非连续混合自时延多智能体系统的饱和分布式控制

Consensus of discontinuous multi-agent systems with hybrid self-delays via saturated distributed control

研究一类非连续混合自时延多智能体系统的全局指数一致性问题.首先,利用具有时变控制增益的分布式负反馈控制器实现智能体之间状态信息交互.考虑到实际系统运行环境与节省控制成本,增设外部饱和环节将控制信号幅值限制在一个合理的范围内,从而提出利用高斯误差函数以及微分中值定理来近似模拟饱和效应,以此降低控制信号的不平滑度.随后,利用Filippov微分包含理论和测度选择定理将多智能体系统的非线性动力学函数映射为Filippov集值函数,再通过广义Halanay不等式和Lyapunov稳定性定理给出该多智能体系统的指数一致性判定条件及其最大容许时延.最后,通过数值仿真验证所提出控制策略的有效性.

This paper investigates the globally and exponentially consensus problem for a kind of multi-agent systems with discontinuous dynamics and hybrid self-delays. Through implementing the distributed negative feedback control strategy with time-varying control gain, the communication of state information among agents is achieved. Since it is impossible for the amplitude of the control signal to reach infinite in practical applications, the saturation strategy is utilized to limit the control effect into certain reasonable ranges. In order to reduce the non-smoothness of control signal,the Gaussian error function and the differential mean value theorem are jointly taken to simulate the saturation effect.Furthermore, the Filippov differential inclusion and the measure selection theorem are utilized to deal with discontinuous differential equations. Then the exponentially consensus criteria and the admissible delay are derived by applying the generalized Halanay inequality and the Lyapunov stability theorem. Finally, the effectiveness of the proposed control strategy is verified by numerical simulation.