Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller

Optimal control of nonlinear partially-unknown systems with unsymmetrical input constraints and its applications to the optimal UAV circumnavigation problem

Aimed at solving the optimal control problem for nonlinear systems with unsymmetrical input constraints, we present an online adaptive approach for partially unknown control systems/dynamics. The designed algorithm converges online to the optimal control solution without the knowledge of the internal system dynamics. The optimality of the obtained control policy and the stability for the closed-loop dynamic optimality are proved theoretically. The proposed method greatly relaxes the assumption on the form of the internal dynamics and input constraints in previous works. Besides, the control design framework proposed in this paper offers a new approach to solve the optimal circumnavigation problem involving a moving target for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our method is compared with that of the existing circumnavigation control law in a numerical simulation and the simulation results validate the effectiveness of our algorithm