Nonfragile Formation Seeking of Unmanned Surface Vehicles: A Sliding Mode Control Approach

Abstract

The nonfragile sliding mode control (SMC) approach is referred in this paper to seek the formation in multiple unmanned surface vehicles (USVs) with environmental disturbances. The USV interaction is firstly portrayed by an undirected connected graph with the fixed manner. With constructing a novel sliding surface, one proves that, if the resultant sliding mode subsystem is asymptotically stable, all networked USVs achieve the prescribed formation pattern with respect to a formation reference function (FRF). Thanks to algebraic graph theory, the FRF is explicitly expressed as a noise-unperturbed system, whose initial condition is merely related to that of each USV. By gathering in-neighboring USVs’ position and velocity information, a distributed control law involving norm-bounded parametric uncertainty is designed such that the constructed sliding surface is capable to be reached in finite time. Then, based on the presented analytical framework, the derived conditions are extended to the case of Markovian topology switching with completely and partially known transition rates. Three numerical simulations validate the theoretical results.