Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

Abstract

This paper investigates the global adaptive finite-time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p 6 1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed-loop system is finite-time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite-time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated.

Adaptive finite‐time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

“…Remark As analyzed in the work of Schwartz, since f i ( i = 1,…, n ) are functions with f i (0, θ ) = 0 for ∀ t ≥ 0 and d 1 ( t ),…, d n ( t ) are continuous differentiable functions, the sufficient regularity conditions (ie, locally Lipschitz conditions) such that system has a unique solution can be satisfied from the explanations in the work of Khalil . In addition, Assumption 2 is frequently used in related works . Next, some definitions and technical lemmas are provided to end this section.…”

“…Due to the fast convergence rate and good performance on robustness and disturbance rejection, the problems of finite‐time stability and stabilization for nonlinear systems have attracted increasing attention. In the work of Bhat and Bernstein, the finite‐time Lyapunov stability theorem was first established, based on which and on backstepping or adding a power integrator technique, remarkable finite‐time stabilization or tracking results have been achieved (see other works and the related references). In particular, an adaptive finite‐time control law was obtained in the form of continuous time‐invariant feedback for nonlinear systems with parametric uncertainty in the work of Hong et al Later, in the work of Hong and Jiang, a constructive partial‐state control design was proposed to investigate the nonsmooth finite‐time stabilization of nonlinear systems with parametric and dynamic uncertainties.…”

“…In particular, an adaptive finite‐time control law was obtained in the form of continuous time‐invariant feedback for nonlinear systems with parametric uncertainty in the work of Hong et al Later, in the work of Hong and Jiang, a constructive partial‐state control design was proposed to investigate the nonsmooth finite‐time stabilization of nonlinear systems with parametric and dynamic uncertainties. In the work of Cai and Xiang, the systematic finite‐time design procedure for a common state‐feedback controller and switching adaptive control were studied for switched nonlinear systems with parametric uncertainty. Based on the sign function and the delicate adaptive technique, finite‐time control was further considered in the works of Jiang and Xie and Sun et al for high‐order nonlinear systems with parametric uncertainties.…”

“…Recently, the adaptive finite‐time control problems of a class of nonlinearly parameterized systems with quantized input signal in the work of Liu et al and unknown control directions in the work of Wu et al were handled, respectively. However, the abovementioned finite‐time control results for nonlinearly parameterized systems failed to consider mismatching disturbances.…”

Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems

“…For a class of switched nonlinear systems with linear uncertain parameters, model reference adaptive control was considered in Wang et al 14 The problem of adaptive stabilization for a class of switched nonlinearly parameterized systems with unstable subsystems was studied in Long et al 15 The problem of tracking control for a class of uncertain switched nonlinear systems in lower triangular form under arbitrary switchings was considered in Zhao et al 16 In Han et al, 17 an adaptive neural control was presented for a class of switched nonlinear systems with switching jumps and uncertainties in both system models and switching signals. The problem of adaptive finite-time stabilization for switched nonlinear systems was investigated in Cai and Xiang 18 and Cai et al, 19 respectively. These research results represent contributions to the field and open the way to the application of adaptive control to switched nonlinear systems.…”