Reinforcement Learning-Based Boundary-Optimized Control of Flexible Manipulators Under Jointly Connected Switching Topologies

This article pioneers the study of boundary-optimized fault-tolerant tracking control for flexible manipulators in a switching digraph with a heterogeneous linear leader. Compared with existing research, the proposed methods have several features. First, a distributed observer is designed to observe the leader's information in a general switching graph where communication can be interrupted. Second, a new partial differential equation (PDE)-based fault observer (FO) is designed to estimate unknown faults using only a few boundary states. Third, a novel long-term integral cost function is formulated to minimize angle-tracking errors, vibration deflections, and control energy in flexible manipulators. The ideal boundary optimal control laws are, then, derived and approximated using actor-critic neural networks (NNs) based on reinforcement learning (RL). Under the proposed fully distributed optimized fault-tolerant controllers, the closed-loop flexible manipulator's error states are proven uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed method is demonstrated through numerical simulation results.