Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

Abstract

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

Finite-time output tracking for a class of switched nonlinear systems

“…In comparison with the existing results on tracking control of switched nonlinear systems [26][27][28][29][30][31][32][33], only boundedness of y d .t / and P y d .t / are required, and no boundedness conditions are imposed on the higher order derivatives of the reference signal y d .t / in this paper. Besides, controllers (32) and (35) only contain the reference signal y d .t /.…”

“…with c i > n i, we have Step n: Consider the following function V n .´1; x 2 ; :::; x n / D V n 1 .´1; x 2 ; :::; x n 1 / C W n .´1; x 2 ; :::; x n /; (30) where W n .´1; x 2 ; :::; x n / D R x n x n .s q n x q n n / 2 1 qn ds. It follows from (21), (26), and (30) that P V n .´1; x 2 ; :::;…”

“…Because non-Lipschitz nonlinearities may be included in system (1), the controller design scheme for switched nonlinear systems in [15] cannot be applicable to the system. To deal with this problem, we adopt the Lyapunov function (30), which is different from that proposed in [15].…”

“…Several methods, such as the common Lyapunov function method, the multiple Lyapunov functions method, and the dwell time approach, have been proposed to study this problem [15][16][17][18][19][20][21][22][23]. Tracking control of switched systems has been widely studied in the literature [24][25][26][27][28][29][30][31][32][33]. For example, the problem of output tracking for a class of switched nonlinear systems with multiple time-varying delays was investigated in [24].…”

“…The output tracking for cascade switched nonlinear systems was considered in [25]. Several adaptive 1018 S. HUANG AND Z. XIANG controllers were proposed to achieve tracking for uncertain switched nonlinear systems in [26][27][28][29][30]. Niu et al investigated the tracking problem of constrained nonlinear switched systems by using barrier Lyapunov functions in [31][32][33].…”