Peaking free output‐feedback exact tracking of uncertain nonlinear systems via dwell‐time and norm observers

Abstract

SUMMARY The control of uncertain nonlinear systems by high‐gain observer based output feedback is addressed. Two tracking sliding mode controllers are designed for a broad class of uncertain nonlinear systems with arbitrary relative degree and unmatched polynomial nonlinearities in the unmeasured states. The proposed strategies are based either on dwell‐time for control activation or on simple norm state observers to remove the peaking phenomenon related with high‐gain observers, depending on the nonlinearity growth conditions. In contrast with previous works, exact tracking is also achieved by means of a switching strategy based on locally exact differentiators. Global or semi‐global stability is proved by using Lyapunov theory and on small‐gain analysis. Simulations show that the proposed methodologies provide better and uniform transient behavior, larger regions of attraction, performance recovery with significantly smaller observer gains and good robustness properties with respect to exogenous disturbances and measurement noise. Copyright © 2011 John Wiley & Sons, Ltd.

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

“…It is well known that, in the time-invariant case, if the internal system (1) is ISS with respect to y, then it admits such norm observer and the plant is minimum phase (Krichman et al, 2001;Oliveira et al, 2013).…”

“…The nonlinearities can also be unmatched, i.e., not in the span of the control input, which is barely considered in the SMC literature, as discussed in Oliveira et al (2013). An important contribution of this paper is to prove that the extension leads to overall signal boundedness (finite-time escape avoidance) and global exact tracking.…”

“…In order to achieve the control objective, our strategy also requires a norm observer (Krichman et al, 2001;Oliveira et al, 2013) for the state η of the internal system (1), according to the following definition.…”

“…The central idea was to obtain an output-feedback version of Drakunov andÖzgüner's periodic switching function method. This was achieved by means of the use of norm state observers (Krichman, Sontag, & Wang, 2001;Oliveira, Peixoto, & Hsu, 2013).…”

Peaking-Free Output-Feedback Adaptive Neural Control Under a Nonseparation Principle

“…Meanwhile, the peaking problem of high-gain observers has also been addressed by hybrid estimation techniques under the nonlinear separation principle in [20]- [22]. In [20], global output-feedback slide mode control (SMC) was proposed for uncertain linear systems, where the sign function of the SMC component is driven by a high-gain observer, while the sign function gain and other components of the controller are generated by state variable filters such that the peaking responses can be avoided without control saturation.…”