Solving the unknown control direction problem for strongly nonlinear systems by means of periodic switching function and norm observers

Abstract

This paper addresses the design of a sliding mode tracking controller for single-input-single-output (SISO) uncertain strongly nonlinear plants with relative degree one and unknown sign of the high frequency gain, i.e., with unknown control direction. We demonstrate that it is possible to achieve global exact tracking using only output-feedback by combining a recently introduced periodic switching function with a novel norm state observer framework. One significant advantage of the new scheme is its robustness to time-varying control direction which has been theoretically justified for jump variations and successfully tested by simulation.