Novel finite time distributed adaptive observer design method

Abstract

The invention discloses a novel finite time distributed adaptive observer design method, and relates to the technical field of distributed multi-agent research. The invention provides an observer design scheme with time-limited convergence and self-adaptive compensation capabilities aiming at the problems of response lagging and insufficient estimation precision when an existing distributed observer processes a time-varying external signal. The method comprises the following steps: constructing a node communication topological structure based on an undirected graph, and determining an adjacent set; vectorization processing is carried out on time-varying signals from an information source, and the time-varying signals are unified into bounded vectors to serve as estimation targets; constructing a local observer structure containing a nonlinear term by taking a node as a unit, and obtaining a preliminary estimation value; and a self-adaptive parameter updating mechanism is introduced, compensation parameters are dynamically adjusted according to the estimation error, and a self-adaptive estimation value is output. The method has the characteristics of quick response and high precision, and is suitable for distributed collaborative estimation control of time-varying information in a multi-agent system.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed multi-agent research, and specifically to a novel finite-time distributed adaptive observer design method. Background Art

[0002] With the continuous advancement of communication technology, computing power, and distributed control theory, multi-agent systems (MAS) have found widespread application in fields such as unmanned swarming, target tracking, distributed sensing, intelligent transportation, and collaborative perception. In such systems, effective observation and rapid estimation of information are crucial to ensuring the stability and real-time performance of the entire system. Distributed observers, as an important tool for addressing information perception and state estimation in multi-agent systems, have become a core issue in this field.

[0003] At present, mainstream research focuses on the following aspects:

[0004] Graph-theory-based distributed observer design: Numerous studies have employed directed or undirected graph models to describe the communication topology between agents, enabling estimation of global states or external signals through information exchange between adjacent nodes. For example, existing methods for linear systems utilize the Laplace matrix to design consistent observers for synchronous state estimation.

[0005] Robustness and Adaptivity Research: Some research introduces adaptive mechanisms or perturbation observation techniques to enhance the system's observation capabilities in the face of parameter uncertainty or external perturbations. For example, some methods construct adaptive observers based on Lyapunov stability theory to achieve estimation and compensation for dynamic targets or time-varying signals.

[0006] Finite-time and fixed-time convergence mechanisms: Traditional observers typically rely on asymptotic convergence, which is difficult to achieve in real-time systems. In recent years, finite-time stability (FTS) has become a research hotspot, with related work incorporating nonlinear control terms or sliding mode control techniques to accelerate convergence. Finite-time observers have been explored in drone formations, robot collaboration, and edge computing task scheduling.

[0007] Although many research results have been achieved, the following key technical challenges still exist:

[0008] Reliance on global information or complete communication topology: Some methods require each node to obtain information from all nodes or leaders, which violates the principles of distributed design and limits their application in large-scale systems.

[0009] The convergence speed is insufficient and it is difficult to meet the real-time control requirements: When faced with sudden or rapidly changing external signals, traditional asymptotic observers have response lags, which affect the collaborative control effect.

[0010] Insufficient accuracy in estimating time-varying information: In the absence of prior knowledge or models, it is difficult for nodes to make high-precision estimates of rapidly changing information, especially in complex scenarios where the trend of the observed signal is unknown.

[0011] In summary, how to design a distributed observer method that relies only on local information, can achieve fast and high-precision estimation of time-varying external signals, and has finite-time convergence characteristics, is still an important problem that needs to be solved urgently in this field. Summary of the Invention

[0012] To solve the technical problem in the prior art that the existing distributed observer cannot quickly and accurately estimate the time-varying external signal, the present invention provides the following technical solutions:

[0013] A novel finite-time distributed adaptive observer design method includes:

[0014] The steps of establishing a communication topology structure of each node in the cluster system, modeling the information interaction relationship between nodes based on an undirected graph, determining the adjacency set of each node, and outputting network structure information;

[0015] The step of receiving a time-varying target signal from an information source node, performing vectorization processing, and unifying the signal into a bounded vector as a target input for distributed estimation;

[0016] Based on the network structure information and the target input, the estimation process is performed on a node-by-node basis, a local observer structure is designed for each node, and a preliminary estimated value of each node is output;

[0017] According to the preliminary estimated value, an adaptive parameter update mechanism is introduced to dynamically adjust the adaptive parameter value according to the current estimated error of each node, and the adaptive estimated value of each node is updated and output.

[0018] Furthermore, a preferred embodiment is provided, wherein the local observer structure includes a nonlinear feedback term, and the nonlinear feedback term is expressed based on a hyperbolic tangent function and is used to achieve convergence of the observation error within a finite time.

[0019] Furthermore, a preferred implementation is provided to dynamically adjust the adaptive parameter value according to the current estimation error of each node. The adjustment process is based on the hyperbolic tangent function to compensate for the error caused by the rapid change of the target signal, and to update and output the adaptive estimation value of each node.

[0020] Furthermore, a preferred embodiment is provided, which also includes a step of performing stability analysis using a Lyapunov function that includes a global observation error and an adaptive parameter error to verify that the estimated values ​​of all nodes can converge to an allowable error range near the target signal within a finite time.

[0021] Furthermore, a preferred embodiment is provided, wherein the communication topology is an undirected connected graph structure, and is divided into blocks by constructing a Laplacian matrix and performing node numbering.

[0022] Furthermore, a preferred embodiment is provided in which the updating of the adaptive parameters depends on the norm of the current estimation error, and an adjustment coefficient is introduced to control the update rate and suppress oscillation.

[0023] A novel finite-time distributed adaptive observer design apparatus is also provided, comprising:

[0024] A module that establishes the communication topology of each node in the cluster system, models the information interaction relationship between nodes based on an undirected graph, determines the adjacency set of each node, and outputs network structure information;

[0025] A module that receives time-varying target signals from information source nodes, performs vectorization processing, and unifies them into bounded vectors as target inputs for distributed estimation;

[0026] Based on the network structure information and the target input, the estimation process is performed on a node-by-node basis, and a module for designing a local observer structure for each node is designed;

[0027] Based on the preliminary estimated value, an adaptive parameter update mechanism is introduced to dynamically adjust the adaptive parameter value according to the current estimated error of each node, and update and output the adaptive estimated value module of each node.

[0028] A computer storage medium is also provided for storing a computer program, and when the computer program is read by a computer, the computer executes the method.

[0029] A computer is also provided, comprising a processor and a storage medium, wherein when the processor reads a computer program stored in the storage medium, the computer executes the method.

[0030] A computer program product is also provided, which is a computer program that implements the method when the computer program is executed.

[0031] Compared with the prior art, the technical solution provided by the present invention is beneficial in that:

[0032] By introducing the hyperbolic tangent function as a nonlinear excitation term, the present invention makes the error convergence behavior of the observer have a finite time characteristic. Compared with the traditional asymptotic convergence method based on linear feedback, the state estimation of the external signal can be completed in a shorter time, which significantly improves the system response speed. It is particularly suitable for scenarios with extremely high timeliness requirements such as unmanned system formation and rapid target capture.

[0033] This invention employs an adaptive parameter design mechanism, leveraging dynamic adjustment rules tied to observation errors, to effectively improve the system's tracking accuracy for time-varying external signals. Compared to traditional distributed observers with fixed parameters, this design automatically adjusts gain based on signal trends, enabling real-time adaptation to unknown variations, significantly reducing the upper error limit and improving observation robustness.

[0034] This design fully leverages network topology information, ensuring topological connectivity and matrix positivity through Laplace matrix partitioning, and ensuring global convergence of observation errors. Unlike some observation methods that require more robust communication structures, this solution relies solely on local neighborhood information for accurate estimation, reducing reliance on central or leading nodes and improving the system's fault tolerance and topological adaptability.

[0035] The observer design method proposed in this paper rigorously proves finite-time convergence via the Lyapunov function and provides an error convergence region and time bounds. Compared with most current observers that only have asymptotic stability or local convergence, this scheme theoretically has stronger convergence guarantees and provides a stable and reliable observation basis for control systems with high safety or closed-loop accuracy requirements.

[0036] It is suitable for distributed collaborative control tasks in multi-agent systems that require fast and high-precision estimation of external time-varying information. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Design a flow chart of the method for distributed adaptive observer;

[0038] Figure 2 Schematic diagram of the network structure of each node;

[0039] Figure 3 The change curve of observation error norm of each node;

[0040] Figure 4 Adaptive parameter change curve of each node. DETAILED DESCRIPTION

[0041] In order to make the advantages and benefits of the technical solution provided by the present invention more clearly reflected, the technical solution provided by the present invention is now further described in detail with reference to the accompanying drawings, specifically:

[0042] Implementation 1: This implementation provides a novel finite-time distributed adaptive observer design method, including:

[0043] The steps of establishing a communication topology structure of each node in the cluster system, modeling the information interaction relationship between nodes based on an undirected graph, determining the adjacency set of each node, and outputting network structure information;

[0044] The step of receiving a time-varying target signal from an information source node, performing vectorization processing, and unifying the signal into a bounded vector as a target input for distributed estimation;

[0045] Based on the network structure information and the target input, the estimation process is performed on a node-by-node basis, a local observer structure is designed for each node, and a preliminary estimated value of each node is output;

[0046] According to the preliminary estimated value, an adaptive parameter update mechanism is introduced to dynamically adjust the adaptive parameter value according to the current estimated error of each node, and the adaptive estimated value of each node is updated and output.

[0047] The local observer structure includes a nonlinear feedback term, which is expressed based on a hyperbolic tangent function and is used to achieve convergence of the observation error within a finite time.

[0048] The adaptive parameter value is dynamically adjusted according to the current estimation error of each node. The adjustment process is based on the hyperbolic tangent function to compensate for the error caused by the rapid change of the target signal, and the adaptive estimation value of each node is updated and output.

[0049] It also includes a step of using a Lyapunov function that includes global observation error and adaptive parameter error to perform stability analysis and verify that the estimated values ​​of all nodes can converge to the allowable error range near the target signal within a finite time.

[0050] The communication topology is an undirected connected graph structure, and is divided into blocks by constructing a Laplace matrix and performing node numbering.

[0051] The update of adaptive parameters depends on the norm of the current estimation error, and an adjustment coefficient is introduced to control the update rate and suppress oscillation.

[0052] Implementation Method 2: This implementation method further describes the technical solution provided in Implementation Method 1 in detail. Specifically:

[0053] This embodiment of the present invention provides a novel finite-time distributed adaptive observer design method suitable for rapid and accurate estimation of time-varying external information in multi-agent systems. The method has a clear structure, logical sequence between steps, and relies only on local information transfer between nodes. The method primarily includes the following steps:

[0054] Step 1: Construct a multi-node network topology and perform vector processing of the observed information

[0055] This step first assumes that there is a cluster system consisting of N+1 nodes, where the node numbered 0 serves as the information source node, and the remaining nodes are numbered 1 to N, constituting the member nodes that need to observe information.

[0056] An undirected graph is used to model the communication topology between nodes within a system. The node set of an undirected graph is {0, 1, ..., N}, and the edge set represents the communication relationship between nodes. If an edge exists between nodes i and j, then they can exchange information with each other.

[0057] The adjacency matrix and Laplacian matrix of the topology are further constructed, and the Laplacian matrix is ​​divided into blocks according to the node number. It is required that the entire topology graph is connected and there is a path between the information source node and any member node to ensure that the observation error can be propagated and converged.

[0058] The information to be observed is then vectorized. If the required observation information is in matrix form, such as a task assignment matrix or a configuration adjustment matrix, it is expanded column by column into vectors. If it is a vector or scalar, its original form is retained. The resulting observed target signal is then unified into a bounded vector form, which serves as the input for the subsequent distributed observer design.

[0059] Step 2: Design a distributed observer with nonlinear finite-time convergence properties

[0060] For each member node, a local distributed observer is constructed based on its neighbor node set and current estimated value. Each observer structure does not rely on global information and only updates its state based on local communication neighborhood information.

[0061] A nonlinear feedback term in the form of a hyperbolic tangent function is introduced into the core structure of the observer to enhance the nonlinear convergence characteristics of the system. The introduction of this nonlinear term ensures that the observation error no longer merely meets asymptotic convergence requirements, but can theoretically guarantee convergence to a region of low error within a finite time.

[0062] The intensity adjustment of the feedback term is controlled by the design parameters, which should be set comprehensively according to factors such as system scale, communication topology and target signal change rate to achieve the required convergence performance and system stability.

[0063] Step 3: Design adaptive parameters to compensate for time-varying information estimation errors

[0064] Considering that the observed target in practical applications is usually a time-varying signal, it is difficult to maintain high-precision estimation by relying solely on a fixed structure. Therefore, adaptive parameters related to the error are introduced into the observer structure.

[0065] The adaptive parameter is dynamically adjusted using a nonlinear update law, and a hyperbolic tangent term is also introduced into its update function, which speeds up the parameter adjustment when the error is large and slows down when the error is small, reflecting the adaptive adjustment capability.

[0066] Furthermore, to ensure the initial stability of the system, the adaptive parameters are set to positive initial values, and their update speed is controlled by a positive gain coefficient. This mechanism effectively compensates for estimation bias caused by drastic changes in the target signal, thereby improving overall observation accuracy.

[0067] Step 4: Construct Lyapunov function for finite time convergence analysis

[0068] In order to ensure that the designed observer structure has theoretical convergence guarantee, a Lyapunov function including the observation error vector and the adaptive parameter error is constructed, and a systematic analysis is carried out from two aspects: asymptotic convergence and finite-time convergence.

[0069] First, they demonstrate that the observation error and the adaptive parameter error generally converge to a small region containing the origin, ensuring the basic stability of the system. Furthermore, through a modified Lyapunov function formulation, combined with the positive definiteness of the Laplace matrix in the network topology, the structural characteristics of the adaptive law, and the derivation of Young's inequality, they prove that the error will converge in a finite time, and obtain a theoretical upper bound on the convergence time.

[0070] This convergence analysis not only improves the theoretical reliability of the system, but also provides a basis and reference for the selection of system parameters in engineering applications.

[0071] Implementation Method 3: Combination Figure 1-4 This embodiment further describes the above technical solution in detail through specific examples, specifically:

[0072] The purpose of this embodiment is to provide a novel finite-time distributed adaptive observer design method that enables accurate, real-time estimation of external information by each node in a distributed network. First, the introduction of a hyperbolic tangent term ensures the observer's finite-time observation performance. Furthermore, an adaptive parameter is introduced to compensate for the impact of real-time variations in the observed information on the observer's accuracy.

[0073] This embodiment is achieved through the following scheme:

[0074] 1) Construct the network structure of each node and perform vector processing on the observed information;

[0075] 2) Design a finite-time distributed adaptive observer;

[0076] 3) Verify the effectiveness of the designed observer, that is, the finite-time convergence of the observation error.

[0077] Methods include:

[0078] Consider a cluster system consisting of N nodes and an information source node, whose serial number is set to 0. Use an undirected graph G = (V, E) to describe the topological relationship between the platforms in the system. , where V = {0, 1, ..., N} is the node set, is an edge set. If edge (i, j) exists, it means that node i can receive interactive information from node j. In addition, N i ={j∈V|(i,j)∈E} represents the neighbor set of the i-th node. For the adjacency matrix of the interaction graph If the edge (i,j) exists, then for the element [A] in row i and column j ij Satisfy [A] ij =1, and the other elements are [A] ij = 0. In addition, the Laplace matrix satisfy In order to facilitate the subsequent design of finite-time distributed observer algorithm, the matrix L1 is divided into blocks according to the nodes to obtain

[0079]

[0080] The topological relationship between each cluster member and the target information source in the system is undirected, so its Laplace matrix L satisfies At the same time, its block matrix L 22 Satisfies the positive definiteness.

[0081] The information that needs to be globally acquired in a distributed system may include dynamic target positions, collaborative control instructions, etc. These cluster key information may generally be in vector form. In some special cases, it may appear in matrix form, such as task allocation matrix, formation configuration adjustment matrix, etc. In order to facilitate the design of distributed observers, the observation signal needs to be expanded. For example, for a time-varying matrix signal A(t) to be observed, use Represents the vector obtained by expanding A(t) by columns. For the information to be observed in scalar or vector form, the subsequent steps can be carried out directly. Considering the actual application environment, It is bounded.

[0082] Considering the topological connection between information sources and cluster members, the following distributed observation error is defined:

[0083]

[0084] Where A is the adjacency matrix of the global topology, [A] ij is the element in its i-th row and j-th column. Represents the real-time observation value of a(t) by member i.

[0085] Considering the time-varying characteristics of the information to be observed, in order to ensure accurate and timely estimation in real-time applications, the following adaptive distributed observer is designed

[0086]

[0087] Among them, ρ1 and ρ2 are the normal value coefficients to be designed. is an adaptive parameter used to compensate for the influence of time-varying information on observation accuracy. Its specific update law is as follows

[0088]

[0089] Among them, γ1, μ1 and c1 are all positive constants, and the initial value of the adaptive parameter must satisfy

[0090] In order to verify the effectiveness of the distributed observer, the global observation error vector is defined as a(t)=[a1(t) T ,…,a N (t) T ] T , considering the communication topology properties, we have

[0091]

[0092] Define the estimation error of each member as This has an impact on the distributed error

[0093]

[0094] in, Represents the stack form of the global estimation error. 22 is positive definite, so the convergence of ε1(t) can be guaranteed Stable convergence, and each member can achieve accurate estimation of time-varying expected information.

[0095] To verify the effectiveness of the observer, we first select the Lyapunov function:

[0096]

[0097] in represents the adaptive parameter error, express An unknown upper bound of is bounded, then Must exist. Taking the derivative of the Lyapunov function and substituting it into the adaptive parameter update law, we get

[0098]

[0099] According to L 22 The positivity and The definition of , the above formula satisfies:

[0100]

[0101] According to Young's inequality, the following inequality satisfies

[0102]

[0103] According to V ob,1 Definition, Ultimate Satisfaction where Γ ob1 =min{2ρ1λ min (L aa ),c1γ1}, Then V ob,1 will eventually converge to a region containing the origin.

[0104] To prove the finite-time convergence property of the proposed observer, the following Lyapunov function is selected:

[0105]

[0106] Taking the derivative of the above formula, we get

[0107]

[0108] Consider L 22 The positive definiteness and adaptive parameters of The definition of , and according to the Young inequality property,

[0109]

[0110] Among them, Γ ob2 =min{2ρ1λ min (L aa ),c1γ1},

[0111] and Then V ob,2 In a limited time T ob,a Converges to a small region containing the origin. Then ε1(t) and It will also converge in a finite time, and then the error will be observed The finite-time convergence of is proved.

[0112] This implementation proposes a novel finite-time distributed adaptive observer design method. Based on a distributed framework, this method effectively improves the rapid response of the observer algorithm by introducing nonlinear terms, enabling finite-time observation of the observed information. By designing adaptive parameters, the impact of real-time information changes on the observer's accuracy is effectively reduced.

[0113] The above further describes the technical solution provided by the present invention in detail through several specific embodiments in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the several specific embodiments described above are not intended to limit the present invention. Any reasonable modification and improvement of the present invention, combination of embodiments and equivalent replacement based on the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A novel finite-time distributed adaptive observer design method, characterized in that: include: The steps of establishing a communication topology structure of each node in the cluster system, modeling the information interaction relationship between nodes based on an undirected graph, determining the adjacency set of each node, and outputting network structure information; The step of receiving a time-varying target signal from an information source node, performing vectorization processing, and unifying the signal into a bounded vector as a target input for distributed estimation; Based on the network structure information and the target input, the estimation process is performed on a node-by-node basis, a local observer structure is designed for each node, and a preliminary estimated value of each node is output; According to the preliminary estimated value, an adaptive parameter update mechanism is introduced to dynamically adjust the adaptive parameter value according to the current estimated error of each node, and the adaptive estimated value of each node is updated and output.

2. A novel finite-time distributed adaptive observer design method according to claim 1, characterized in that: The local observer structure includes a nonlinear feedback term, which is expressed based on a hyperbolic tangent function and is used to achieve convergence of the observation error within a finite time.

3. A novel finite-time distributed adaptive observer design method according to claim 1, characterized in that: The adaptive parameter value is dynamically adjusted according to the current estimation error of each node. The adjustment process is based on the hyperbolic tangent function to compensate for the error caused by the rapid change of the target signal, and the adaptive estimation value of each node is updated and output.

4. A novel finite-time distributed adaptive observer design method according to claim 1, characterized in that: It also includes a step of using a Lyapunov function that includes global observation error and adaptive parameter error to perform stability analysis and verify that the estimated values ​​of all nodes can converge to the allowable error range near the target signal within a finite time.

5. A novel finite-time distributed adaptive observer design method according to claim 1, characterized in that: The communication topology is an undirected connected graph structure, and is divided into blocks by constructing a Laplace matrix and performing node numbering.

6. A novel finite-time distributed adaptive observer design method according to claim 1, characterized in that: The update of adaptive parameters depends on the norm of the current estimation error, and an adjustment coefficient is introduced to control the update rate and suppress oscillation.

7. A novel finite-time distributed adaptive observer design device, characterized in that: include: A module that establishes the communication topology of each node in the cluster system, models the information interaction relationship between nodes based on an undirected graph, determines the adjacency set of each node, and outputs network structure information; A module that receives time-varying target signals from information source nodes, performs vectorization processing, and unifies them into bounded vectors as target inputs for distributed estimation; Based on the network structure information and the target input, the estimation process is performed on a node-by-node basis, and a module for designing a local observer structure for each node is designed; Based on the preliminary estimated value, an adaptive parameter update mechanism is introduced to dynamically adjust the adaptive parameter value according to the current estimated error of each node, and update and output the adaptive estimated value module of each node.

8. A computer storage medium for storing a computer program, characterized in that When the computer program is read by a computer, the computer executes the method according to claim 1 .

9. A computer comprising a processor and a storage medium, characterized in that When the processor reads the computer program stored in the storage medium, the computer executes the method according to claim 1 .

10. A computer program product, being a computer program, characterized in that When the computer program is executed, the method according to claim 1 is implemented.

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