Sampling consistency control method, system and medium for nonlinear multi-agent system

Abstract

The present invention discloses a sampling consistency control method, system, and medium for a nonlinear multi-agent system, comprising the following steps: S101: obtaining system model parameters, including a nonlinear function #imgabs0#, an impulse gain #imgabs1#, a sampling period #imgabs2#, a communication topology #imgabs3#, and a leader-follower dynamic equation; S102: verifying assumptions; S103: constructing a Lyapunov function #imgabs4# and analyzing the stability of the error system in combination with impulse perturbations; S104: deriving consistency conditions using the Lyapunov method and impulse theory, calculating key parameters, and determining impulse gain and sampling period constraints; S105: selecting parameters that meet the conditions; S106: constructing a sampling controller with impulse perturbations; and S107: implementing the controller and performing numerical simulations. The present invention exhibits strong immunity to impulse perturbations: the design of the impulse gain #imgabs5# effectively offsets transient interference in the input channel, improving system robustness; and employing a sampled data control strategy that updates the control signal only at discrete sampling moments, reducing communication overhead.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system collaborative control, and specifically to a sampling consistency control method, system and medium for a nonlinear multi-agent system. Background Art

[0002] The collaborative control of multi-agent systems (MAS) has important applications in areas such as drone formations, smart grids, and distributed robotics. Consistency control, as a core issue, requires that the states of all agents in the system eventually converge to a consensus or track the trajectory of the leader.

[0003] Existing research mainly focuses on the design of continuous-time protocols or discrete-time protocols. However, in practical applications, continuous control is difficult to achieve due to limited communication resources or external interference (such as impulse noise), while traditional discrete control methods are not robust enough to nonlinear dynamics and impulse disturbances.

[0004] Currently, there have been many achievements in sampling data control for linear multi-agent systems, but the research on sampling consistency of nonlinear systems still faces challenges:

[0005] 1. Nonlinear dynamic complexity: Nonlinear terms may make system stability analysis difficult, requiring the introduction of constraints such as Lipschitz conditions;

[0006] 2. Impact of pulse disturbances: Instantaneous pulse noise in the input channel can disrupt the continuity of the control signal, making traditional methods difficult to directly apply.

[0007] 3. Topology dynamics: Rapid switching of communication topology or partial instantaneous disconnection may weaken the control effect.

[0008] Existing literature has limited research on sampled data control of nonlinear multi-agent systems subject to impulsive disturbances. In particular, the combination of leader-follower consistency and stability conditions involving control scenarios has been underexplored. Therefore, designing robust control protocols that are resistant to impulsive disturbances while ensuring efficient communication has become a pressing technical challenge. Summary of the Invention

[0009] The purpose of the present invention is to provide a sampling consistency control method, system and medium for a nonlinear multi-agent system, so as to solve the problems raised in the above background technology, such as how to design a sampling data controller to ensure the leader-follower consistency of a nonlinear multi-agent system in the presence of input channel pulse disturbances; how to extend the consistency control to inclusive control in a multi-leader scenario and provide clear stability conditions; and how to reduce the communication burden through parameter optimization while ensuring the exponential convergence of the system under pulse interference.

[0010] To achieve the above-mentioned objectives, the present invention provides the following technical solutions: a sampling consistency control method for a nonlinear multi-agent system. The core of this method is to design a sampling controller with impulse disturbance compensation for a multi-agent system with nonlinear dynamics and whose input channels are subject to impulse disturbances, under the assumption that the communication topology is undirectedly connected and the nonlinear function satisfies the Lipschitz condition.

[0011] The controller includes a feedback term based on the neighbor state error, an impulse perturbation gain term, and a sampling period parameter. The stability of the error system is analyzed using Lyapunov functions and impulse system theory. The invention reveals the key conditions for achieving leader-follower consistency and inclusive control:

[0012] A sufficiently large control gain must be selected (make sure ), the pulse gain that satisfies the inequality constraint and sampling period (satisfy ).

[0013] Through parameter optimization and pulse disturbance suppression, this method can drive the system to achieve exponential consistency convergence under sampling communication and pulse interference. The specific steps are as follows:

[0014] S101 obtains system model parameters, including nonlinear functions , pulse gain , sampling period , Communication topology diagram and leader-follower dynamics equations;

[0015] S102 Verify the following assumptions: the topology is undirected and connected with at least one follower connected to the leader (Assumption 1), the nonlinear function satisfies the Lipschitz condition (Assumption 2), and the multi-leader topology condition is verified when control is included (Assumption 4);

[0016] S103 Constructing Lyapunov functions , combined with pulse disturbance to analyze the stability of the error system;

[0017] S104 uses Lyapunov method and pulse theory to derive consistency conditions and calculate key parameters; , and determine the pulse gain and sampling period constraints;

[0018] S105, selecting parameters that meet the conditions;

[0019] S106 Constructing a Sampling Controller with Impulse Perturbations: Designing for a Single Leader Scenario , the multi-leader scenario is extended to ;

[0020] S107 implements the controller and performs numerical simulations to verify the effectiveness of leader-follower consistency (Example 1) and inclusive control (Example 2), and demonstrates exponential synchronization performance through state trajectory convergence.

[0021] The present invention also accordingly provides a control system for implementing the above method and a computer-readable storage medium storing computer program instructions for executing the method.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] 1. Strong anti-pulse disturbance capability: through pulse gain The design can effectively offset the instantaneous interference of the input channel and improve the robustness of the system;

[0024] 2. High communication efficiency: Using a sampled data control strategy, the control signal is updated only at discrete sampling moments, reducing the communication burden;

[0025] 3. Clear theoretical guarantee: Based on Lyapunov stability theory, sufficient conditions for parameter selection are given to ensure exponential convergence of the system;

[0026] 4. Strong scalability: Expand from single-leader consistency to multi-leader inclusive control, adapting to complex task scenarios;

[0027] 5. Solid theoretical foundation: Based on mature theories such as Lyapunov stability and averaging method.

[0028] 6. Wide application potential: Suitable for distributed control scenarios such as drone formations and robot group collaboration. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the method flow of the present invention;

[0030] Figure 2 This is a diagram of a four-follower single-leader communication topology, where node 0 is the leader and nodes 1-4 are followers. The solid line represents two-way communication between followers, and the dotted line represents one-way information transmission from the leader to the followers.

[0031] Figure 3 is based on the parameter of Theorem 1 ( ) shows that the four follower states asymptotically track the leader state. The convergence process of

[0032] Figure 4 This is a schematic diagram of the control communication topology of four followers and two leaders. Nodes 5 and 6 are leaders. The dotted line represents the unidirectional connection from the leader to the followers. The topology satisfies the strong connectivity condition of Assumption 4.

[0033] Figure 5 Under the conditions of Theorem 2 ( ), showing that the follower state eventually converges to the convex hull region formed by the two leader states. DETAILED DESCRIPTION

[0034] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0035] See also Figure 1-5 The present invention provides a technical solution: a sampling consistency control method, system and medium for a nonlinear multi-agent system, specifically including:

[0036] Step S101: Obtain system model parameters, communication topology and dynamic equations

[0037] Specific implementation method:

[0038] Nonlinear functions :Determine the nonlinear dynamic model through system identification or physical modeling, such as by fitting experimental data or deducing based on physical laws. In the design stage, it is assumed that The Lipschitz condition is known and satisfied (subsequent verification).

[0039] Pulse perturbation gain : Set the pulse gain sequence according to the actual interference characteristics (such as sudden load changes, signal noise) , subsequent stability conditions must be met.

[0040] Sampling period :Preliminary setting of sampling period based on communication bandwidth limitation and system dynamic characteristics , subsequent optimization needs to be combined with consistency conditions.

[0041] Communication topology diagram : Obtain the topology through neighbor discovery or pre-defined rules. For a leader-follower system, ensure that the topology is undirected and connected, and that at least one follower is connected to the leader (Assumption 1).

[0042] Dynamic equations: The dynamic equations of the leader and follower are defined as:

[0043] Followers:

[0044] Leaders:

[0045] This step lays the foundation for control design, clarifies the system's nonlinear characteristics, pulse disturbance form, communication constraints, and target dynamics, and ensures that subsequent analysis and controller design have clear mathematical model support.

[0046] Step S102: Verify the assumptions

[0047] Specific implementation method:

[0048] Communication topology verification (Assumption 1):

[0049] Check the adjacency matrix Whether it is a symmetric matrix (undirected).

[0050] Use graph theory algorithms such as depth-first search to verify the connectivity of the topology.

[0051] Ensure that there is at least one follower directly connected to the leader (ie, the matrix Zhengding).

[0052] Lipschitz condition verification (Assumption2):

[0053] For nonlinear functions Perform global analysis and calculate its Lipschitz constant , ensuring satisfaction .

[0054] Multi-leader topology verification (Assumption4):

[0055] If it contains a control scenario, verify the enhanced diagram The Laplace matrix of Does it satisfy the submatrix Positive and The row sum is 1.

[0056] Assumptions are the premise for the validity of theoretical results, and algebraic verification and graph theory analysis are required to ensure that the system meets the constraints of communication topology, nonlinear characteristics and multi-leader scenarios.

[0057] Step S103: Construct Lyapunov function and analyze stability

[0058] Specific implementation method:

[0059] Construct a Lyapunov function:

[0060] Defining the error variable , build function:

[0061]

[0062] Stability analysis:

[0063] calculate The time derivative of , combined with the impulse disturbance term Analyze error dynamics.

[0064] Using inequality techniques (such as the Gronwall-Bellman lemma) to derive the upper bound on the error, we can prove that exponential decay.

[0065] By constructing the Lyapunov function, the consistency problem is transformed into the error system stability problem, and the influence of impulse disturbance on the quantization convergence rate is combined to provide a theoretical basis for parameter design.

[0066] Steps S104 and S105: derive consistency conditions and determine parameter constraints and select parameters

[0067] Specific implementation method:

[0068] Calculation of key parameters:

[0069] calculate .

[0070] Deriving inequalities ,

[0071] in ,

[0072] .

[0073] Parameter selection:

[0074] Control gain Need to be large enough to meet .

[0075] Pulse gain and sampling period The feasible range needs to be determined by numerically solving the inequality.

[0076] Through the Lyapunov method and impulse system theory, the coupling constraints of control gain, impulse perturbation intensity and sampling period are clearly defined to ensure the exponential convergence of the system under limited communication and interference.

[0077] Step S106: Constructing a sampling controller with pulse disturbance

[0078] Specific implementation method:

[0079] Single leader scenario: The controller is designed to:

[0080]

[0081] in The sampling time The error update value after .

[0082] Multi-leader scenario:

[0083] The expanded error variable is , the controller is adjusted to:

[0084]

[0085] The controller integrates neighbor state error feedback and impulse disturbance compensation, reduces the communication load through periodic sampling, and suppresses the impact of sudden interference on consistency.

[0086] Step S107: Implement the controller and verify performance

[0087] Specific implementation method:

[0088] Numerical simulation:

[0089] Use MATLAB / Simulink or Python to build a multi-agent system model and set the initial state (as in Example 1 ).

[0090] Simulate dynamic switching of communication topology and pulse disturbance scenarios, apply controllers and record state trajectories.

[0091] Performance Verification:

[0092] Draw the follower and leader status curves to verify (single leader) or (Multiple leaders).

[0093] Through the error norm The exponential decay curve of θ is used to quantitatively analyze the convergence rate.

[0094] The effectiveness of the theoretical results is verified through simulation experiments, and the robust consistency performance of the system under pulse perturbations and sampling communications is intuitively demonstrated, providing a reference for practical engineering applications.

[0095] This approach addresses the challenge of cooperative control of nonlinear multi-agent systems under impulsive disturbances and limited communication through systematic modeling, hypothesis verification, stability analysis, and controller design. The key innovation lies in integrating sampling control with an impulse compensation mechanism, balancing communication efficiency and anti-interference capabilities through parameter optimization. This approach provides theoretical support and practical examples for scenarios such as drone formations and smart grids.

[0096] Example:

[0097] This embodiment aims to specifically illustrate the application process and effect of the sampling data leader following consistency control method of a nonlinear multi-agent system based on impulse disturbance.

[0098] Application of step S101: obtaining system model, nonlinear function, impulse perturbation gain and topology information;

[0099] Consider a nonlinear multi-agent system consisting of 4 followers and 1 leader.

[0100] Follower Dynamics:

[0101]

[0102] in, For follower status, is the control input, the nonlinear function . Leader Dynamics:

[0103]

[0104] Communication topology: such as Figure 1 As shown, the topology is an undirected connected graph, and at least one follower is directly connected to the leader (satisfying assumption 1).

[0105] Pulse perturbation gain: .

[0106] Application of step S102: Verifying the assumptions

[0107] Communication topology conditions: The topology is undirected and connected, and follower 1 is directly connected to the leader (satisfying assumption 1).

[0108] Lipschitz condition for nonlinear function:

[0109]

[0110] satisfy (Assumption 2 is satisfied).

[0111] matrix Positive definiteness: calculated , , which satisfies the positive definite condition.

[0112] Application of step S103: constructing Lyapunov function and analyzing its stability

[0113] Construct a Lyapunov function:

[0114]

[0115] Calculate its derivative and analyze the stability of the error system in combination with the pulse disturbance to obtain:

[0116]

[0117] in, ,

[0118] , .

[0119] Application of steps S104 and S105: deriving consistency conditions and selecting parameters

[0120] By the stability condition of Theorem 1:

[0121] :

[0122]

[0123] verify , the conditions are met.

[0124] Select Parameter: Control Gain ,satisfy ,and .

[0125] Application of step S106: Constructing a sampling controller with pulse disturbance

[0126] The controller is designed to:

[0127]

[0128] in, is the neighbor state error at the sampling moment, is the Dirac function.

[0129] Application of step S107: simulation verification

[0130] Simulation scenario 1 (conditions met):

[0131] parameter: .

[0132] Initial state: .

[0133] Results: As Figure 3 As shown, the follower status Fast convergence to leader state within 5 seconds , verifying the leader-follow consistency.

[0134] Simulation scenario 2 (communication topology conditions are not met):

[0135] Modify the topology to a disconnected graph (remove the connection between follower 1 and the leader).

[0136] Result: Follower states diverge, verifying the necessity of topological connectivity.

[0137] Expanded to include control

[0138] Consider a system with 4 followers and 2 leaders, with a communication topology like Figure 4 shown.

[0139] Nonlinear functions .

[0140] parameter: .

[0141] Results: As Figure 5 As shown, the follower state converges to the convex hull of the leader state, verifying the effectiveness of the inclusion control.

[0142] This example demonstrates the effectiveness of leader-following consistency and inclusive control in a nonlinear multi-agent system under impulse perturbations and sampled data control through parameter setting, controller construction, and simulation analysis. Furthermore, comparative experiments highlight the critical role of communication topology connectivity and parameter selection.

[0143] Further explanation on parameter selection:

[0144] Feedback gain : In the embodiment, the feedback gain is obtained by the control gain in Theorem 1 With pulse gain Specifically, Inequality conditions must be met , to ensure the exponential stability of the error system. In actual design, The selection needs to weigh the following factors:

[0145] Stability requirements: Need to be large enough to meet , but too large will lead to saturation of the control input;

[0146] Pulse perturbation effect: Pulse gain Need to meet ,in It is recommended to determine the The allowed range, for example, To avoid matrix singularity.

[0147] Regarding the expansion of the system model:

[0148] Although this study focuses on the analysis and verification of nonlinear multi-agent systems with impulsive disturbances, its core approach (constructing error systems and designing sampling control protocols based on Lyapunov function methods, algebraic graph theory, and impulsive system theory) can be further extended to a wider range of system models.

[0149] High-order nonlinear systems: For nonlinear agents with high-order dynamics (such as Euler-Lagrange systems or strict feedback systems), the error system can be reconstructed by designing distributed observers or backstepping, and adaptive laws can be introduced to compensate for the unmodeled dynamics. In this case, stability analysis requires the integration of high-order Lyapunov-Krasovskii functions and the theory of impulsive differential equations.

[0150] Time-varying topology and parameters: If the communication topology or system parameters change dynamically over time (such as switching topology or time-varying coupling strength), the coupling constraints between the topology switching rate and the sampling period can be derived using the average dwell time method or topology-dependent Lyapunov function under the quasi-periodic sampling assumption to ensure exponential convergence of the consistency error.

[0151] Mixed disturbance scenario: In addition to impulse disturbance, continuous external disturbance (such as bounded noise, periodic disturbance) or model uncertainty can be further considered. By integrating robust control techniques (such as disturbance observer, Control), design a composite controller to suppress the influence of mixed disturbances, and introduce dissipative theory in stability analysis to ensure that the error is uniformly bounded within a finite neighborhood.

[0152] Heterogeneous multi-agent systems: When the follower and leader dynamics do not fully match (e.g., heterogeneous nonlinearities or different orders), distributed protocols can be designed through dynamic surface control or output regulation theory, using virtual leaders or reference models to coordinate the heterogeneous dynamics and extending the error system to include dynamic difference terms.

[0153] About topology switching mode:

[0154] This study mainly conducts theoretical analysis and design for fixed communication topologies (e.g., assumptions 1 and 4 explicitly require topological connectivity), and does not involve dynamic topology switching scenarios. Positive definiteness, sampling period The constraints are derived based on a fixed topology. To extend to a switching topology scenario, the following mechanisms must be introduced:

[0155] Joint connectivity assumption: requires that the switching topology is jointly connected within the time window and the average Laplacian matrix satisfies the original paper Symmetric positive definite conditions for .

[0156] Switching rate, constraining the topology switching frequency to be consistent with the pulse control period and gain Coordinated design to avoid frequent switching that destroys the exponential convergence of the error system.

[0157] Time-varying matrix eigenvalue analysis: It is necessary to use the time-varying Lyapunov function or matrix measure theory to replace the fixed matrix in the original theorem The eigenvalue conditions (such as ) is replaced by the worst-case boundary value under the switching topology.

[0158] Such extensions require the reconstruction of the error dynamic equations under the switching topology and the adjustment of the gain constraints in the pulse control protocol (e.g., Its rigorous proof requires a combination of switching system theory and the theory of impulse differential equations, which is beyond the scope of the current paper.

[0159] A sampling consistency control system for a nonlinear multi-agent system comprises: a processor, a memory and executable instructions stored in the memory; when the processor executes the instructions, the sampling controller design, parameter selection and consistency condition verification containing pulse disturbances are realized.

[0160] A computer-readable storage medium stores computer program instructions, which, when executed by a processor, implement steps S101-S107.

[0161] System implementation:

[0162] The leader-follower consistency control system proposed in the present invention can be implemented on a distributed multi-agent platform. Equipped with local computing units and memory, it stores dynamic models, state information, communication topology weights, leader reference trajectories, and pulse control algorithms. Agents exchange state information through intermittent communication networks (based on topology graphs). The adjacency matrix Connecting Matrix with Leaders ), and receives neighbor status and leader information at the sampling time.

[0163] The functions of the system parameter design unit, stability verification unit, and pulse gain calculation unit are completed in the offline stage to determine the control gain. , Maximum allowable sampling period , pulse gain and Lyapunov function parameters .

[0164] The control signal generation unit and the pulse execution unit run in real time on the local processor of each agent. Collect neighbor status , own status and leader status , calculate the nominal control quantity , and superimpose the impulse disturbance term Generate actual control input The execution unit will It acts on nonlinear dynamic systems and simultaneously handles the impact of pulse instantaneous action on the actuator.

[0165] The rapid reconstruction of communication topology and pulse timing synchronization are key links. It is necessary to ensure that the sampling cycles of all intelligent agents are strictly synchronized through the timestamp protocol and adopt a communication coding strategy that is resistant to pulse interference. The condition verification requires online calculation of the matrix at each topology switch. The characteristic value of the pulse gain is dynamically adjusted To maintain system stability. Real-time monitoring of the Lyapunov function V(t) can be embedded in the local computing unit to trigger the adaptive adjustment mechanism to ensure the exponential convergence of the error system. This paper proposes an effective method and system for achieving leader-follower consistency and inclusive control of nonlinear multi-agent systems under impulse disturbance and sampled data control. By combining the Lyapunov function method, algebraic graph theory and impulse system theory, a distributed control protocol that is resistant to impulse interference is designed, and a sufficient condition for ensuring the exponential convergence of the error system is established (as shown in Theorem 1). The synchronization problem of traditional continuous control strategies in communication-limited and sudden disturbance scenarios is solved. The proposed parameter collaborative design criteria (such as control gain , sampling period With pulse gain The constraint relationship of the system provides a theoretical basis for stability verification and dynamic adjustment in actual systems.

[0166] Those skilled in the art will appreciate that the pulse control mechanism, sampled data protocol, and topology feature analysis techniques described in this invention can be freely combined and applied to various scenarios, including single-leader following and multi-leader inclusive control. The numerical simulation verification scheme, parameter adaptive adjustment strategy, and communication topology dynamic reconstruction method described in the embodiments can be extended to other nonlinear multi-agent systems through equivalent replacement or improvement, without departing from the core concepts of the present invention.

[0167] The above embodiments are only specific implementations of the present invention and are not intended to limit the scope of protection of the present invention. Any technical variations, parameter optimizations, or application expansions based on the pulse disturbance suppression, sampled data consistency, and Lyapunov stability analysis framework shall be included within the scope of the claims of the present invention.

Claims

1. A sampling consistency control method for nonlinear multi-agent systems, characterized in that: The following steps are involved: S101. Obtain system model parameters, including nonlinear functions , pulse gain , sampling period , Communication topology diagram and leader-follower dynamics equations; S102. Verify the following assumptions: the topology is undirected and connected, at least one follower is connected to the leader, the nonlinear function satisfies the Lipschitz condition, and the multi-leader topology condition is verified when control is included; S103. Constructing Lyapunov functions , combined with pulse disturbance to analyze the stability of the error system; S104. Use Lyapunov method and pulse theory to derive consistency conditions and calculate key parameters: And there is a constant Make the inequality Established, of which: And determine the pulse gain and sampling period constraints, where is the Lyapunov function parameter; S105, selecting parameters that meet the conditions; S106. Constructing a sampling controller with pulse disturbances: Design in a single-leader scenario: The multi-leader scenario is extended to ; in , To control the gain, is the pulse gain, is the Dirac function; S107. Implement the controller and perform numerical simulations to verify the effectiveness of leader-follower consistency and inclusive control, and prove the exponential synchronization performance through state trajectory convergence.

2. The sampling consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The multi-agent system consists of a leader and N followers, and the dynamic equation of each agent is: Followers: , Leaders: , in For follower status, is the control input containing pulse disturbance, To satisfy the Lipschitz condition Nonlinear function of Communication topology It is an undirected connected graph with at least one follower directly connected to the leader.

3. The sampling consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The control gain Determined by the algebraic Riccati equation or Lyapunov inequality, , and the sampling period satisfy ,in .

4. The sampling consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The pulse gain Need to meet , to ensure that the Lyapunov function shows a decaying trend at the sampling time.

5. The sampling consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The method is extended to include In the control scenario with multiple leaders, the communication topology must satisfy the requirement that each follower has a directed path with at least one leader. The controller form is expanded to: in , and the consistency condition is adjusted to: in is the Laplacian matrix of the follower subgraph.

6. The sampling consistency control method for a nonlinear multi-agent system according to claim 5, characterized in that: The nonlinear function in the control scenario must satisfy the extended Lipschitz condition: in and .

7. A control system for implementing the method according to any one of claims 1 to 6, characterized in that: include: a processor, a memory, and executable instructions stored in the memory; When the processor executes the instructions, the sampling controller design, parameter selection and consistency condition verification containing pulse disturbance are realized.

8. A computer-readable storage medium, characterized in that Computer program instructions are stored, and when the instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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