Adaptive output feedback control for a class of planar nonlinear systems

Abstract

This paper is concerned with the problem of global adaptive stabilization by output feedback for a class of planar nonlinear systems with uncertain control coefficient and unknown growth rate. The control coefficient is not supposed to have known upper bound, and this relaxes the corresponding requirement in the existing literature (see e.g. 1, 2. First, by the universal control method, an observer is constructed based on the dynamic high‐gain K‐filters. Then, the control design procedure is developed to obtain the stabilizing controller and dynamic compensator for the uncertainties in the control coefficient. It is shown that the global stability of the closed‐loop system can be guaranteed by the appropriate choice of the design parameters. A simulation example is also provided to illustrate the correctness of the theoretical results. © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

“…However, the results in the aforementioned literature are only applicable for systems with known control coefficients. When the control coefficients are uncertain/unknown, the output feedback control design becomes much more challenging and difficult, and few results have been obtained up to now 11–14.…”

“…Assumption A2 shows that there is an uncertain control coefficient g in system (1). These two assumptions make such a class of systems essentially different from those studied in 2, 4, 6, 9, 11–15. Specifically, with the precise information on control coefficient, the output feedback stabilization for nonlinear systems with constant and polynomial‐of‐output growth rates was considered in 2, 4, 6, 9, 15, respectively.…”

“…Mainly due to the known control coefficient, simple Luenberger‐type observers are adopted in 2, 4, 6, 9, 15 but cannot be employed to the case of uncertain control coefficient. Recently, without the precise information on control coefficient, the output feedback stabilization for various nonlinear systems with known or unknown constant growth rates was studied in 11–14. Since control coefficient is uncertain, two kinds of K‐filters for observer design are developed in 11–14, but inapplicable to the case of polynomial‐of‐output growth rate.…”

“…Recently, without the precise information on control coefficient, the output feedback stabilization for various nonlinear systems with known or unknown constant growth rates was studied in 11–14. Since control coefficient is uncertain, two kinds of K‐filters for observer design are developed in 11–14, but inapplicable to the case of polynomial‐of‐output growth rate. According to the above discussion, we see that the control design methods in 2, 4, 6, 9, 11–15 cannot be applied to the output feedback stabilization of system (1) which includes the leading systems investigated in 9 as a special case.…”

Global set‐point tracking control for a class of nonlinear systems with iISS inverse dynamics

“…[19,20]), investigation of achieving global tracking via output feedback for such class of nonlinear systems with uncertain control coefficients is an interesting subject of future study. The novelty of the proposed approach in this paper lies in that the treatment of the unmodeled dynamic states, and the controller can reduce to a linear or even a traditional PI control law under the iISS condition.…”