Distributed fixed-time Nash equilibrium seeking algorithm for multiple ASVs: A hybrid event-triggered approach

In this article, the fixed-time Nash equilibrium (FTNE) seeking problem of multiple autonomous surface vehicles (ASVs) is considered. As individuals fight for an allocation of specific shared but restricted resources, two novel FTNE seeking algorithms are designed for this topic through an error decomposition method. First, a model-based control algorithm with only one convergence time function in a single-layer structure is designed to achieve Nash equilibrium within a fixed time. Then, a FTNE algorithm with a three-layer structure is presented for multiple ASVs subject to system uncertainties. In particular, this paper proposes a hybrid fixed -time event-triggered approach for reducing controller update frequencies and communication frequencies of two algorithms simultaneously, which is capable of decreasing resource consumption in a constrained resource environment. Furthermore, rigorous sufficient criteria are established for fixed-time convergence through Lyapunov stability analysis, and the upper bound on settling time without the requirement of initial conditions is derived. Finally, simulation examples are given to demonstrate the viability of two algorithms.