Adaptive Fixed-Time Output-Feedback Optimal Time-Varying Formation Control for Multiple Omnidirectional Robot Systems

This article presents an adaptive fuzzy fixed-time output feedback control approach for achieving an optimal time-varying formation (TVF) of multiple omnidirectional robot systems (MORSs) with uncertain external disturbances. Given that only output variables of the system are measurable, the method employs fuzzy state observers to reconstruct other unmeasured states. Novel performance index functions that incorporate exponential power terms are developed to achieve the optimization of a formation control system's performance. This function is utilized to design a fixed-time optimal scheme based on an identifier–actor–critic structure, which is a well-established control framework. Through rigorous analysis, it is proved that the proposed scheme guarantees fixed-time boundedness of all signals in the system and achieves formation control at a minimum cost. The comparative simulations and data analyses verify the effectiveness and superiority of the proposed control algorithm.