Prescribed-Time Distributed Time-Varying Nash Equilibrium Seeking for Formation Placement Control

This brief studies the formation placement problems for multi-cluster system with convergent time requirements based on a time-varying Nash equilibrium (NE) seeking approach. In order to determine the placement of each agent that subject to formation constraints in each cluster within a prescribed setting time, a basic centralized time-varying NE seeking algorithm based on time transformation approach is designed. In addition, by applying a prescribed-time distributed observer, an extended distributed time-varying NE seeking algorithm is proposed. Compared with existing results, the convergence time can be appointed in advance according to specific mission requirements. Finally, the effectiveness of proposed algorithms is verified by numerical simulations.