具有执行器饱和的多智能体系统H_(∞)边界一致性控制

H_(∞)Boundary Consensus Control for Multi-Agent Systems with Actuator Saturation

为了解决具有时空耦合特性的多智能体系统在执行器饱和约束下的一致性跟踪问题,文章提出了一种受限H_(∞)边界控制策略.首先针对领导者与跟随者的时空动力学行为特征,运用克罗内克积与等价有向图,将跟踪问题转化为镇定问题,构建出由多个抛物线型偏微分方程(partial differential equation,PDE)组成的一致性误差系统.其次,通过改进李雅普诺夫方法和沃廷格不等式,推导出同时满足H_(∞)增益和指数稳定的充分条件.再次,融合不变集理论,在线性矩阵不等式(linear matrix inequality,LMI)多目标优化的框架下,解决了N eumann边界控制器的饱和问题.最后,通过对比仿真验证了所提出方法的有效性.

In order to solve the tracking problem of multi-agent systems with spatiotemporal coupling characteristics under the actuators saturation,this paper proposes a constrained H_(∞)boundary consensus control strategy.First,by applying the Kronecker product and equivalent directed graph,the original consensus tracking problem is transformed into the stabilization problem of multi-agent error systems,whose model involves the multiple parabolic partial differential equations(PDEs)with Neumann boundary conditions.Subsequently,a sufficient condition on the H_(∞)norm and exponential stability is obtained by improving the Lyapunov-based method and Wirtinger’s inequality.Then,the actuator saturation problem of Neumann boundary control is addressed by using the invariant set theory in the multi-objective optimization framework of linear matrix inequality(LMI).Finally,the comparison simulation results demonstrate the effectiveness of proposed methodology.