On prescribed-time convergence of Nash equilibrium seeking over switching topologies with dynamic event-triggered communication

This paper investigates the problem of prescribed-time Nash equilibrium seeking in switching directed networks for high-order nonlinear multi-agent systems. Two main challenges are addressed: transient uncertainties caused by nonlinear couplings and rapid topology switching, as well as the practical design of implementable controllers under communication constraints. The core difficulty lies in capturing the gradient-propagation perturbations induced by fast topological switching and the time-varying mismatches arising from event-triggered sampling. To overcome these challenges, a dynamic switching event-triggered feedback framework is developed, which incorporates a time-varying scaling function that leverages local gradient estimates and neighboring triggering patterns, thereby significantly reducing the communication burden. The proposed triggering rule accommodates switching directed topologies with switching signals having no finite accumulation points, guarantees prescribed-time convergence, and precludes Zeno behavior. Furthermore, a prescribed-time adaptive filtered feedback strategy is devised to mitigate the complexity growth inherent in high-order systems. Rigorous sufficient conditions for prescribed-time convergence are established with explicit parameter constraints. The effectiveness of the proposed approach is validated through two comparative simulation examples.