Higher-Order Sliding Modes for the Output-Feedback Control of Nonlinear Uncertain Systems

This chapter examines some aspects of the output-feedback control problem for nonlinear uncertain plants, with special emphasis on possible applications of recent results about higher order sliding modes (HOSMs). This regime is established when the simultaneous, finite-time, zeroing of an output quantity (the sliding quantity), and of a certain number of its derivatives, is ensured. In this work, for any step of an output feedback variable structure control design, namely, the definition of the sliding variable, the synthesis of the control law, and the state estimation, a survey of proposals characterized by a finite-time convergence transient is presented. Some different types of sliding surfaces in the state space, such that the associated constrained motion is characterized by a finite-time converging dynamics, are recalled. The use of a discontinuous control to make them attractive and invariant is then analyzed. Finally, real-time differentiators based on HOSMs for estimating the output derivatives are considered. The twofold objective of the present chapter is to survey the most recent results on HOSMs and to highlight their possible role in improving existing approaches, to motivate and to draw possible lines for future research.

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