Resilient prescribed performance optimal control for underactuated unmanned surface vehicle: A differential game...

This paper investigates the predefined optimal control problem for underactuated unmanned surface vehicles (USVs) in non-cooperative adversarial scenarios, with a focus on enabling defending USVs to achieve effective collision avoidance in obstacle environments while performing optimal interception of attacking USVs. In the guidance stage, the Nash equilibrium point of the game is solved analytically using geometric methods as the expected interception point for both parties. To ensure that USVs maintain a safe distance from obstacles during the game, control barrier functions (CBFs) are introduced to formulate a quadratic programming problem, which strictly enforces safety constraints while minimizing adjustments to the game strategy. In the controller design stage, in order to satisfy the transient and steady state performance constraints of the system states, a robust controller based on predefined time functions and error transformation is designed. By incorporating an elastic term mechanism, this controller enhances the flexibility of error constraints while meeting the prescribed performance bounds. Theoretical analysis proves the optimality of the guidance strategy and the semi-globally uniformly ultimately bounded (SGUUB) stability of the closed-loop system. Finally, simulation results demonstrate the effectiveness, safety and superiority of the proposed algorithm in complex adversarial scenarios.