Saturated Adaptive Pinning Control and Consensus of Discontinuous Multi-Agent Systems

This paper studies the consensus problem for a kind of multi-agent systems with nonlinear and discontinuous dynamics through distributed adaptive control. By applying saturation strategy, the control signal is limited into a reasonable range in order to simulate the practical applications. Then utilize the Gaussian error function and the differential mean value theorem to simulate the saturation effect. By designing the adaptive updating law, appropriate control gain is finally obtained. According to Filippov differential inclusion and measure selection theorem as well as Lyapunov stability theorem, sufficient conditions for achieving the consensus of multi-agent systems are derived. Ultimately, the validity of our conclusion is verified by establishing a numerical simulation.