Anti-disturbance multi-agent discrete-continuous hybrid specified-time state estimation method

Abstract

The application discloses a disturbance-resistant multi-agent discrete-continuous hybrid specified-time state estimation method, and belongs to the field of distributed state estimation of multi-agent systems, and comprises the following steps: S1, considering the state dynamics of the multi-agent system and the influence of external disturbance, a dynamic equation of the multi-agent system is constructed; S2, based on the dynamic equation of the multi-agent system, an augmented state estimation error equation and an extended state observer of the multi-agent system are constructed; S3, an estimation error dynamic equation in a discrete time domain is constructed, and the convergence of the augmented state estimation error is analyzed; S4, a discrete sampling interval is designed, so that the augmented state estimation error converges to zero within a specified time. The above-mentioned disturbance-resistant multi-agent discrete-continuous hybrid specified-time state estimation method can effectively cope with external disturbance, fuse the advantages of discrete and continuous time, be faster, more accurate and robust, and ensure that the state estimation of the multi-agent system is efficient and reliable.

Description

Technical Field

[0001] This invention relates to the field of distributed state estimation technology for multi-agent systems, and more particularly to a method for perturbation-resistant multi-agent discrete-continuous hybrid state estimation at a specified time. Background Technology

[0002] In recent years, unmanned swarm systems have been widely used in agriculture, logistics, military and other fields due to their advantages in multi-agent cooperation, and accurate state estimation is the core foundation for mission execution. However, external disturbances in complex environments, communication constraints and convergence performance requirements pose serious challenges to traditional state estimation methods.

[0003] Existing distributed state estimation methods are mainly divided into two categories: those based on Kalman filters and those based on observers. Among them, the Kalman filter-based method, although it utilizes local information for estimation, cannot achieve mean-square optimal convergence when the system has uncertainties such as unmodeled dynamics and external disturbances. Furthermore, it relies on information exchange between nodes, resulting in a degradation in 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 information about their neighbors or the global network, which makes them susceptible to communication channel transmission delays and network attacks. For example, the accuracy of state estimation in existing distributed adaptive protocols drops significantly when communication is interrupted or attacked.

[0006] 2. Uncontrollable convergence time: Traditional observers mostly achieve asymptotic convergence, which cannot meet the strict requirements of completing accurate state estimation within a specified time in tasks such as UAV formation coordination and unmanned vehicle swarm obstacle avoidance. Furthermore, 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 aforementioned issues, existing technologies have not yet proposed a state estimation method that combines localized communication, time-specified convergence, and strong robustness. Summary of the Invention

[0008] The purpose of this invention is to provide a perturbation-resistant multi-agent discrete-continuous hybrid state estimation method for a specified time, thereby solving the aforementioned technical problems.

[0009] To achieve the above objectives, this invention provides a perturbation-resistant multi-agent discrete-continuous hybrid time-specified state estimation method, comprising the following steps:

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

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

[0012] S3. By constructing the dynamic equation of the estimation error 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 the dynamic equations of a multi-agent system are linear time-invariant equations, introduce external disturbances and establish the continuous-time dynamic equations of a single agent:

[0016]

[0017] In the formula, x i y i u i d i Let represent the state variables, output vector, control input, and external disturbance of node i, respectively. n, m, p, and q all represent the dimensions of the matrix, and p, q < m < n; Let represent the derivative of the state variable with respect to time; 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. These represent the system matrix set, the control input matrix set, the output matrix, and the external disturbance matrix set, respectively.

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

[0019]

[0020] In the formula, Indicates 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's state with external disturbances to construct augmented state variables;

[0023] S22. Based on augmented state variables, combined with the continuous-time dynamic equation of a single agent and external perturbation d i The dynamic equations are used to construct the augmented state estimation error equation;

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

[0025] S24. Design a consensus control protocol based on the estimated values ​​from the extended state observer.

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

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

[0028]

[0029] In the formula, Represents the augmented state variable η i The derivative; Let represent the augmented system matrix, input matrix, and output matrix, respectively.

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

[0031]

[0032] In the formula, 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 The extended state observer at time step; Indicates t k Extended state observer at time η; i (t k ) represents t k The expansion state at any given moment; and Where δ→0;

[0033] The expression for the consensus control protocol designed in step S24 is as follows:

[0034]

[0035] In the formula, and Let i and j represent the state estimates of node i and node j, respectively. Indicates the estimated value of external disturbance; a ij Represents the adjacency matrix;

[0036] And when the extended state observer converges, there is Substituting formula (5) into formula (1) at this point, we get:

[0037]

[0038] As t→∞, lim t→∞ ||x i (t)-x j (t)||=0, x i (t) and x j (t) represent 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 control is (A,B), and the output matrix C satisfies rank(C)=m;

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

[0042] Condition 3: System matrix observation

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

[0044] S31. Based on formulas (3) and (4), derive the estimation error. The dynamic equation:

[0045]

[0046] In the formula, Indicates the augmented state estimation error The derivative; and They represent Time and t k The time estimation error;

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

[0048]

[0049] In the formula, and They represent t respectively k+1 Time and The time estimation error;

[0050] S33. Set the feedback gain matrix Where the positive definite matrix P is a linear matrix inequality The solution is obtained by constructing a function relating the estimation error. The Lyapunov function V of the quadratic form, prove It conforms to Hurwitz stability, thus verifying the estimation error. Converges in the continuous-time domain:

[0051]

[0052] Furthermore, the time derivative of the Lyapunov function satisfy

[0053]

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

[0055] S34. Denote the discrete sampling interval τ. k =t k -t k-1 , A k The state transition matrix is ​​used to design the discrete sampling system using formula (8). The necessary and sufficient condition for convergence is: the state transition matrix Schur is stable.

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

[0057] S41, Let the discrete sampling interval τ k =1, and the state transition matrix of the augmented state estimation error is set as follows: or

[0058] S42, by rank get:

[0059]

[0060] S43. By configuring matrix L, so that All eigenvalues ​​are 0; and for an n-order zero-power matrix P0, P0 satisfies n =0, yielding the estimation error for the augmented state. satisfy:

[0061]

[0062] In the formula, This represents the estimation error of the augmented state after n+q sampling intervals; This represents the augmented state estimation error at the initial time.

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

[0064] Preferably, step S5 is included after step S4: recording the estimation error of each node in the multi-agent system. Consistency error With system state variable x i Data that changes over time, and plotted as an image.

[0065] Therefore, the present invention employs the above-mentioned perturbation-resistant multi-agent discrete-continuous hybrid time-defined 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. By using the augmented state method to construct the augmented state error equation, the system state and disturbance are analyzed together, the system information is comprehensively processed, and a complete framework is provided for observer design and error analysis.

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

[0069] 4. Configure a zero-power matrix to achieve convergence of estimation error within a specified time, breaking through the limitations of traditional asymptotic convergence. It can make the error strictly return to zero within a preset time, meeting the requirements of scenarios with high real-time and accuracy requirements (such as rapid collaboration of multiple agents).

[0070] 5. Prove the Hurwitz stability of the continuous-time error system using Lyapunov functions, and use the Schur stability condition analysis for discrete-time systems to ensure the stability of the system in different time domains.

[0071] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0072] Figure 1 This is a flowchart of a perturbation-resistant multi-agent discrete continuous hybrid time-specified state estimation method according to the present invention;

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

[0074] Figure 3 The state estimation error of each agent node in the simulation experiment of this invention. The graph shows the changes over time; where (a) is... The first component (b) is a graph showing the change over time. The second component Graph showing changes over time; (c) is The third component Graph showing changes over time;

[0075] Figure 4 This is the external perturbation estimation error of each agent node in the simulation experiment of this invention. The graph shows the changes over time; where (a) is... The first component (b) is a graph showing the change over time. The second component Graph showing changes over time;

[0076] Figure 5 The consistency error ξ of each agent node in the simulation experiment of this invention is... i The graph shows the change over time; where (a) represents ξ. i The first component ξ i1 Graph showing the change over time; (b) represents ξ. i The second component ξ i2 Graph showing the change over time; (c) represents ξ. i The third component ξ i3 Graph showing changes over time;

[0077] Figure 6 The system state x of the simulation experiment of this invention i The graph shows the change over time; where (a) represents x. i The first component x i1 (b) shows the change over time; x i The second component x i2 Graph showing the change over time; (c) represents x i The third component x i3 Graph showing changes over time. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0079] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

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

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

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

[0083] Step S1 specifically includes the following steps:

[0084] S11. Assuming the dynamic equations of a multi-agent system are linear time-invariant equations, introduce external disturbances and establish the continuous-time dynamic equations of a single agent:

[0085]

[0086] In the formula, x i y i u i d i Let represent the state variables, output vector, control input, and external disturbance of node i, respectively. n, m, p, and q all represent the dimensions of the matrix, and p, q < m < n; Let represent the derivative of the state variable with respect to time; 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. These represent the system matrix set, the control input matrix set, the output matrix, and the external disturbance matrix set, respectively.

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

[0088]

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

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

[0091] Step S2 specifically includes the following steps:

[0092] S21. Combine the agent's state with external disturbances to construct augmented state variables;

[0093] The augmented state variables constructed in step S21

[0094] S22. Based on augmented state variables, combined with the continuous-time dynamic equation of a single agent and external perturbation d i The dynamic equations are used to construct the augmented state estimation error equation;

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

[0096]

[0097] In the formula, Represents the augmented state variable η i The derivative; Let represent the augmented system matrix, input matrix, and output matrix, respectively.

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

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

[0100]

[0101] In the formula, 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; Indicate The extended state observer at time step; Indicates t k Extended state observer at time η; i (t k ) represents t k The expansion state at any given moment; and Where δ→0;

[0102] As shown in Equation (4), the extended state observer only uses local information for estimation and does not need to communicate with neighboring nodes. Therefore, it avoids transmission delays caused by node communication and the risk of network attacks on the communication channel. Furthermore, by using discrete time t... k Applying pulse signals to the observer, this discrete-continuous hybrid design allows for the configuration of poles in 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 control is (A,B), and the output matrix C satisfies rank(C)=m;

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

[0106] Condition 3: System matrix observation

[0107] S24. Design a consensus control protocol based on the estimated values ​​from the extended state observer.

[0108] The expression for the consensus control protocol designed in step S24 is as follows:

[0109]

[0110] In the formula, and Let i and j represent the state estimates of node i and node j, respectively. Indicates the estimated value of external disturbance; a ij Represents the adjacency matrix;

[0111] And when the extended state observer converges, there is Substituting formula (5) into formula (1) at this point, we get:

[0112]

[0113] As t→∞, lim t→∞ ||x i (t)-x j (t)||=0, x i (t) and x j (t) represent 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 dynamic equation of the estimation error 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. Based on formulas (3) and (4), derive the estimation error. The dynamic equation:

[0117]

[0118] In the formula, Indicates the augmented state estimation error The derivative; and They represent Time and t k The time estimation error;

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

[0120]

[0121] In the formula, and They represent t respectively k+1 Time and The time estimation error;

[0122] S33. Set the feedback gain matrix Where the positive definite matrix P is a linear matrix inequality The solution is obtained by constructing a function relating the estimation error. The Lyapunov function V of the quadratic form, prove It conforms to Hurwitz stability, thus verifying the estimation error. Converges in the continuous-time domain:

[0123]

[0124] Furthermore, the time derivative of the Lyapunov function satisfy

[0125]

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

[0127] S34. Denote the discrete sampling interval τ k =t k -t k-1 , A k The state transition matrix is ​​used to design the discrete sampling system using formula (8). The necessary and sufficient condition for convergence is: the state transition matrix Schur is stable.

[0128] It should be noted that when the discrete trigger interval t k+1 -t k When the design is very small, that is When the poles are close to the unit circle, problems arise such as reduced response speed, decreased stability margin, and reduced anti-interference capability. Therefore, by applying pulses to the extended state observer at discrete moments, the state transition matrix is... A gain matrix is ​​configured beforehand. Then, configuring matrix L will 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 transition matrix of the augmented state estimation error is set as follows: or

[0132] S42, by get:

[0133]

[0134] S43. By configuring matrix L, so that All eigenvalues ​​are 0; and for an n-order zero-power matrix P0, P0 satisfies n =0, yielding the estimation error for the augmented state. satisfy:

[0135]

[0136] In the formula, This represents the estimation error of the augmented state after n+q sampling intervals; This represents the augmented state estimation error at the initial time.

[0137] S44. Set the discrete sampling interval τ k =Δ, where Δ is any positive constant, thus yielding the augmented state estimation error. The time to converge to zero is And since n+q is a fixed value, the convergence time T and the discrete sampling interval τ are obtained. k The relationship is as follows: For a given multi-agent system dynamic, n+q is a constant, therefore the augmented state estimation error... The convergence time depends only on the discrete sampling interval, thus enabling convergence at any preset time.

[0138] Step S4 is followed by step S5: recording the estimation error of each node in the multi-agent system. Consistency error With system state variable x i Data that changes over time, and plotted as an image.

[0139] Simulation Experiment

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

[0141] Its Laplace matrix for:

[0142]

[0143] Simulation modeling of a multi-agent system under external disturbances is performed, with the parameters selected as follows:

[0144] τ k =1.

[0145] Furthermore, the above parameter settings satisfy the three conditions for the existence of an extended state observer.

[0146] Then, by solving the LMI (linear matrix inequality) and pole placement calculations, we obtain:

[0147]

[0148] It has been verified that Schur is stable, and Therefore, the estimation error It converges at t=5.

[0149] Each node's estimation error Divided into state estimation error External disturbance estimation error and the consistency error of agent network nodes and system state x i The curve showing how it changes with time t is as follows Figures 3-6 As shown, by Figure 3 , Figure 4 It can be seen that the estimation error converges to zero after t > 5τ = 5. From Figure 5 and Figure 6 It can be seen that under the influence of external disturbances (in sinusoidal form), the consistency of the multi-agent system can be achieved by using the control law shown in formula (5).

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

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

Claims

1. A perturbation-resistant multi-agent discrete-continuous hybrid state estimation method for a specified time, characterized in that: Includes the following steps: S1. Considering the state dynamics of the multi-agent system and the influence of external disturbances, construct the dynamic equations of the multi-agent system. S2. Based on the dynamic equations of the multi-agent system constructed in step S1, construct the augmented state estimation error equations and extended state observers of the multi-agent system. S3. By constructing the dynamic equation of the estimation error 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. Based on the state transition matrix of the augmented state in the discrete time domain, design the discrete sampling interval and pulse update parameters so that the state transition matrix satisfies the zero-power property, thereby driving the augmented state estimation error to converge precisely to zero after a finite number of discrete samplings. Step S2 specifically includes: S21. Combine the agent's state with external disturbances to construct augmented state variables. , , Representing nodes respectively The state variables and external disturbances; S22. Based on augmented state variables, combined with the continuous-time dynamic equation of a single agent and external perturbations. Based on the dynamic equations, we construct the augmented state estimation error equation, expressed as follows: （3）； In the formula, Representing augmented state variables The derivative; , , Let represent the augmented system matrix, input matrix, and output matrix, respectively. , , ; and Representing nodes respectively The output vector and control input; , , , , , , , Both represent the dimensions of the matrix, and ; , , , The parameters represent the system matrix, control input matrix, output matrix, and unknown input matrix, respectively. , , , , , , , These represent the system matrix set, the control input matrix set, the output matrix, and the external disturbance matrix set, respectively. Denotes the perturbation matrix, and ; S23. Construct an extended state observer based on augmented state variables. The expression is as follows: （4）； In the formula, Represents the augmented state estimate The derivative; Denotes the feedback gain matrix, and , It is a positive definite matrix that satisfies the linear matrix inequality. The solution; This represents the configuration matrix to be designed; Represents the identity matrix; express The extended state observer at time step; express The extended state observer at time step; express The expansion state at any given moment; and ,in ; The extended state observer satisfies the following conditions: Condition 1: System matrix control And the output matrix satisfy ; Condition 2: External disturbance With control input When acting on a multi-agent system through the same channel, a constant matrix exists. Make ; Condition 3: System matrix observation ; S24. Based on the estimated values ​​from the extended state observer, design a consensus control protocol, expressed as follows: （5）； In the formula, and Representing nodes respectively and nodes State estimate; This represents the estimated value of the external disturbance; Represents the adjacency matrix; Indicates the number of nodes in a multi-agent system; After the extended state observer achieves convergence, there is , Substituting formula (5) into formula (1) at this point, we get: （6）； when hour, , , and They represent Time Node and nodes With state variables, multi-agent systems will achieve consistency.

2. The disturbance-resistant multi-agent discrete-continuous hybrid time-defined state estimation method according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Assuming the dynamic equations of a multi-agent system are linear time-invariant equations, introduce external disturbances and establish the continuous-time dynamic equations of a single agent: （1）； In the formula, This represents the derivative of the state variable with respect to time. S12. Assuming the external disturbance is generated by a linear dynamic system whose eigenvalues ​​are distributed at different positions on the imaginary axis, construct the external disturbance. The dynamic equation: （2）； In the formula, Indicates external disturbance The derivative of .

3. The disturbance-resistant multi-agent discrete-continuous hybrid time-defined state estimation method according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Based on formulas (3) and (4), derive the estimated error. The dynamic equation: （7）； In the formula, Indicates the augmented state estimation error The derivative; and They represent Time and The time estimation error; S32. According to formula (7), the equation for the estimation error in the discrete time domain is obtained: （8）； In the formula, and They represent Time and The time estimation error; S33. Set the feedback gain matrix The positive definite matrix Linear matrix inequalities The solution is obtained by constructing a function relating the estimation error. Lyapunov function of quadratic form ,prove It conforms to Hurwitz stability, thus verifying the estimation error. Converges in the continuous-time domain: （9）； Furthermore, the time derivative of the Lyapunov function satisfy （10）； Therefore, the estimation error It converges in the continuous time domain; S34. Record the discrete sampling interval. , , The state transition matrix is ​​used to design the discrete sampling system using formula (8). The necessary and sufficient condition for convergence is: the state transition matrix Schur is stable.

4. The disturbance-resistant multi-agent discrete-continuous hybrid time-defined state estimation method according to claim 3, characterized in that: Step S4 Specifically, the following steps are included: S41, Let the discrete sampling interval be... Let the state transition matrix of the augmented state estimation error be... or ; S42, by , ,get: （11）； S43, By configuring the matrix ,make All eigenvalues ​​are 0; and for Zero-order power matrix satisfy The augmented state estimation error is obtained. satisfy: （12）； In the formula, Indicates the process The estimation error of the augmented state after one sampling interval; This represents the augmented state estimation error at the initial time. S44. Set the discrete sampling interval , For any positive constant, the augmented state estimation error is obtained. The time to converge to zero is ,and The convergence time is obtained by setting a fixed value. With discrete sampling interval The relationship.

5. The disturbance-resistant multi-agent discrete-continuous hybrid time-specified state estimation method according to claim 1, characterized in that: Step S4 is followed by step S5: recording the estimation error of each node in the multi-agent system. Consistency error With system state variables Data that changes over time, and plotted as an image.

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