On estimation of the domain of attraction for sliding mode control of underactuated nonlinear systems

Abstract

SUMMARYA system is considered underactuated if the number of the actuator inputs is less than the number of degrees of freedom for the system. Sliding mode control for underactuated systems has been shown to be an effective way to achieve system stabilization. It involves exponentially stable sliding surfaces so that when the closed‐loop system trajectory reaches the surface, it moves along the surface while converging to the origin. In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using sliding mode control in the presence of system uncertainties is presented. Specifically, it is shown that the closed‐loop system trajectories reach the sliding surface in finite time, and a constructive methodology to determine exponential stability of the closed‐loop system on the sliding surface is developed, which ensures asymptotic stability of the overall closed‐loop system. Furthermore, the aforementioned framework provides the basis to determine an estimate of the domain of attraction for the closed‐loop system with uncertainties. Finally, the results developed in the paper are experimentally validated using a linear inverted pendulum testbed to show a good match between the actual domain of attraction of the upward equilibrium state of the pendulum and its analytical estimate.Copyright © 2012 John Wiley & Sons, Ltd.

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

“…Therefore, it can drive the output functions to desirable trajectories without any tracking errors. However, to keep the nonlinear dynamical system attracted to the sliding surface, the drawback of sliding mode control technology is the chattering phenomenon of discrete switching models …”

Adaptive Integral Sliding Mode Based Course Keeping Control of Unmanned Surface Vehicle

“…In order to make control robust to disturbances and uncertainties, several approaches has been proposed in the SMC literature, see [22][23][24][25][26][27][28][29][30][31][32]. Some proposals of advanced sliding manifolds include recursive nonlinear sliding manifolds [33][34][35], adaptive integral sliding mode approach [36][37][38], non linear full order dynamics [39,40], sliding surfaces with adaptive damping parameters [41][42][43] and, in the last years, a vast collection of homogeneity based works, see [44] for instance.…”

Design of LMI‐based sliding mode controller with an exponential policy for a class of underactuated systems

“…In [41], an integral backstepping SMC is proposed for the control of underactuated systems where the SMC method supplies robustness and the backstepping algorithm provides an immune control to matched and mismatched uncertainties. In [42], a general framework is presented using SMC that provides sufficient conditions for asymptotic stabilization of uncertain underactuated nonlinear systems. In [43], SMC approach is proposed for the control of an underactuated wheeled inverted pendulum system with matched and unmatched uncertainties.…”