Reduction of matched and unmatched uncertainties for a class of nonlinear perturbed systems via robust control

Abstract

Summary The aim of this paper is to design a robust control for stabilization of a class of nonlinear perturbed system subject to matched and unmatched disturbances. Here, the concept of dynamic sliding mode control and the attractive ellipsoid method advantages are used to design a robust nonlinear control algorithm, which reduces considerably the perturbation effects. Hence, in finite time, the dynamic sliding mode control brings the system trajectory to a specific configuration. After this time, the controller reduces the perturbation effects by using the high‐gain control obtained in the attractive ellipsoid method. Thus, based on the solution of a specific matrix inequality, the feedback control of the system guarantees that the trajectory will be stabilized in the ultimate uniform bounded sense. To illustrate the theoretical results, a numerical example with a comparative study is introduced. Finally, the performance of the controller designed in this paper is tested on an electromechanical real‐time system.

Generalized Linear Quadratic Control for a Full Tracking Problem in Aviation

“…In [14], a terminal sliding mode and back-stepping control was successfully implemented in a real-time unmanned aerial vehicle. In [15], a robust controller, based on linear feedback representation to reduce dynamic uncertainties and external disturbances was designed and implemented in real-time underactuaded system.…”

Adaptive Finite-Time Control of Nonlinear Quantized Systems With Actuator Dead-Zone

“…then, the nonlinear systemρ = f (ρ, ς) is SGPFS. Remark 1: Similar to the finite-time investigates in [50] and [67], Lemma 1 gives an important criterion of SGPFS, which will be employed in the subsequent finite-time stability analysis.…”

“…On the base of the Lyapunov stability theory in [42], [43], the finite-time stability issues of the systems were discussed in [44]- [48]. Reference [49] discussed the problem of adaptive-robust stabilization of the Furuta's pendulum around unstable equilibrium, [50] designed a robust control for stabilization of a kind of nonlinear perturbed system with matched and unmatched disturbances, the controllers in [49] and [50] guarantee the ultimate uniform bound stabilization or controllers based on attractive ellipsoid method. In order to ensure the finite-time stability of nonlinear systems, some control programs were designed in [51]- [53] for a kind of nonlinear systems with hysteretic characteristics.…”

Disturbance observer‐based two‐Layer control strategy design to deal with both matched and mismatched uncertainties

“…Due to their unique features, designing a controller that be able to optimally and robustly manage nonlinear systems subjected to mismatched uncertainties has been the desire of researchers. In this respect, different control methods have been proposed to make nonlinear systems immune against mismatched uncertainties; such as robust control methods, 14‐20 adaptive control schemes, 21‐24 and hybrid control systems 25‐33 . In dealing with mismatched uncertainties, an appropriate controller should make an uncertain nonlinear system robust, while achieving a desired performance.…”

“…Coping with mismatched uncertainties in nonlinear systems has received an increasing attention in the last decade. In order to reduce the effects of mismatched uncertainties on a nonlinear system, Ordaz et al 14 proposed a robust controller based on the dynamic sliding mode control (SMC) and the attractive ellipsoid method. However, based on their simulation results, their proposed control system has been unable to completely eradicate the effects of mismatched uncertainties.…”