Multi-agent robust specified time state estimation method based on discrete continuous mixing

Abstract

The invention discloses a multi-agent robust specified time state estimation method based on discrete continuous mixing, and belongs to the field of distributed state estimation of an agent system, and the method comprises the following steps: S1, analyzing the uncertainty of a multi-agent system and a measurement noise model, and building a system dynamic equation; s2, designing a transformation matrix based on a null space and a system dynamic equation, and constructing a multi-agent system consistency error; s3, constructing a state space equation of the state observer based on the consistency error of the multi-agent system; and S4, based on the state space equation of the state observer, realizing specified time convergence of the estimation error through the power return-to-zero characteristic of the power zero matrix. According to the multi-agent robust specified time state estimation method based on discrete continuous mixing, state estimation is carried out only by using relative output information between neighbors without depending on relative input information between the neighbors, use of communication channels is avoided, and the method has the characteristic of network attack immunity.

Description

Technical Field

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

[0002] In recent years, unmanned technology has played an important role in agriculture, logistics, military and other fields, among which unmanned systems represented by drones and unmanned vehicles have become the focus of attention. However, due to the limitations of payload, perception, communication and energy, a single unmanned system is limited in its ability to perform tasks in complex environments. Therefore, people have begun to study unmanned swarm systems to enhance their task execution capabilities through information interaction between multiple unmanned systems.

[0003] Accurate state estimation of unmanned swarm systems is a basic requirement for completing tasks in complex environments. Good state estimation can ensure the decision-making and control reliability of unmanned swarm systems and further affect the completion of tasks. At present, the state estimation methods for unmanned swarm systems include building a distributed sensor network for a single unmanned system, using various heterogeneous sensors to perceive, estimate, and fuse, so as to estimate the state of itself or the environment. Or, a distributed sensor network is built for the unmanned swarm system as a whole, making full use of the sensor measurement information of other individuals to improve the accuracy of its own state estimation. The former may reduce the reliability of the operation of the swarm system when a single sensor is interfered with or even fails. The latter makes up for the above shortcomings by estimating the state through the measurement information of other individual sensors, but requires individuals to obtain the control input information of all nodes in the cluster. Therefore, it is difficult to apply when there are uncertain factors such as unmodeled dynamics in the system and the communication is non-real-time.

[0004] Existing distributed state estimation research is mainly divided into Kalman filter-based methods and observer-based methods. The Kalman filter-based method couples the Kalman filter theory with the state estimation problem of multi-agent systems, and only uses local node information without the need for a fusion center for state estimation.

[0005] For example, G. Battistelli, L. Chisci, G. Mugnai et al. in "Consensus-based Linear and Nonlinear Filtering" and G. Battistelli, L. Chisci in "Stability of Consensus Extended Kalman Filter for Distributed State Estimation" designed the state estimation fusion and distributed estimator update simultaneously, thus obtaining a distributed state estimation algorithm based on consistency; At the same time, S. Battilotti, F. Cacace, M. dAngelo, etc. gave the corresponding distributed state estimation algorithm for continuous-time systems in "Asymptotically Optimal Consensus-based Distributed Filtering of Continuous-time Linear Systems". However, in order to relax the local observability or local detectability conditions, the estimation convergence of the above distributed state estimation algorithm cannot achieve the optimality in the mean square sense.

[0006] P. Duan, Y. Lv, Z. Duan et al. studied the distributed state estimation problem of continuous-time linear systems with time-correlated measurement noise in "Distributed State Estimation for Uncertain Linear Systems with a Recursive Architecture". They proposed a new augmented leader-follower information fusion strategy to collect measurements and system matrices, in which each sensor only communicates with its neighbors, and gave a minimum upper bound on the estimation error covariance.

[0007] Observer-based distributed state estimation methods consider the joint observability or detectability of the system and construct local observers for nodes in the network to estimate the overall state of the system.

[0008] For example, Y. Lv, J. Zhou, Q. Wang and G. Wen studied the output feedback consistency problem of linear multi-agent systems under directed communication topology in "Attack-free Protocol Design with Distributed Noncontinuous Appointed-time Unknown Input Observer", using only relative output measurements to generate observers and control inputs.

[0009] Y. Lv, G. Wen, and T. Huang studied the consistency problem of multi-agent systems under directed graphs in "Adaptive protocol design for distributed tracking with relative output information: A distributed fixed-time observer approach" and designed a fully distributed adaptive protocol based on unknown input observers.

[0010] In "Fully Distributed Adaptive NN-Based Consensus Protocol for Nonlinear MASs: An Attack-Free Approach", Y. Lv, J. Zhou, G. Wen, X. Yu and T. Huang publicly proposed a fully distributed adaptive protocol for nonlinear multi-agent systems based on "Adaptive protocol design for distributed tracking with relative output information: A distributed fixed-time observer approach" to solve the consensus control problem.

[0011] It can be seen that the existing distributed sensor networks suffer from performance degradation when there is uncertainty in the system. Summary of the invention

[0012] To solve the above problems, the present invention provides a multi-agent robust specified time state estimation method based on discrete-continuous hybrid. By adopting a distributed robust state estimation method with unknown input, an unknown input observer is designed to achieve specified time estimation, breaking through the performance bottleneck of traditional distributed filtering under system uncertainty, and improving the state estimation performance of distributed sensor networks.

[0013] To achieve the above object, the present invention provides a multi-agent robust specified time state estimation method based on discrete-continuous hybrid, comprising the following steps: S1. Analyze the uncertainty of multi-agent system and measurement noise model and establish the system dynamic equation; S2, design the transformation matrix based on the null space and system dynamic equations to construct the consistency error of the multi-agent system; S3. Based on the consistency error of the multi-agent system, construct the state space equation of the state observer; S4. Based on the state space equation of the state observer, the specified time convergence of the estimation error is achieved through the property of the nilpotent matrix returning to zero.

[0014] Preferably, step S1 specifically includes the following steps: S11. Introduce uncertainty input to construct the system dynamic equation: (1) In the formula, , , , Respectively represent nodes states, outputs, control inputs, and uncertainty inputs, and , , , , , , , They represent the state set, output set, control input set and uncertainty input set respectively. , , , Respectively , , , The dimension of represents the time derivative of the state variable; Indicates the number of nodes in the multi-agent system; , , , denote the parameters of the system matrix, input matrix, output matrix and uncertainty input matrix respectively, and , , , , , , , They represent the system matrix set, input matrix set, output matrix set and uncertainty input matrix set respectively; S12. Input the matrix in formula (1) and the uncertainty input matrix Augmented to Matrix ,remember is the unknown input matrix, and the control input , uncertainty input Merge into ,remember For unknown input, , ,and , Respectively represent the unknown input matrix set and the unknown input set, assuming that the matrix dimensions satisfy the relationship: ; Transforming formula (1) yields the following formula: (2).

[0015] Preferably, in step S11, the control input of each agent The design method is as follows: (3) In the formula, represents a positive constant; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; Indicates delay; Indicates the initial time; And set the control input The correlation matrix parameters of , which satisfies the following linear matrix inequality: (4) The value of satisfies: (5) In the formula, is the Laplace matrix No. eigenvalues, ; According to formula (4), solve the linear matrix inequality to obtain the correlation matrix parameters that meet the conditions. , and then calculate the correlation matrix parameters , complete the design of control input.

[0016] Preferably, in step S11, it is assumed that the system dynamic equation is a linear time-invariant equation. , , , are all constant matrices, considering the sine function , cosine function and coefficient Exponential function For uncertainty input Modeling.

[0017] Preferably, step S2 specifically includes the following steps: S21. Calculate the consistency error of each node in the multi-agent system : (6) In the formula, Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; Representation Node Status; S22, the overall consistency error of the multi-agent system , the overall state of the multi-agent system , we get the following formula: (7) In the formula, represents the communication topology Laplace matrix, symbol Represents the Kronecker product operation of the matrix; represents the identity matrix; S23, combined with formula (2) and formula (6), the consistency error of each node in the multi-agent system is obtained The dynamic equation of: (8) In the formula, Representation Node Consistency Error Derivative with respect to time; Representation Node unknown input; Representation Node unknown input; Representation Node Consistency Error The output, Representation Node Output: S24, take , ,in, express The unit matrix, represents the intermediate transformation matrix; then ; Defining new states , and substitute get: (9) Get Status The dynamic equation formula is as follows: (10) In the formula, Defined as state Output: express The identity matrix of order.

[0018] Preferably, step S3 specifically includes the following steps: S31, structure for the state Estimated unknown input observer : (11) In the formula, represents the closed-loop feedback matrix; Represents the feedback gain matrix, which is used to construct the nilpotent matrix; ,in , express The unknown input observer at time t; express The unknown input observer at time t; Representation Node exist Output at the moment; Representation Node exist Output at the moment; express The state of the moment; S32. Reconstructing the consistency error of multi-agent system based on state estimation and output measurement: Set the initial value condition to , when the estimation error When ,get ,in Representation Node Consistency error estimate With Node Consistency Error The difference is the estimated error of the consistency error.

[0019] Preferably, step S4 specifically includes the following steps: S41, set the estimated error to , The state equation and update equation are: (12) (13) In the formula, express The estimated error of the moment; express The estimated error of the moment; express Status of the moment ; S42. Solve formula (12) to obtain: (14) in ,Pick , and remember ,get: (15) S43, in Apply pulses at all times and get: (16) Get the estimated error exist and There is a time between Constant multiple relationship, and then get: (17) in ; S44, will Designed as a nilpotent matrix, the feedback gain matrix The following conditions are met: (18) in The minimum power that satisfies formula (18); S45, when hour, , so there is , realizing the unknown observer At the estimated specified time Internal consistency error accurate estimate of .

[0020] Preferably, step S4 further includes step S5: recording the estimated error of the consistency error of each node in the multi-agent system , consistency error , Network node status Data changing over time and plotting it.

[0021] The present invention has the following beneficial effects: 1. The unknown input observer can achieve accurate estimation within a specified time or even an arbitrarily small time, thus meeting the requirements of real-time response in special scenarios; 2. Only the relative output information between adjacent nodes is used to generate control input, which does not rely on the relative input information between neighbors, thus avoiding the use of communication channels and having the characteristics of immunity to network attacks; 3. The designed state estimation method can effectively handle uncertain inputs and has good robustness, thus ensuring higher estimation accuracy.

[0022] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the discrete-continuous hybrid multi-agent robust specified time state estimation method of the present invention; Figure 2 It is a network communication topology diagram of the simulation experiment of the present invention; Figure 3 is the estimated error of the consistency error of each intelligent agent node in the simulation experiment of the present invention Time-varying graph; where Figure 3 (a) The first component Plots of changes over time; Figure 3 (b) The second component Plots of changes over time; Figure 3 (c) The third component Plots of changes over time; Figure 3 (d) The fourth component Plots of changes over time; Figure 4 is the consistency error of each intelligent agent node in the simulation experiment of the present invention Time-varying graph; where Figure 4 (a) The first component Plots of changes over time; Figure 4 (b) The second component Time-varying graphs; Figure 4 (c) The third component Plots of changes over time; Figure 4 (d) The fourth component of Time-varying graphs; Figure 5 is the state of each agent in the simulation experiment of the present invention Time-varying graph; where Figure 5 (a) The first component Plots of changes over time; Figure 5 (b) The second component Plots of changes over time; Figure 5 (c) The third component Plots of changes over time; Figure 5 (d) The fourth component Graph of changes over time. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical scheme and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention are further described in detail 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 this application, 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 reference numerals throughout represent the same or similar elements or elements with the same or similar functions.

[0025] It should be noted that the terms "include", "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or server comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or devices.

[0026] Like reference numerals and letters denote similar items in the following drawings, and thus, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0027] like Figure 1 As shown, a multi-agent robust specified time state estimation method based on discrete-continuous hybrid includes the following steps: S1. Analyze the uncertainty of multi-agent system and measurement noise model and establish the system dynamic equation; Step S1 specifically includes the following steps: S11. In the state estimation problem of multi-agent systems, there are many unknown uncertain factors in the actual environment, including system noise and environmental noise, unmodeled dynamics, actuator failures, etc. Therefore, in order to study the impact of uncertainty factors on state estimation performance, uncertainty input is introduced to construct the system dynamic equation: (1) In the formula, , , , Respectively represent nodes states, outputs, control inputs, and uncertainty inputs, and , , , , , , , They represent the state set, output set, control input set and uncertainty input set respectively. , , , Respectively , , , The dimension of represents the time derivative of the state variable; Indicates the number of nodes in the multi-agent system; , , , denote the parameters of the system matrix, input matrix, output matrix and uncertainty input matrix respectively, and , , , , , , , They represent the system matrix set, input matrix set, output matrix set and uncertainty input matrix set respectively; In step S11, the control input of each agent The design method is as follows: (3) In the formula, represents a positive constant; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; Indicates delay; Indicates the initial time; And set the control input The correlation matrix parameters of , which satisfies the following linear matrix inequality: (4) The value of satisfies: (5) In the formula, is the Laplace matrix No. eigenvalues, ; According to formula (4), solve the linear matrix inequality to obtain the correlation matrix parameters that meet the conditions. , and then calculate the correlation matrix parameters , complete the design of control input.

[0028] It should be noted that the Dynamic consensus of linear multi-agent systems published by Z. Li, Z. Duan, and G. Chen can prove that the communication topology Under the condition of containing a spanning tree, the consistency of the multi-agent system can be achieved by designing the control input as shown in formula (4).

[0029] In step S11, it is assumed that the system dynamic equation is a linear time-invariant equation. , , , are all constant matrices, considering the sine function , cosine function and coefficient Exponential function For uncertainty input Modeling.

[0030] S12. Input the matrix in formula (1) and the uncertainty input matrix Augmented to Matrix , and the control input , uncertainty input Merge into ,at this time , , and assuming that the matrix dimensions satisfy the relationship: ; Transforming formula (1) yields the following formula: (2).

[0031] S2, design the transformation matrix based on the null space and system dynamic equations to construct the consistency error of the multi-agent system; Step S2 specifically includes the following steps: S21. In practical estimation problems, multi-agent systems need to estimate the consistency error of each node. For control input The generation of consistency is achieved, so the consistency error of each node of the multi-agent system is calculated : (6) In the formula, Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; Representation Node Status; S22, the overall consistency error of the multi-agent system , the overall state of the multi-agent system , we get the following formula: (7) In the formula, represents the communication topology Laplace matrix, symbol Represents the Kronecker product operation of the matrix; represents the identity matrix; S23, combined with formula (2) and formula (6), the consistency error of each node in the multi-agent system is obtained The dynamic equation of: (8) In the formula, Representation Node Consistency Error Derivative with respect to time; Representation Node unknown input; Representation Node unknown input; Representation Node Consistency Error The output, Representation Node Output: S24, take , ,in, express The unit matrix, represents the intermediate transformation matrix; then ; Defining new states , and substitute get: (9) Get Status The dynamic equation formula is as follows: (10) In the formula, Defined as state Output: express The identity matrix of order.

[0032] S3. Based on the consistency error of the multi-agent system, construct the state space equation of the state observer; Step S3 specifically includes the following steps: S31, structure for the state Estimated unknown input observer : (11) In the formula, represents the closed-loop feedback matrix; Represents the feedback gain matrix, which is used to construct the nilpotent matrix; ,in , express The unknown input observer at time t; express The unknown input observer at time t; Representation Node exist Output at the moment; Representation Node exist Output at the moment; express The state of the moment; S32. Reconstructing the consistency error of multi-agent system based on state estimation and output measurement: Set the initial value condition to , when the estimation error When ,get ,in Representation Node Consistency error estimate With Node Consistency Error The difference is the estimated error of the consistency error.

[0033] S4. Based on the state space equation of the state observer, the specified time convergence of the estimation error is achieved through the property of the nilpotent matrix returning to zero.

[0034] Step S4 specifically includes the following steps: S41, set the estimated error to , The state equation and update equation are: (12) (13) In the formula, express The estimated error of the moment; express The estimated error of the moment; express Status of the moment ; S42. Solve formula (12) to obtain: (14) in ,Pick , and remember ,get: (15) S43, in Apply pulses at all times and get: (16) Get the estimated error exist and There is a time between Constant multiple relationship, and then get: (17) in ; S44, will Designed as a nilpotent matrix, the feedback gain matrix The following conditions are met: (18) in The minimum power that satisfies formula (18); S45, when hour, , so there is , realizing the unknown observer At the estimated specified time Internal consistency error accurate estimate of .

[0035] Step S4 also includes step S5: recording the estimated error of each node in the multi-agent system , consistency error , Network node status Data changing over time and plotting it.

[0036] Simulation experiment 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 in the figure satisfies the conditions of having a directed spanning tree and can design control inputs to achieve consistency in the multi-agent system.

[0037] Its Laplace matrix for ;

[0038] The multi-agent system is simulated and modeled, and the multi-agent system parameters are selected as follows: ;

[0039] according to , , the calculated matrix and as follows: ;

[0040] Then we get: ;

[0041] Then construct the nilpotent matrix and select the delay and the closed-loop feedback matrix As shown below: ;

[0042] Therefore, in the expression of the nilpotent matrix In, only Requires individual design.

[0043] And since the necessary and sufficient condition for a nilpotent matrix is ​​that all characteristic roots of the nilpotent matrix are 0, the eigenvalues ​​are all configured to zero through pole configuration, so we choose for: ;

[0044] Get the nilpotent matrix for: ;

[0045] It has been verified that the nilpotent matrix satisfy , the construction of the nilpotent matrix is ​​completed, and the unknown input observer will achieve convergence of the estimation error after the fourth pulse signal is applied, that is, assuming , then the unknown input observer will be The exact convergence of the estimation error is achieved after the moment .

[0046] The estimated error of the consistency error of each node , consistency error and the agent network node status Over time The changing curve is Figure 3-Figure 5 As shown by Figure 3 It can be seen that the estimation error exist Then it converges to zero. Figure 4 It can be seen that under the control input designed by formula (4), the consistency error of each network node is can all converge to 0. Figure 5 It can be seen that the status of the three network nodes has been consistent in a short time.

[0047] From the above simulation experiments, combined with the actual multi-agent system consistency control task, it can be seen that the multi-agent robust specified time state estimation method based on discrete-continuous hybrid designed by the present invention can accurately estimate the consistency error of the multi-agent system with uncertain input within the specified time, thereby verifying the effectiveness and accuracy of the present invention.

[0048] Therefore, the present invention adopts the above-mentioned multi-agent robust specified time state estimation method based on discrete-continuous hybrid, and only uses the relative output information between neighbors for state estimation, does not rely on the relative input information between neighbors, avoids the use of communication channels, and has the characteristics of immunity to network attacks.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. 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 solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-agent robust specified time state estimation method based on discrete-continuous hybrid, characterized by: The following steps are involved: S1. Analyze the uncertainty of multi-agent system and measurement noise model and establish the system dynamic equation; S2, design the transformation matrix based on the null space and system dynamic equations to construct the consistency error of the multi-agent system; S3. Based on the consistency error of the multi-agent system, construct the state space equation of the state observer; S4. Based on the state space equation of the state observer, the specified time convergence of the estimation error is achieved through the property of the nilpotent matrix returning to zero.

2. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 1 is characterized by: Step S1 specifically includes the following steps: S11. Introduce uncertainty input to construct the system dynamic equation: (1) In the formula, , , , Respectively represent nodes states, outputs, control inputs, and uncertainty inputs, and , , , , , , , They represent the state set, output set, control input set and uncertainty input set respectively. , , , Respectively , , , The dimension of represents the time derivative of the state variable; Indicates the number of nodes in the multi-agent system; , , , denote the parameters of the system matrix, input matrix, output matrix and uncertainty input matrix respectively, and , , , , , , , They represent the system matrix set, input matrix set, output matrix set and uncertainty input matrix set respectively; S12. Input the matrix in formula (1) and the uncertainty input matrix Augmented to Matrix ,remember is the unknown input matrix, and the control input , uncertainty input Merge into ,remember is an unknown input. , ,and , Respectively represent the unknown input matrix set and the unknown input set, assuming that the matrix dimensions satisfy the relationship: ; Transforming formula (1) yields the following formula: (2)。 3. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 2 is characterized by: In step S11, the control input of each agent The design method is as follows: (3) In the formula, represents a positive constant; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; Indicates delay; Indicates the initial time; And set the control input The correlation matrix parameters of , which satisfies the following linear matrix inequality: (4) The value of satisfies: （5） In the formula, is the Laplace matrix No. eigenvalues, ; According to formula (4), solve the linear matrix inequality to obtain the correlation matrix parameters that meet the conditions. , and then calculate the correlation matrix parameters , complete the design of control input.

4. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 3 is characterized by: In step S11, it is assumed that the system dynamic equation is a linear time-invariant equation. , , , are all constant matrices, considering the sine function , cosine function and coefficient Exponential function For uncertainty input Modeling.

5. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 4 is characterized by: Step S2 specifically includes the following steps: S21. Calculate the consistency error of each node in the multi-agent system : （6） In the formula, Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; Representation Node Status; S22, the overall consistency error of the multi-agent system , the overall state of the multi-agent system , we get the following formula: （7） In the formula, represents the communication topology Laplace matrix, symbol Represents the Kronecker product operation of the matrix; represents the identity matrix; S23, combined with formula (2) and formula (6), the consistency error of each node in the multi-agent system is obtained The dynamic equation of: (8) In the formula, Representation Node Consistency Error Derivative with respect to time; Representation Node unknown input; Representation Node unknown input; Representation Node Consistency Error The output, Representation Node Output: S24, take , ,in, express The unit matrix, represents the intermediate transformation matrix; then ; Defining new states , and substitute get: （9） Get Status The dynamic equation formula is as follows: (10) In the formula, Defined as state Output: express The identity matrix of order.

6. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 5 is characterized by: Step S3 specifically includes the following steps: S31, construction for the state Estimated unknown input observer : (11) In the formula, represents the closed-loop feedback matrix; Represents the feedback gain matrix, which is used to construct the nilpotent matrix; ,in , express The unknown input observer at time t; express The unknown input observer at time t; Representation Node exist Output at the moment; Representation Node exist Output at the moment; express The state of the moment; S32. Reconstructing the consistency error of multi-agent system based on state estimation and output measurement: Set the initial value condition to , when the estimation error When ,get ,in Representation Node Consistency error estimate With Node Consistency Error The difference.

7. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 6 is characterized by: Step S4 The specific steps include: S41, set the estimated error to , The state equation and update equation are: (12) (13) In the formula, express The estimated error of the moment; express The estimated error of the moment; express Status of the moment ; S42. Solve formula (12) to obtain: （14） in ,Pick , and remember ,get: （15） S43, in Apply pulses at all times and get: （16） Get the estimated error exist and There is a time between Constant multiple relationship, and then get: （17） in ; S44, will Designed as a nilpotent matrix, the feedback gain matrix The following conditions are met: （18） in The minimum power that satisfies formula (18); S45, when hour, , so there is , realizing the unknown observer At the estimated specified time Internal consistency error accurate estimate of .

8. The multi-agent robust specified time state estimation method based on discrete-continuous hybrid according to claim 7 is characterized by: Step S4 also includes step S5: recording the estimated error of the consistency error of each node in the multi-agent system , consistency error , Network node status Data changing over time and plotting it.

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