Prescribed‐Time Distributed Nash Equilibrium Seeking Over Uncertain Communication Topologies

This work studies distributed Nash equilibrium (NE) seeking for nonlinear multi‐agent systems (MASs) subject to bounded disturbances under uncertain communication topologies. Instead of assuming a fixed graph, the time‐varying and uncertain communication links are described by a Takagi–Sugeno (T–S) fuzzy model. For the unknown nonlinear terms, we employ fuzzy logic approximators and design an adaptive mechanism to estimate the norm of associated unknown parameter vectors. In addition, external disturbances are addressed through a reduced‐order disturbance compensator that combines observed disturbance values with a boundary‐layer signal. Then, a two‐phase control framework is developed to guarantee that all agents' trajectories achieve convergence within a prescribed time and asymptotically converge to the NE afterwards. Numerical simulations validate fast and accurate NE‐seeking performance under uncertain communication environments and demonstrate robustness against modeling uncertainties and time‐varying disturbances.