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具有扰动的二阶多智能体系统预定时间一致性控制

Prespecified-time Consensus Control for Second-order Multi-agent Systems with Disturbances

  • 摘要: 针对受外部扰动的二阶多智能体系统一致性控制问题,提出一种基于滑模技术的分布式预定时间控制策略。首先,在无向图条件下设计二阶分布式预定时间观测器,在有效解决代数环问题的同时降低通信负担,确保每个跟随者能够在预定时间内精确估计领导者状态信息。其次,基于系统状态误差设计新型分布式预定时间滑模面,有效提高系统收敛速度。进一步地,设计一种考虑外部扰动的预定时间一致性分布式控制协议,保证系统状态跟踪误差在预定时间内收敛至零点。此外,结合代数图论以及李雅普诺夫理论,严格证明闭环系统的预定时间稳定性,并推导出系统初始状态未知情况下的稳定时间上界估计值。最后,通过数值仿真对比实验验证本文策略与理论分析的有效性与可行性。结果表明:与有限时间控制策略相比,本文策略的收敛时间与系统初始值无关且收敛性能更优;与固定时间控制策略相比,本文策略的收敛时间上界独立于智能体初始状态及控制器参数,仅由单一时间参数决定,具有收敛时间预估精确、设定便捷、保守性低等显著优势。

     

    Abstract: Aiming at the consensus control problem of second-order multi-agent systems with external disturbances, a distributed predefined-time control strategy based on sliding mode technology was proposed. Under undirected graph conditions, a second-order distributed predefined-time observer was designed to resolve the algebraic loop issue while reducing communication burden, and it was ensured that each follower could accurately estimate the leader’s state information within a predefined time. Using the system state error, a novel distributed predefined-time sliding surface was designed to improve the convergence speed effectively. Furthermore, a predefined-time consensus distributed control protocol considering external disturbances was designed to guarantee the system state tracking error convergence to zero within the predefined time. Additionally, through algebraic graph theory and Lyapunov theory, the predefined-time stability of the closed-loop system was rigorously proven, and the upper bound of the stabilization time was derived for unknown initial states. Finally, comparative numerical simulations verified the effectiveness and feasibility of the proposed strategy and theoretical analysis. The results show that compared with finite-time control strategies, the convergence time of the proposed strategy is independent of the system’s initial values and its convergence performance is proven superior, whereas against fixed-time control strategies, the upper bound of the convergence time is not only independent of the agents’ initial states and controller parameters but is solely determined by a single time parameter, with significant advantages of precise convergence time estimation, simplified parameter tuning, and reduced conservatism.

     

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