Adaptive finite‐time optimal time‐varying formation control for second‐order stochastic nonlinear multiagent systems

Summary This work addresses a fuzzy‐based finite‐time optimal time‐varying formation (TVF) control issue for a class of second‐order stochastic multi‐agent systems (SMASs) with unknown nonlinearities. First, novel optimal cost functions with exponential power terms are constructed, which enables the SMASs to achieve finite‐time stability in the mean square sense with minimum cost. Then, based on the cost functions, an optimal controller is proposed, in which fuzzy logic systems (FLSs) are used as universal approximators to identify the unknown uncertainties. Theorem analyses show that the proposed control strategy can guarantee the mean‐square finite‐time bounded of all signals in the system and then the TVF control task can be simultaneously realized with minimum cost. Finally, the effectiveness of the presented control method is verified by a multiple omni‐directional robot system.