一类分数阶多智能体系统的协调跟踪控制

Coordinated tracking control for a class of fractional-order multi-agent system

针对分数阶多智能体系统的协调跟踪控制问题,首先,引入Caputo分数阶概念及证明方法,采用领导跟随多智能体系统的一致性控制算法,并通过线性矩阵不等式(Linear Matrix Inequality,LMI)来求解控制算法中的待设计参数,以保证所有智能体状态最终能够收敛到预期目标值;然后,借助Lyapunov稳定性理论、代数图论等方法得到分数阶多智能体系统实现领导跟随一致性的充分条件;最后,通过数值仿真验证理论结果的有效性。

Aiming at the coordination tracking control problem of fractal-order multi-agent system,firstly,the Caputo fractional-order concept and the proof method are introduced,the consensus control algorithm of leader-following multi-agent system is adopted,and the parameters to be designed in the control algorithm are solved by linear matrix inequality(LMI)to ensure that all agent states can eventually converge to the expected target value.Then,by using Lyapunov stability theory,algebraic graph theory and other methods,we get the sufficient conditions for the fractional-order multi-agent system to achieve the lead-following consensus.Finally,the validity of the theoretical results is verified by numerical simulation.