Distributed leaderless impulsive consensus of non-linear multi-agent systems with input saturation

Abstract

This paper aims to propose dynamic consensus protocols for a class of non-linear saturated multi-agent systems. Due to the existence of non-linear dynamics of each agent, the system does not satisfy the condition named asymptotically null controllable with bounded controls (ANCBC). As a result, the widely-adopted method of low-gain feedback to solve consensus control problems for linear multi-agent systems with input saturation cannot be used. To step back, even if the system is linear and meets the ANCBC condition, the existing low-gain method or that combined with adaptive method can only make the system eventually reach zero consensus, which is unable to bring the system to dynamic consensus. In addition, from the view of energy conservation, this study proposes the impulsive control method to reduce the energy consumption of the controller. By taking advantages of the stability theory of impulsive systems, as well as the properties of Laplacian matrix and convex hull, corresponding distributed dynamic consensus protocols are proposed. Still, the shape reference set is introduced to assess the attraction domain of the leaderless MASs. Finally, the performance of the proposed anti-saturation impulsive control algorithm is demonstrated by extensive numerical experiments.