution; L represents the configuration matrix to be designed; I represents the identity matrix; express Extended state observer at time t; Indicates t k The extended state observer at time η i (t k ) represents t k the state of expansion at any moment; and Where δ→0;

[0033] The consistency control protocol expression designed in step S24 is as follows:

[0034]

[0035] Where, and Represent the estimated state values ​​of node i and node j respectively; represents the estimated value of external disturbance; a ij represents the adjacency matrix;

[0036] And when the extended state observer achieves convergence, we have Substituting formula (5) into formula (1) yields:

[0037]

[0038] When t→∞, lim t→∞ ||x i (t)-x j (t)||=0, x i (t) and x j (t) represents the state variables of node i and node j at time t respectively, and the multi-agent system will achieve consistency.

[0039] Preferably, the extended state observer constructed in step S23 satisfies the following conditions:

[0040] Condition 1: The system matrix controls (A, B), and the output matrix C satisfies rank(C) = m;

[0041] Condition 2: External disturbance d i With control input u i Acting on a multi-agent system through the same channel, there exists a constant matrix Let D = BM, M represents a constant matrix;

[0042] Condition 3: System matrix observation

[0043] Preferably, step S3 specifically includes the following steps:

[0044] S31. According to formula (3) and formula (4), derive the estimated error The dynamic equation of:

[0045]

[0046] Where, represents the augmented state estimation error The derivative of and Respectively time and t k Estimation error of the moment;

[0047] S32. According to formula (7), the equation of the estimation error in the discrete time domain is obtained:

[0048]

[0049] Where, and Respectively represent t k+1 Moment and Estimation error of the moment;

[0050] S33, set feedback gain matrix The positive definite matrix P is a linear matrix inequality The solution is constructed by constructing the estimated error The quadratic Lyapunov function V, prove It complies with Hurwitz stability, thus verifying the estimation error Converges in the continuous-time domain:

[0051]

[0052] Then the derivative of the Lyapunov function with respect to time satisfy

[0053]

[0054] Therefore, the estimation error It is convergent in the continuous time domain;

[0055] S34, record the discrete sampling interval τ k =t k -t k-1 , A k Represents the state transfer matrix, and the discrete sampling system is designed by formula (8) The necessary and sufficient conditions for convergence are: the state transfer matrix It is Schur that is stable.

[0056] Preferably, step S4 specifically includes the following steps:

[0057] S41, let the discrete sampling interval τ k =1, and the state transfer matrix of the augmented state estimation error is set to or

[0058] S42, by rank get:

[0059]

[0060] S43, by configuring the matrix L, The eigenvalues ​​of are all 0; and for the n-order nilpotent matrix P0, P0 is satisfied n = 0, and the estimation error of the augmented state is obtained satisfy:

[0061]

[0062] Where, represents the estimation error of the augmented state after n+q sampling intervals; represents the augmented state estimation error at the initial moment;

[0063] S44, set discrete sampling interval τ k =Δ, Δ is any positive constant, and the augmented state estimation error is obtained The time for convergence to zero is And n+q is a fixed value, so the convergence time T and discrete sampling interval τ are obtained k relationship.

[0064] Preferably, step S4 is followed by step S5: recording the estimated error of each node in the multi-agent system Consistency error and the system state variable x i Data that changes over time and plots it.

[0065] Therefore, the present invention adopts the above-mentioned anti-disturbance multi-agent discrete-continuous hybrid specified time state estimation method, which has the following beneficial effects:

[0066] 1. Consider external disturbances to construct the system dynamic equations and model the disturbances to make the model more realistic. At the same time, the control protocol includes disturbance compensation terms to effectively enhance the anti-disturbance capability and improve the accuracy of state estimation.

[0067] 2. Use the augmented state method to construct the augmented state error equation, combine the system state with the disturbance for analysis, comprehensively process the system information, and provide a complete framework for observer design and error analysis;

[0068] 3. The discrete-continuous hybrid state observer combines the advantages of two time domains. The continuous part dynamically adjusts the estimated value, and the discrete part is corrected by pulse signals, improving the efficiency and accuracy of state and disturbance estimation.

[0069] 4. Configuring a nilpotent matrix enables the estimated error to converge within a specified time, breaking through the limitations of traditional asymptotic convergence. The error can be strictly reduced to zero within a preset time, meeting the requirements of scenarios with high real-time and accuracy requirements (such as rapid collaboration of multiple intelligent agents).

[0070] 5. The Hurwitz stability of the continuous-time error system is proved by Lyapunov function, and the Schur stability condition is used for discrete-time analysis to ensure the stability of the system in different time domains.

[0071] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 This is a flow chart of a disturbance-resistant multi-agent discrete-continuous hybrid specified time state estimation method of the present invention;

[0073] Figure 2 It is a network communication topology diagram of the simulation experiment of the present invention;

[0074] Figure 3 is the state estimation error of each intelligent agent node in the simulation experiment of the present invention Time-varying graph; (a) is The first component Time-varying graph; (b) The second component of Time-varying graph; (c) The third component Time-varying graphs;

[0075] Figure 4 is the external disturbance estimation error of each intelligent agent node in the simulation experiment of the present invention Time-varying graph; (a) is The first component Time-varying graph; (b) The second component of Time-varying graphs;

[0076] Figure 5 is the consistency error ξ of each agent node in the simulation experiment of the present invention i Time-varying graph; where (a) is ξ i The first component ξ i1 Time-varying graph; (b) is ξ i The second component ξ i2 Time-varying graph; (c) is ξ i The third component ξ i3 Time-varying graphs;

[0077] Figure 6 is the system state x of the simulation experiment of the present invention i Time-varying graph; where (a) is x i The first component x i1 Time-varying graph; (b) is x i The second component x i2 Time-varying graph; (c) is x i The third component x i3 Graph of changes over time. DETAILED DESCRIPTION

[0078] In order to make the purposes, technical solutions and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, where the same or similar numbers throughout represent the same or similar elements or elements with the same or similar functions.

[0079] It should be noted that the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or devices.

[0080] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0081] like Figure 1 As shown, a disturbance-resistant multi-agent discrete-continuous hybrid specified time state estimation method includes the following steps:

[0082] S1. Consider the state dynamics of the multi-agent system and the influence of external disturbances, and construct the dynamic equation of the multi-agent system;

[0083] Step S1 specifically includes the following steps:

[0084] S11. Assuming that the dynamic equation of the multi-agent system is a linear steady-state equation, introduce external disturbances and establish the continuous-time dynamic equation of a single agent:

[0085]

[0086] Where x i 、y i 、u i d i denote the state variable, output vector, control input and external disturbance of node i respectively, and n, m, p, q all represent the dimensions of the matrix, and p, q<m<n; represents the time derivative of the state variable; N represents the number of nodes in the multi-agent system; A, B, C, and D represent the parameters of the system matrix, control input matrix, output matrix, and unknown input matrix, respectively, and Respectively represent the system matrix set, control input matrix set, output matrix and external disturbance matrix set;

[0087] S12. Assume that the external disturbance is generated by a linear dynamic system, whose eigenvalues ​​are distributed at different positions on the imaginary axis, and construct the external disturbance d i The dynamic equation of:

[0088]

[0089] Where, represents the external disturbance d i The derivative of ; G represents the perturbation matrix, and

[0090] S2. Based on the dynamic equation of the multi-agent system constructed in step S1, construct an augmented state estimation error equation and an extended state observer of the multi-agent system;

[0091] Step S2 specifically includes the following steps:

[0092] S21. Combine the agent state with the external disturbance to construct the augmented state variable;

[0093] The augmented state variable constructed in step S21

[0094] S22, based on augmented state variables, combining the continuous-time dynamic equations of a single agent and the external disturbance d i Dynamic equation of the state estimation error equation is constructed;

[0095] The augmented state estimation error equation constructed in step S22 is expressed as follows:

[0096]

[0097] Where, represents the augmented state variable η i The derivative of denote the augmented system matrix, input matrix, and output matrix respectively, and

[0098] S23. Construct an extended state observer based on the augmented state variable;

[0099] The extended state observer constructed in step S23 The expression is as follows:

[0100]

[0101] Where, represents the augmented state estimate The derivative of ; F represents the feedback gain matrix, and P is a positive definite matrix that satisfies the linear matrix inequality The solution; L represents the configuration matrix to be designed; I represents the identity matrix; express Extended state observer at time t; Indicates t k The extended state observer at time η i (t k ) represents t k the state of expansion at any moment; and Where δ→0;

[0102] From formula (4), we can see that the extended state observer only uses local information for estimation and does not need to communicate with neighboring nodes, thus avoiding the transmission delay caused by node communication and the risk of network attacks on the communication channel. k By applying a pulse signal to the observer, this discrete-continuous hybrid design method can configure the poles of the augmented state estimation error, thereby effectively improving the convergence speed of the estimation error.

[0103] The extended state observer constructed in step S23 satisfies the following conditions:

[0104] Condition 1: The system matrix controls (A, B), and the output matrix C satisfies rank(C) = m;

[0105] Condition 2: External disturbance d i With control input u i Acting on a multi-agent system through the same channel, there exists a constant matrix Let D = BM, M represents a constant matrix;

[0106] Condition 3: System matrix observation

[0107] S24. Design a consistency control protocol based on the estimated value of the extended state observer.

[0108] The consistency control protocol expression designed in step S24 is as follows:

[0109]

[0110] Where, and Represent the estimated state values ​​of node i and node j respectively; represents the estimated value of external disturbance; a ij represents the adjacency matrix;

[0111] And when the extended state observer achieves convergence, we have Substituting formula (5) into formula (1) yields:

[0112]

[0113] When t→∞, lim t→∞ ||x i (t)-x j (t)||=0, x i (t) and x j (t) represents the state variables of node i and node j at time t respectively, and the multi-agent system will achieve consistency.

[0114] S3. By constructing the estimation error dynamic equation in the discrete time domain and combining Lyapunov stability theory and Schur stability conditions, the convergence of the augmented state estimation error is analyzed;

[0115] Step S3 specifically includes the following steps:

[0116] S31. According to formula (3) and formula (4), derive the estimated error The dynamic equation of:

[0117]

[0118] Where, represents the augmented state estimation error The derivative of and Respectively time and t k Estimation error of the moment;

[0119] S32. According to formula (7), the equation of the estimation error in the discrete time domain is obtained:

[0120]

[0121] Where, and Respectively represent t k+1 Moment and Estimation error of the moment;

[0122] S33, set feedback gain matrix The positive definite matrix P is a linear matrix inequality The solution is constructed by constructing the estimated error The quadratic Lyapunov function V, prove It complies with Hurwitz stability, thus verifying the estimation error Converges in the continuous-time domain:

[0123]

[0124] Then the derivative of the Lyapunov function with respect to time satisfy

[0125]

[0126] Therefore, the estimation error It is convergent in the continuous time domain;

[0127] S34, record the discrete sampling interval τ k =t k -t k-1 , A k Represents the state transfer matrix, and the discrete sampling system is designed by formula (8) The necessary and sufficient conditions for convergence are: the state transfer matrix It is Schur that is stable.

[0128] It should be noted that when the discrete trigger interval t k+1 -t k The design is very small, that is When the pole of is close to the unit circle, there are problems such as reduced response speed, reduced stability margin and reduced anti-interference ability. Therefore, by applying pulses to the extended state observer at discrete moments, the state transfer matrix Configure a gain matrix before Then configure the matrix L to solve the above problem.

[0129] S4. Design a discrete sampling interval so that the augmented state estimation error converges to zero within a specified time.

[0130] Step S4 specifically includes the following steps:

[0131] S41, let the discrete sampling interval τ k =1, and the state transfer matrix of the augmented state estimation error is set to or

[0132] S42, by get:

[0133]

[0134] S43, by configuring the matrix L, The eigenvalues ​​of are all 0; and for the n-order nilpotent matrix P0, P0 is satisfied n = 0, and the estimation error of the augmented state is obtained satisfy:

[0135]

[0136] Where, represents the estimation error of the augmented state after n+q sampling intervals; represents the augmented state estimation error at the initial moment;

[0137] S44, set discrete sampling interval τ k =Δ, Δ is any positive constant, and the augmented state estimation error is obtained The time for convergence to zero is And n+q is a fixed value, so the convergence time T and discrete sampling interval τ are obtained k That is, for a certain multi-agent system dynamics, n+q is a fixed constant, so the augmented state estimation error The convergence time is only related to the discrete sampling interval, so the convergence can be achieved at any preset time.

[0138] Step S4 is followed by step S5: recording the estimated error of each node in the multi-agent system Consistency error and the system state variable x i Data that changes over time and plots it.

[0139] Simulation experiment

[0140] In this simulation experiment, we consider a network consisting of three agent nodes (agent 1, agent 2 and agent 3). Figure 2 The leaderless directed communication topology shown.

[0141] Its Laplace matrix for:

[0142]

[0143] The multi-agent system and external disturbance are simulated and modeled, and the parameters are selected as follows:

[0144] τ k =1.

[0145] And the above parameter settings meet the three conditions for the existence of the extended state observer.

[0146] Then, by solving LMI (linear matrix inequality) and pole placement calculation, we can get:

[0147]

[0148] Proven, is Schur stable, and Therefore, the estimation error Convergence is achieved at t=5.

[0149] The estimated error at each node State estimation error and external disturbance estimation error and the consistency error of the agent network nodes and the system state x i The curve that changes with time t is as follows Figure 3-Figure 6 As shown by Figure 3 、 Figure 4 It can be seen that the estimation error converges to zero after t>5τ=5. Figure 5 and Figure 6 It can be seen that under the action of external disturbance (in the form of a sine function), the consistency of the multi-agent system can be achieved by adopting the control rate shown in formula (5).

[0150] From the above simulation experiments, combined with the actual multi-agent system consistency control task, it can be seen that the method designed by the present invention can accurately estimate the consistency error of the multi-agent system with external disturbances within a specified time, thereby verifying the effectiveness and accuracy of the present invention.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method, characterized by: The following steps are involved: S1. Consider the state dynamics of the multi-agent system and the influence of external disturbances, and construct the dynamic equation of the multi-agent system; S2. Based on the dynamic equation of the multi-agent system constructed in step S1, construct an augmented state estimation error equation and an extended state observer of the multi-agent system; S3. By constructing the estimation error dynamic equation in the discrete time domain and combining Lyapunov stability theory and Schur stability conditions, the convergence of the augmented state estimation error is analyzed; S4. Design a discrete sampling interval so that the augmented state estimation error converges to zero within a specified time.

2. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Assuming that the dynamic equation of the multi-agent system is a linear steady-state equation, introduce external disturbances and establish the continuous-time dynamic equation of a single agent: Where x i 、y i 、u i d i denote the state variable, output vector, control input and external disturbance of node i respectively, and n, m, p, q all represent the dimensions of the matrix, and p, q<m<n; represents the time derivative of the state variable; N represents the number of nodes in the multi-agent system; A, B, C, and D represent the parameters of the system matrix, control input matrix, output matrix, and unknown input matrix, respectively, and Respectively represent the system matrix set, control input matrix set, output matrix and external disturbance matrix set; S12. Assume that the external disturbance is generated by a linear dynamic system, whose eigenvalues ​​are distributed at different positions on the imaginary axis, and construct the external disturbance d i The dynamic equation of: Where, represents the external disturbance d i The derivative of ; G represents the perturbation matrix, and 3. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 2, characterized in that: Step S2 specifically includes the following steps: S21. Combine the agent state with the external disturbance to construct the augmented state variable; S22, based on augmented state variables, combining the continuous-time dynamic equations of a single agent and the external disturbance d i Dynamic equation of the system, construct the augmented state estimation error equation; S23. Construct an extended state observer based on the augmented state variable; S24. Design a consistency control protocol based on the estimated value of the extended state observer.

4. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 3, characterized in that: The augmented state variable constructed in step S21 The augmented state estimation error equation constructed in step S22 is expressed as follows: Where, represents the augmented state variable η i The derivative of denote the augmented system matrix, input matrix, and output matrix respectively, and The extended state observer constructed in step S23 The expression is as follows: Where, represents the augmented state estimate The derivative of ; F represents the feedback gain matrix, and P is a positive definite matrix that satisfies the linear matrix inequality The solution; L represents the configuration matrix to be designed; I represents the identity matrix; express Extended state observer at time t; Indicates t k The extended state observer at time η i (t k ) represents t k the state of expansion at any moment; and Where δ→0; The consistency control protocol expression designed in step S24 is as follows: Where, and Represent the estimated state values ​​of node i and node j respectively; represents the estimated value of external disturbance; a ij represents the adjacency matrix; And when the extended state observer achieves convergence, we have Substituting formula (5) into formula (1) yields: When t→∞, lim t→∞ ||x i (t)-x j (t)||=0, x i (t) and x j (t) represents the state variables of node i and node j at time t respectively, and the multi-agent system will achieve consistency.

5. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 4, characterized in that: The extended state observer constructed in step S23 satisfies the following conditions: Condition 1: The system matrix controls (A, B), and the output matrix C satisfies rank(C) = m; Condition 2: External disturbance d i With control input u i Acting on a multi-agent system through the same channel, there exists a constant matrix Let D = BM, M represents a constant matrix; Condition 3: System matrix observation 6. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 4, characterized in that: Step S3 specifically includes the following steps: S31. According to formula (3) and formula (4), derive the estimated error The dynamic equation of: Where, represents the augmented state estimation error The derivative of and Respectively time and t k Estimation error of the moment; S32. According to formula (7), the equation of the estimation error in the discrete time domain is obtained: Where, and Respectively represent t k+1 Moment and Estimation error of the moment; S33, set feedback gain matrix The positive definite matrix P is a linear matrix inequality The solution is constructed by constructing the estimated error The quadratic Lyapunov function V, prove It complies with Hurwitz stability, thus verifying the estimation error Converges in the continuous-time domain: Then the derivative of the Lyapunov function with respect to time satisfy Therefore, the estimation error It is convergent in the continuous time domain; S34, record the discrete sampling interval τ k =t k -t k-1 , A k Represents the state transfer matrix, and the discrete sampling system is designed by formula (8) The necessary and sufficient conditions for convergence are: the state transfer matrix It is Schur that is stable.

7. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 6, characterized in that: Step S4 The specific steps include: S41, let the discrete sampling interval τ k =1, and the state transfer matrix of the augmented state estimation error is set to or S42, by get: S43, by configuring the matrix L, The eigenvalues ​​of are all 0; and for the n-order nilpotent matrix P0, P0 is satisfied n = 0, and the estimation error of the augmented state is obtained satisfy: Where, represents the estimation error of the augmented state after n+q sampling intervals; represents the augmented state estimation error at the initial moment; S44, set discrete sampling interval τ k =Δ, Δ is any positive constant, and the augmented state estimation error is obtained The time for convergence to zero is And n+q is a fixed value, so the convergence time T and discrete sampling interval τ are obtained k relationship.

8. The disturbance-resistant multi-agent discrete-continuous hybrid time state estimation method according to claim 1, characterized in that: Step S4 is followed by step S5: recording the estimated error of each node in the multi-agent system Consistency error and the system state variable x i Data that changes over time and plots it.

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