Optimal consensus control for multiagent networks of distributed parameter systems

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2026-06-01 Epub Date: 2026-01-16 DOI:10.1016/j.cnsns.2026.109745

Jin You , Yan Li , Xiangyang Cao , YangQuan Chen

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引用次数: 0

Abstract

In this paper, diffusive representation (DR) is shown to be effective in addressing optimal consensus control problems in DPS-based multiagent systems (MASs) for both leader-following and leaderless cases, leading to significant advancements in meeting engineering requirements, facilitating cost savings and enhancing efficiency for optimal performance. First, the concept of DR approach is introduced to transform the original causal convolution pseudo-differential operator (PDO) into DPS, exhibiting infinite dimensional properties. Second, the proposed spatial product operation helps establish a theoretical system of the converted DPSs, including the linear representation for state space model, the Lyapunov functions and the reformulation of LQR optimal control problem with generalized performance indexes. Furthermore, the inverse optimality technique is conducted to develop distributed strategies for the cooperative control of the distributed parameter multiagent systems using DR approach, and derive the solution of globally optimal LQR problem. Finally, fractional-order multiagent systems (FOMASs) to both leaderless and leader-follower UAV formation control scenarios are presented to validate the effectiveness of the proposed results.

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分布参数系统多智能体网络的最优一致性控制

在本文中，扩散表示（DR）在解决基于dps的多智能体系统（MASs）中领导者跟随和无领导者情况下的最优共识控制问题上是有效的，从而在满足工程要求，促进成本节约和提高效率以实现最佳性能方面取得了重大进展。首先，引入DR方法的概念，将原因果卷积伪微分算子（PDO）转化为具有无限维特性的DPS。其次，提出的空间积运算有助于建立转换后的dps的理论体系，包括状态空间模型的线性表示、Lyapunov函数和广义性能指标的LQR最优控制问题的重新表述。在此基础上，利用逆最优性技术开发了分布式多智能体系统协同控制的分布式策略，并推导了全局最优LQR问题的解。最后，将分数阶多智能体系统（FOMASs）应用于无领导和领导-跟随无人机编队控制场景，验证了所提结果的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.