Regulation of lower triangular and non‐triangular nonlinear systems with uncertain high‐order nonlinearities via dynamic gain control

Abstract

Summary In this paper, we consider a global regulation problem of a class of nonlinear systems that have uncertain high‐order nonlinear terms. In particular, we introduce new high‐order lower triangular and non‐triangular conditions and propose a controller with dynamic gains to regulate the system with uncertain high‐order nonlinearities. In designing our controller, the information of the growth rate is not required, and the forms of the high‐order nonlinearities are more relaxed. We verify that the proposed method is applicable to the system which cannot be regulated by the existing methods. Examples and simulation results are given for clear illustration. Copyright © 2016 John Wiley & Sons, Ltd.

Controller design for a class of nontriangular nonlinear systems with input dependent growth rate

“…5,6 It is clear that the aforementioned control methods require the system to satisfy the triangular structure, which plays an important role in the controller design procedure. However, some real systems, such as the continuously stirred tank reactor system 7 and the Chua's circuit, 8 fail to meet the condition and some currently available controllers cannot work. In the work of Krishnamurthy and Khorrami, 9 a high-gain scaling-based state-feedback controller was constructed for the nontriangular nonlinear system under certain conditions and the control result has been further generalized to a more general class of nontriangular systems.…”

“…In the work of Krishnamurthy and Khorrami, 9 a high-gain scaling-based state-feedback controller was constructed for the nontriangular nonlinear system under certain conditions and the control result has been further generalized to a more general class of nontriangular systems. 8,10 For second-order nontriangular systems, Cai et al 11 proposed a backstepping-based robust adaptive control scheme to make the closed-loop system bounded.…”