针对多智能体系统会受到外部干扰而使系统结构随机发生改变的问题,提出了当切换信号服从半马尔可夫过程时,领导跟随随机多智能体系统实现均方一致的控制算法。运用代数图论、半马尔可夫过程的转移速率与驻留时间分布函数相关性质和Lyapunov稳定性理论等理论工具,对控制算法进行了稳定性分析。通过设计合适的脉冲控制协议,给出了系统实现均方一致性的充分条件。条件表明,若脉冲间隔具有某一上界,均方一致性仍可实现。最后,数值仿真验证了结果的有效性。
Aiming at the problem that the multi-agent system structure will change randomly due to external disturbances, a mean-square consensus control algorithm is proposed for leader-follower multi-agent system when switching signals obey semi-Markov process. The stability of the control algorithm is analyzed by algebraic graph theory, the properties of the transition rate and the distribution function of the dwell time of semi-Markov procession and Lyapunov stability theory. The results show that sufficient conditions for the system to achieve mean square consensus is given by the designed impulsive control protocol. In addition, if the pulse interval has an upper bound, the mean square consensus can still be achieved. Finally, the validity of the proposed condition is verified by the numerical example.
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