Uncertain multi-agent state estimation method at specified time based on dual observers

Abstract

The present invention discloses an uncertain multi-agent specified time state estimation method based on a dual observer, which belongs to the field of multi-agent system state estimation and collaborative control, and includes the following steps: S1, analyzing the uncertainty of the multi-agent system and the noise model, and establishing the system dynamic equation; S2, designing the transformation matrix based on the null space and the system dynamic equation, and constructing the multi-agent system consistency error dynamic equation; S3, constructing a dual observer based on the system state equation and the output equation; S4, introducing time lag information to establish a non-homogeneous linear equation system with a reversible coefficient matrix, and inversely solving the state estimation value. The present invention adopts the above-mentioned uncertain multi-agent specified time state estimation method based on a dual observer, based on the multi-agent system dynamics, regards the control input of each node as an unknown input, and introduces an uncertainty term, and proposes a new full-order distributed specified time observer to estimate the precise consistency error within any preset time.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent system state estimation and cooperative control, and in particular to an uncertain multi-agent specified time state estimation method based on a dual observer. Background Art

[0002] In the past two decades, cooperative control of multi-agent systems has been widely studied due to the widespread application of cooperative behavior in nature and industry. As a fundamental problem, the consensus problem is also the most concerned issue in cooperative control. The basic task of the consensus problem is to make the state of each network node reach a consensus through a distributed control protocol designed based only on local information.

[0003] The existing research on distributed control protocol design is as follows:

[0004] H. Zhang, F. Lewis, and A. Das in "Optimal design for synchronization of cooperative systems: State feedback, observer and output feedback" and Z. Li, Z. Duan, G. Chen, and L. Huang in "Consensus of multi-agent systems and synchronization of complex networks: A unified viewpoint" both proposed a distributed protocol for consensus tracking of linear multi-agent systems.

[0005] The consensus tracking problem of heterogeneous linear multi-agent systems was studied by Y. Su and J. Huang in "Cooperative output regulation of linear multi-agent systems by output feedback" and by Y. Lv, Z. Li, and Z. Duan in "Distributed PI control for consensus of heterogeneous multiagent systems over directed graphs".

[0006] L. Zhu, Z. Chen, and RH Middleton's "A general framework for robust output synchronization of heterogeneous nonlinear networked systems", M. Lu and L. Liu's "Robust output consensus of networked heterogeneous nonlinear systems by distributed output regulation", and T. Liu and J. Huang's "A distributed observer for a class of nonlinear systems and its application to a leader-following consensus problem" all studied heterogeneous nonlinear multi-agent systems.

[0007] Based on the small gain condition, M. Lu and L. Liu proposed a distributed protocol for consistency tracking of heterogeneous linear multi-agent systems in "Cooperative output regulation of linear multi-agent systems by a novel distributed dynamic compensator". The generation of this protocol only uses the relative output information between neighbors and does not require communication exchange.

[0008] Z. Li, W. Ren, X. Liu, and L. Xie in "Distributed consensus of linear multiagent systems with adaptive dynamic protocols" and Y. Lv, Z. Li, Z.Duan, and J. Chen in "Distributed adaptive output feedback consensus protocolsfor linear systems on directed graphs with a leader of bounded input" disclosed that they estimated global connectivity information by introducing adaptive control methods and designed fully distributed adaptive protocols for undirected graphs and directed graphs, respectively. The protocols require the absolute output of each network node and the observation information of the neighbor observer.

[0009] Y. Lv, Z. Li, and Z. Duan proposed a fully distributed adaptive protocol for leader-follower directed graphs with relative output information based on neighbor nodes and their observers in "Distributed adaptive consensus protocols for linear multi-agent systems over directed graphs with relative output information", but this protocol can only solve the case where the leader control input is zero.

[0010] For the case where the error dynamics of a multi-agent system include unknown inputs, we consider using unknown input observer design methods commonly used in the field of fault diagnosis. In the past few decades, unknown input observers have been well developed, for example:

[0011] F. Yang and RW Wilde proposed a direct design algorithm for full-order observers in "Observers for linear systems with unknown inputs".

[0012] M. Darouach, M. Zasadzinski, and SJ Xu in "Full-order observers for linear systems with unknown inputs" gave necessary and sufficient conditions for the existence of unknown input observers.

[0013] M. Valcher studied the case of discrete-time linear systems in "State observers for discrete-time linear systems with unknown inputs".

[0014] M. Hou and P. Muller designed a reduced-order unknown input observer in "Design of observers for linear systems with unknown inputs".

[0015] H. Trinh, TD Tran, and T. Fernando proposed a new unknown input observer design method in "Disturbance decoupled observers for systems with unknown inputs" and derived the relaxation existence conditions.

[0016] It can be seen that the existing technologies mostly consider single-aspect uncertainty factors. For the state estimation and collaborative control of complex network systems under uncertain environments, the following uncertainty factors are not considered:

[0017] 1. Uncertainty caused by noise in the system itself and the measurement process;

[0018] 2. Uncertainty caused by model uncertainty, external environmental interference, and complex interactions between individuals;

[0019] 3. Uncertainty introduced by incomplete knowledge of the topological structure or dynamic changes over time. Summary of the invention

[0020] In order to solve the problem of performance degradation of existing distributed sensor networks when there is uncertainty in the system, the present invention provides an uncertain multi-agent specified time state estimation method based on a dual observer. Based on the dynamics of the multi-agent system, the control input of each node is regarded as an unknown input, and an uncertainty term is introduced. A new full-order distributed specified time observer is proposed to estimate the precise consistency error within any preset time.

[0021] To achieve the above object, the present invention provides an uncertain multi-agent specified time state estimation method based on a dual observer, comprising the following steps:

[0022] S1. Analyze the uncertainty of multi-agent system and noise model, and establish the system dynamic equation;

[0023] S2. Design the transformation matrix based on the null space and the system dynamic equations, and construct the dynamic equations of the consistency error of the multi-agent system;

[0024] S3, construct a dual observer based on the system state equation and output equation;

[0025] S4. Introduce time-delay information to establish a non-homogeneous linear equation system with an invertible coefficient matrix and inversely solve the state estimate.

[0026] Preferably, step S1 specifically includes the following steps:

[0027] S11. Introduce uncertainty input into the multi-agent system composed of N agents and construct the system dynamic equation:

[0028] (1)

[0029] 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;

[0030] 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: ;

[0031] The equivalent transformation formula (1) yields the following formula:

[0032] (2).

[0033] 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.

[0034] Preferably, step S2 specifically includes the following steps:

[0035] S21. Design the control input for each agent in a multi-agent system :

[0036] (3)

[0037] In the formula, Represents the consistency error of each node, which is defined as ; Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; is the communication topology coupling parameter; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; represents the time lag parameter; Indicates the initial time;

[0038] And set the control input The correlation matrix parameters of , which satisfies the following linear matrix inequality:

[0039] (4)

[0040] The value of satisfies:

[0041] (5)

[0042] In the formula, is the Laplace matrix No. eigenvalues, ;

[0043] 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;

[0044] S22, according to the consistency error The definition of is combined with formula (2) to obtain the consistency error The dynamic equation of:

[0045] (6)

[0046] 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.

[0047] Preferably, in step S3, the dynamic equation of the dual observer is defined based on formula (2):

[0048] (7)

[0049] In the formula, and are the states of observer 1 and observer 2 of the dual observer, and Respectively represent the time derivatives of the states of observer 1 and observer 2 of the dual observer; transformation matrix satisfy ; and They respectively represent feedback gain matrices with different values; and denote the measurement gain matrices of observer 1 and observer 2 of the dual observer respectively;

[0050] Set the transformation matrix ,in, Represents the identity matrix, and the poles are arranged so that , The real parts of all eigenvalues ​​are less than 0, so we can deduce that , The expression is as follows:

[0051] (8).

[0052] Preferably, step S4 specifically includes the following steps:

[0053] S41. Settings , , , , ,in, , , , Both represent dual observers Matrix parameters; express The identity matrix of order;

[0054] S42. Introducing time-delay parameters into the dual observer state , forming a full-order distributed specified-time observer:

[0055] (9)

[0056] In the formula, represents an intermediate variable; Representation Node Consistency error estimate.

[0057] Preferably, in step S42, In time interval The initial value is set to zero.

[0058] Preferably, step S4 further comprises step S5: verifying the dual observer specified time estimate;

[0059] It specifically includes the following steps:

[0060] From formula (7), we get:

[0061] (10)

[0062] In the formula, Represents a dual observer Derivative with respect to time;

[0063] make ,in Represents an intermediate variable; ,as well as

[0064] ;

[0065] get The dynamic expression is as follows:

[0066] (11)

[0067] In the formula, express Derivative with respect to time; Representation Node Control input of

[0068] Solving formula (11) yields the following formula:

[0069] (12)

[0070] Or written as the following formula:

[0071] (13)

[0072] according to as well as , get when Sometimes:

[0073] (14)

[0074] Therefore, when hour , get the node consistency error estimation error , thus achieving the specified time Accurate state estimation.

[0075] Preferably, step S5 further includes step S6: recording the consistency error estimation error of each node in the multi-agent system , consistency error , Network node status Data changing over time and plotting it.

[0076] The present invention has the following beneficial effects:

[0077] 1. Based on the dynamics of multi-agent systems, the control input of each node is regarded as an unknown input, and an uncertainty term is introduced. A new full-order distributed specified time observer is proposed. The main idea is to design a feedback gain matrix in the complementary space of the control input matrix. At the same time, two different distributed observers with time delays are introduced in the final distributed observer expression. The feedback gain matrix in the complementary space of the control input matrix plays a key role in offsetting the influence of unknown inputs, and the time delay provides an additional degree of freedom to achieve the specified time estimation of the accurate consistency error. Compared with the existing Kalman filter estimation method, it can achieve the specified time convergence of the estimation error and has a wider range of application scenarios;

[0078] 2. The unknown input observer design method is introduced into the distributed protocol design. Each network node can only obtain the relative output information of the adjacent network nodes. Compared with the previous control protocol that relies on the absolute output information and the observation information of the adjacent nodes, it avoids the use of communication channels and has the characteristics of network attack immunity.

[0079] 3. It can effectively handle uncertain inputs, has good robustness, and can ensure higher estimation accuracy.

[0080] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a flow chart of a method for estimating the state of an uncertain multi-agent at a specified time based on a dual observer of the present invention;

[0082] Figure 2 It is a network communication topology diagram of a simulation example of the present invention;

[0083] Figure 3 is the estimated error of each agent node in the simulation example 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 of Time-varying graphs;

[0084] Figure 4 is the consistency error of each intelligent agent node in the simulation example of the present invention Time-varying graph; where Figure 4 (a) The first component Time-varying graphs; Figure 4 (b) The second component Time-varying graphs; Figure 4 (c) The third component Time-varying graphs; Figure 4 (d) The fourth component of Time-varying graphs;

[0085] Figure 5 is the state of each agent in the simulation instance of the present invention Time-varying graph; where Figure 5 (a) The first component Time-varying graphs; Figure 5 (b) The second component Time-varying graphs; Figure 5 (c) The third component Time-varying graphs; Figure 5 (d) The fourth component of Graph of changes over time. DETAILED DESCRIPTION

[0086] 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.

[0087] 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.

[0088] 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.

[0089] like Figure 1 As shown, a method for estimating the state of an uncertain multi-agent specified time based on a dual observer includes the following steps:

[0090] S1. Analyze the uncertainty of multi-agent system and noise model, and establish the system dynamic equation;

[0091] Step S1 specifically includes the following steps:

[0092] S11. Uncertainty in the agent system comes from many aspects. First, the noise in the system itself and the measurement process will cause uncertainty. Second, model uncertainty, external environmental interference, and complex interactions between individuals will also cause uncertainty. Third, the incomplete knowledge of the topological structure or dynamic changes over time will also introduce uncertainty. In order to study the impact of uncertainty factors on state estimation performance, uncertainty input is introduced into the multi-agent system composed of N agents, and the system dynamic equation is constructed:

[0093] (1)

[0094] 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;

[0095] 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.

[0096] 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: ;

[0097] The equivalent transformation formula (1) yields the following formula:

[0098] (2).

[0099] S2. Design the transformation matrix based on the null space and the system dynamic equations, and construct the dynamic equations of the consistency error of the multi-agent system;

[0100] Step S2 specifically includes the following steps:

[0101] S21. Design the control input for each agent in a multi-agent system :

[0102] (3)

[0103] In the formula, Represents the consistency error of each node, which is defined as ; Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; is the communication topology coupling parameter. Take a constant value; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; represents the time lag parameter; Indicates the initial time;

[0104] And set the control input The correlation matrix parameters of , which satisfies the following linear matrix inequality:

[0105] (4)

[0106] The value of satisfies:

[0107] (5)

[0108] In the formula, is the Laplace matrix No. eigenvalues, ;

[0109] 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.

[0110] 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 tree formation, the consistency of the multi-agent system can be achieved by designing the control input as shown in formula (3).

[0111] S22, according to the consistency error The definition of is combined with formula (2) to obtain the consistency error The dynamic equation of:

[0112] (6)

[0113] 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.

[0114] S3, construct a dual observer based on the system state equation and output equation;

[0115] In step S3, the dynamic equation of the dual observer is defined based on formula (2):

[0116] (7)

[0117] In the formula, and are the states of observer 1 and observer 2 of the dual observer, and Respectively represent the time derivatives of the states of observer 1 and observer 2 of the dual observer; transformation matrix satisfy ; and They respectively represent feedback gain matrices with different values; and denote the measurement gain matrices of observer 1 and observer 2 of the dual observer respectively;

[0118] Set the transformation matrix ,in, Represents the identity matrix, and the poles are arranged so that , The real parts of all eigenvalues ​​are less than 0, so we can deduce that , The expression is as follows:

[0119] (8).

[0120] S4. Introduce time-delay information to establish a non-homogeneous linear equation system with an invertible coefficient matrix and inversely solve the state estimate.

[0121] Step S4 specifically includes the following steps:

[0122] S41. Settings , , , , ,in, , , , Both represent dual observers Matrix parameters; express The identity matrix of order;

[0123] S42. Introducing time-delay parameters into the dual observer state , forming a full-order distributed specified-time observer:

[0124] (9)

[0125] In the formula, represents an intermediate variable; Representation Node Consistency error estimate;

[0126] In step S42, In time interval The initial value is set to zero.

[0127] Preferably, step S4 further comprises step S5: verifying the dual observer specified time estimate;

[0128] It specifically includes the following steps:

[0129] From formula (7), we get:

[0130] (10)

[0131] In the formula, Represents a dual observer Derivative with respect to time;

[0132] make ,in Represents an intermediate variable; ,as well as

[0133] ;

[0134] get The dynamic expression is as follows:

[0135] (11)

[0136] In the formula, express Derivative with respect to time; Representation Node Control input of

[0137] Solving formula (11) yields the following formula:

[0138] (12)

[0139] Or written as the following formula:

[0140] (13)

[0141] according to as well as , get when Sometimes:

[0142] (14)

[0143] Therefore, when hour , get the node consistency error estimation error . It is proved that the dual observer Can estimate the specified time The exact consistency error within , where the time lag parameter Can be set to arbitrarily small.

[0144] Step S5 also includes step S6: recording the consistency error estimation error of each node in the multi-agent system , consistency error , Network node status Data changing over time and plotting it.

[0145] Simulation Example

[0146] In this simulation example, consider Figure 2 The shown diagram is a leaderless directed communication topology consisting of three network nodes. This topology meets the conditions of a directed spanning tree and can be used to design a control protocol to achieve the consistency of the multi-agent system. And the Laplace matrix for:

[0147] ;

[0148] The multi-agent system is simulated and modeled, and the multi-agent system parameter selection is as follows:

[0149] ;

[0150] After completing the system model settings, set the dual observer parameters as follows:

[0151] ;

[0152] Direct calculation by the simulation program , , , And other parameters.

[0153] like Figure 3 As shown, the estimated error exist Then it converges to zero. Figure 4 As shown, under the control input designed by the present invention, the consistency error of each network node All converge to 0. Figure 5 As shown, the states of the three network nodes are consistent in a short time, thereby proving the effectiveness and accuracy of the present invention.

[0154] Therefore, the present invention adopts the above-mentioned uncertain multi-agent specified time state estimation method based on dual observer. Based on the dynamics of the multi-agent system, the control input of each node is regarded as an unknown input, and an uncertainty term is introduced to propose a new full-order distributed specified time observer to estimate the precise consistency error within any preset time.

[0155] 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 method for estimating uncertain multi-agent states at specified times based on dual observers, characterized in that: The following steps are involved: S1. Analyze the uncertainty of multi-agent system and noise model, and establish the system dynamic equation; Step S1 specifically includes the following steps: S11. Introduce uncertainty input into the multi-agent system composed of N agents and 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, 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; 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: ; The equivalent transformation formula (1) yields the following formula: (2)； S2. Design the transformation matrix based on the null space and the system dynamic equations, and construct the dynamic equations of the consistency error of the multi-agent system; Step S2 specifically includes the following steps: S21. Design the control input for each agent in a multi-agent system : (3) In the formula, Represents the consistency error of each node, which is defined as ; Represents the communication topology adjacency matrix Corresponding to Line Elements of a column; is the communication topology coupling parameter; Indicates control input The correlation matrix parameters of , represents a positive definite matrix; represents the time lag parameter; 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; S22, according to the consistency error The definition of is combined with formula (2) to obtain the consistency error The dynamic equation of: (6) 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: S3, construct a dual observer based on the system state equation and output equation; In step S3, the dynamic equation of the dual observer is defined based on formula (2): (7) In the formula, and are the states of observer 1 and observer 2 of the dual observer, and Respectively represent the time derivatives of the states of observer 1 and observer 2 of the dual observer; transformation matrix satisfy ; and They respectively represent feedback gain matrices with different values; and denote the measurement gain matrices of observer 1 and observer 2 of the dual observer respectively; Set the transformation matrix ,in, Represents the identity matrix, and the poles are arranged so that , The real parts of all eigenvalues ​​are less than 0, so we can deduce that , The expression is as follows: （8）； S4, introduce time-delay information to establish a non-homogeneous linear equation system with an invertible coefficient matrix, and inversely solve the state estimate; Step S4 specifically includes the following steps: S41. Settings , , , , ,in, , , , Both represent dual observers Matrix parameters; express The identity matrix of order; S42. Introducing time-delay parameters into the dual observer state , forming a full-order distributed specified-time observer: (9) In the formula, represents an intermediate variable; Representation Node Consistency error estimate.

2. The method for estimating states of uncertain multi-agents at specified times based on dual observers according to claim 1, characterized in that: In step S42, In time interval The initial value in is set to zero.

3. The uncertain multi-agent specified time state estimation method based on dual observer according to claim 2 is characterized by: Step S4 also includes step S5: verifying the dual observer specified time estimate; It specifically includes the following steps: From formula (7), we get: （10） In the formula, Represents a dual observer Derivative with respect to time; make ,in Represents an intermediate variable; ,as well as ； get The dynamic expression is as follows: (11) In the formula, express Derivative with respect to time; Representation Node Control input of Solving formula (11) yields the following formula: （12） Or written as the following formula: (13) according to as well as , get when Sometimes: （14） Therefore, when hour , get the node consistency error estimation error , thus achieving the specified time Accurate state estimation.

4. The uncertain multi-agent specified time state estimation method based on dual observer according to claim 3 is characterized by: Step S5 also includes step S6: recording the consistency error estimation 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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