Stabilization of uncertain chained nonholonomic systems using adaptive output feedback

Abstract

In this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed‐loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input‐state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Adaptive stabilization for nonholonomic mobile robots with uncertain dynamics and unknown visual parameters

“…Due to the theorem of Brockett (1983), it is well known that a nonholonomic system cannot be stabilized at a single equilibrium point by any continuous, time-invariant, statefeedback controller. To solve this problem, several other approaches have been proposed (Astolfi, 1996;Hu et al, 2004;Kolmanovsky and McClamroch, 1995;Samson, 2005;Yuan et al, 2009). A wheeled mobile robot is a typical nonholonomic system.…”

Output Feedback Stabilization of Uncertain Nonholonomic Chained Systems

“…0 0 u = ), the x -subsystem is uncontrollable. It can be avoided by utilizing the following discontinuous state scaling transformation [4,11]…”

“…Using the special algebra structures of the canonical forms, various feedback strategies have been proposedto stabilize nonholonomic systems in the literature. Recently, adaptive control strategies were proposed to stabilize the nonholonomic systems with uncertainties using input-state scaling technique [10] [11]. For the controller design of the uncertain nonholonomic systems, the unknown virtual control coefficients and the uncertain drift nonlinearities are the main difficulties.…”

Adaptive Control for Simultaneous Stabilization and Tracking of Unicycle Mobile Robots

“…According to Brockett's theorem [1], such systems cannot be asymptotically stabilized by smooth or even continuous, pure-state feedback. Owing to the challenging nonlinear nature of nonholonomic systems, limited types of controllers have been proposed for the stabilization problem, including: discontinuous time-invariant feedback [2][3][4][5][6], smooth time-varying Manuscript received March 18, 2014; revised September 29, 2014; accepted February 28, 2015. The authors are with the College of Electrical and Information Engineering, Hunan University, Changsha 410082, China.…”

“…According to Brockett's theorem , such systems cannot be asymptotically stabilized by smooth or even continuous, pure‐state feedback. Owing to the challenging nonlinear nature of nonholonomic systems, limited types of controllers have been proposed for the stabilization problem, including: discontinuous time‐invariant feedback , smooth time‐varying feedback , and hybrid feedback . Specifically, the first time‐varying control method was proposed by Samson in for the stabilization of a cart.…”