Adaptive Fuzzy Bipartite Time‐Varying Formation Tracking Control for Multiple Lagrangian Systems With Lumped Uncertainties via Finite‐Time Hierarchical Mechanism

Abstract

ABSTRACTThis article explores the bipartite time‐varying formation tracking problem for multiple Lagrangian systems in the presence of lumped uncertainties, including friction, external disturbances, and actuator faults. To tackle this challenging problem, a finite‐time hierarchical mechanism is designed without prior knowledge of uncertainties, which decomposes the above issue into two sub‐control problems: 1) the distributed finite‐time estimation problem and 2) the local adaptive fuzzy tracking problem. The distributed estimator algorithm is developed to achieve a finite‐time bipartite time‐varying formation configuration under a cooperative‐antagonistic interaction topology. Further, these estimated states are employed to construct the adaptive fuzzy tracking controller based on fuzzy‐logic systems and fault‐tolerant techniques. Lyapunov functions are utilized to ensure that the considered systems attain the desired formation while maintaining finite‐time stability of tracking errors. Finally, simulation experiments are performed to verify the effectiveness of the proposed control algorithm.