Combined backstepping and HOSM control design for a class of nonlinear MIMO systems

Abstract

Summary This paper presents a control design algorithm that combines backstepping and high‐order sliding modes. It is known that backstepping can achieve asymptotic stability for nonlinear systems in strict‐feedback form in spite of parametric uncertainties. Nevertheless, when external perturbations are also present, only practical stability can be ensured. For the same aforementioned perturbed conditions, the combined design presented in this paper can achieve finite‐time exact tracking/regulation. At the same time, the semi‐global or global stability obtained through backstepping is preserved, and the gains of the high‐order sliding modes controller can be reduced with respect to its direct application. The design is based on recently reported combined designs that are based on the idea of virtual controls, which can contain terms based on high‐order sliding modes algorithms. The proposal also extends previous results to the multiple‐input–multiple‐output case. Copyright © 2016 John Wiley & Sons, Ltd.

Global second‐order sliding mode control for nonlinear uncertain systems

“…Sliding mode control (SMC) has been widely used for the control of systems under bounded uncertainties/disturbances and unmodeled dynamics. [1][2][3][4][5][6] The main disadvantages or constraints of the implementation of conventional SMC are two folds (eg, the works of Levant 7 and Estrada et al 8 ). The first is the requirement on the relative degree to be equal to one.…”

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

“…However, with such modifications, only semi-global boundedness of tracking error can be guaranteed, and the introduction of first-order pseudo-differentiation may also result in the so-called peak phenomenon, which will be analyzed in details. Motivated by the concept of exact backstepping tracking [33][34][35], HOSM differentiator [36][37][38] is introduced in this paper to estimate the time derivatives of the virtual control laws so as to guarantee exact tracking performance. The HOSM exact differentiator is defined as [36]…”

Finite‐time tracking control for a class of nonlinear systems with multiple mismatched disturbances

“…Based on finite‐time control method and FTDO technique, the finite‐time output regulation problem for a class of integrator systems with mismatched perturbations is investigated in Reference 34. For a general class of multiinput‐multioutput nonlinear systems with matched and mismatched perturbations, 35 proposes a finite‐time tracking control scheme by combining backstepping and high‐order sliding mode control design, which enhances the results in Reference 31.…”