Discrete-Time Control for Double-Integrator Systems With State Constraint and Learning Gain

This brief investigates a barrier Lyapunov function based discrete-time control with Q-learning based gains for double-integrator systems with state constraint. It is found, from the stability proof, that the high conservatism of analysis for the stabilization of discrete-time system with state constraint is revealed, where the explicit selection of constant high gain is challenging. To address this problem, the fuzzy Q-learning algorithm is employed to search for the nearly optimal control gains for both fast response and low steady-state error in the long view of performance consideration. The numerical and experimental results verify the effectiveness of the proposed method, and varying gains based on fuzzy approximation Q-learning can aid to reduce the steady-state error while fast response to the reference motion trajectories.