Disturbance attenuation with fast global finite‐time convergence for generalized high‐order uncertain nonlinear systems

Abstract

Summary This paper focuses on the problem of disturbance attenuation with fast global finite‐time convergence (FTC) for a class of generalized high‐order uncertain nonlinear systems. Combining the fast finite‐time stabilization technique with a delicate manipulation of sign functions, a new control approach is proposed to attenuate the serious uncertainties substantially, including time‐varying control coefficients, nonlinear parameters, and external disturbances, while achieving the performance evaluated in terms of L2‐L2p gain. A notable feature of the control strategy is the fast FTC, which greatly shortens the convergent time when the initial state is far away from the origin. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Output feedback stabilization within prescribed finite time of asymmetric time‐varying constrained nonholonomic systems

“…Proposition 1. For any initial condition p 0 (0) ∈ Ω p 0 , the corresponding solution p 0 (t) of the p-subsystem under (14) is well defined on [0, T) and satisfies p 0 (t) ∈ Ω p 0 .…”

“…11 As a consequence, pursuing finite-time stabilization has received widely attention in recent years. [12][13][14][15][16][17][18] Particularly, by using state feedback, a pioneering work was carried out in Reference 19 by studying finite-time stabilization using state feedback for a kind of nonholonomic systems with some weak drifts. Subsequently, the works [20][21][22] further extended the results in Reference 19 to the nonholonomic systems with uncertain parameters and/or perturbed terms.…”

“…Moreover, finite‐time stable systems also perform other appealing properties such as better robustness and disturbance rejection 11 . As a consequence, pursuing finite‐time stabilization has received widely attention in recent years 12‐18 . Particularly, by using state feedback, a pioneering work was carried out in Reference 19 by studying finite‐time stabilization using state feedback for a kind of nonholonomic systems with some weak drifts.…”

Online reinforcement learning control via discontinuous gradient

“…However, this control scheme uses known parameters. In the work of Sun et al , 23 a nonlinear‐$$$ {\mathscr{H}}_{\infty } $$$ SM controller is presented, making use of the nominal system parameters. On the other hand, in the work of Fu et al , 24 a $$$ {\mathscr{H}}_{\infty } $$$ control with variable gains to estimate uncertainties, is applied to polynomial systems with time‐varying parameters and additive perturbations.…”

Disturbance‐observer‐based adaptive neural control for switched nonlinear systems with average dwell time

“…The DO can dynamically estimate the disturbance and make accurate compensation, which has been widely considered in uncertain nonlinear systems 14,15 . In recent years, the DO has been deeply studied in the aspects of mismatched uncertainty compensation and disturbance finite‐time estimation 16‐20 . Considering the complex situation of unmeasurable system states, the coupling problem of disturbance estimation and state estimation was solved skillfully 21 .…”