Adaptive Position Tracking with Hard Constraints—Barrier Lyapunov Functions Approach

Abstract

A servo control with unknown system parameters and constraints imposed on the maximal tracking error is considered. The barrier Lyapunov functions approach is applied to assure the preservation of constraints in any condition. The system’s performance is examined for three methods of controller design based on: quadratic Lyapunov functions; on barrier Lyapunov functions if only position constraints are imposed; and on barrier Lyapunov functions if both position and velocity constraints are present. The tuning rules are discussed and several experiments demonstrating features of the proposed control and the influence of the parameters are presented.