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

Abstract

This 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.