Optimal Robust Containment Control for Human-Quadrotor Formation via Critic Neural Network Learning with Relaxed PE Conditions

This paper proposes a novel optimal robust containment control framework for a group of quadrotors with human-operated leaders. Different from the conventional containment task, external disturbances are considered in the dynamic model of followers and human instructions are modeled as the control input for the dynamics of leaders to enhance the maneuverability of the quadrotor team. This framework consists of two parts. First, a distributed trajectory generator is proposed to derive containment state reference for each follower using only observable leaders’ data. Based on the distributed trajectory generator, the containment control problem is transformed into an optimal robust tracking control problem. Furthermore, a zero-sum differential game-based position containment controller is proposed to solve the optimization. To obtain the game’s optimal solution, a critic neural network (NN) is employed with a novel weight adaption law using dynamic regression extension and mixing (DREM) technology. Unlike conventional gradient-based methods, this law achieves weight convergence under relaxed persistent excitation (PE) conditions while enhancing the transient performance for the training of the critic NN. Finally, theoretical analysis is given to prove the stability of the closed-loop system and the efficacy of the proposed control method is demonstrated through simulation.