Trajectory tracking for uncertain (non)minimum phase systems by monitoring function and time-scaling based sliding mode control

Abstract

In this paper we combine the sliding mode control (SMC) strategy with monitoring functions and time-scaling to solve the problem of trajectory tracking for linear minimum or non-minimum phase systems. Unlike other publications which in general assume full/partial state availability, the complete knowledge of the non-minimum phase plant parameters, or just handle the stabilization/regulation problem, here we deal with the tracking objective by assuming the plant is subject parametric uncertainties and applying only output feedback. When using the time-scaling technique, we may expect that the tracking of the reference model occurs slowly, depending on the time-scaling parameter. This is the price to be paid for considering a more general framework of uncertainty. Global asymptotic stability with respect to compact sets is demonstrated for the closed-loop system, where the output tracking error ultimately achieves arbitrarily small residual sets. Simulation results illustrate the performance of our control algorithm.