Time-varying formation for MSVs with input and prescribed performance constraints by fixed-time event-triggered sliding mode control

Abstract

This work develops a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve the control performance, ensure the navigation safety and reduce the communication burden. At first, a fixed-time adaptive radial basis function neural network (FxRBFNN) observer is designed to provide the estimations for external environmental disturbances and model parameters uncertainties. Then, observer-based fixed-time distributed time-varying formation event-triggered control law is proposed based on the novel fixed-time auxiliary dynamic system (FxADS), the proposed prescribed performance function, the designed fixed-time nonsingular terminal sliding mode (FxNTSM) manifold and the proposed uniform exact differentiator. Finally, the system stability is proved by Lyapunov theory. The salient features as follows. First, to enhance the convergence performance for time-varying formation control method, a novel hyperbolic cosecant prescribed performance function (PPF) is introduced. Second, a novel FxADS is proposed to confront input constraints. Third, the proposed scheme is combined with a relative threshold event-triggered strategy to reduce the unnecessary updates of actuators under the premise of ensuring the control performance. Fourth, to avoid the proposed formation control law including adjacent vessel accelerations, this work proposed an improved uniform exact differentiator to identify them. Numerical simulations confirm that the proposed scheme has superior control performance.