Optimizing Fixed-Time Generalized Nash Equilibrium Seeking in Multi-Autonomous Aerial Vehicle Games

Abstract

This study addresses a fixed-time generalized noncooperative game involving multiple autonomous aerial vehicles (AAVs) that encounter challenges such as discontinuous communication and external disturbances. Each AAV, motivated by self-interest, seeks to optimize its performance function by adjusting its actions within shared equality and inequality constraints. To facilitate this, a fixed-time generalized Nash equilibrium (GNE) seeking algorithm is proposed for games with shared equality constraints, incorporating an internal dynamic system to ensure compliance with these constraints. By employing penalty methods, an auxiliary performance function is developed to manage games with mixed constraints. Furthermore, an error decomposition method and a fixed-time observer are introduced to address the issues of discontinuous communication and external disturbances. The study establishes sufficient conditions for the convergence of the fixed-time GNE seeking algorithm and provides an explicit upper bound on the settling time based on Lyapunov stability theory. The effectiveness of the proposed algorithms is demonstrated through various simulation examples.