The output feedback control for uncertain nonholonomic systems

Abstract

This paper considers the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) by output feedback for a class of uncertain nonholonomic systems. By combining the nonsmooth change of coordinates and output feedback domination design together, we construct a simple linear time-varying output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The simulation demonstrates the effectiveness of the proposed controller.

Output-feedback control for nonholonomic systems with linear growth condition

“…The system (1) is similar to that in [12], but the x 0 -subsystem is different from that. Here system (1) contains the nonlinear function φ 0 (t, x 0 ).…”

“…One of the consequences of the necessary condition is that the nonholonomic systems is not stabilizable by stationary continuous state feedback. To overcome this impossibility, a number of approaches have been proposed for the problem, which can be classified as a) Discontinuous time-invariant stabilization [6] ; b) Time-varying stabilization [7−8] ; c) Hybrid stabilization [9] ; see the survey paper [10][11][12][13][14] for more details and references therein.…”

“…Hence, it is important and necessary to consider the output feedback control problem for uncertain nonholonomic systems. The output feedback issue has been studied for asympotic and exponential stability properties for the chained systems with uncertainties [11][12][13]15] . The output feedback control problem for uncertain nonholonomic systems are much difficult and still largely open.…”

“…Meanwhile, the nonlinear function in the first subsystem makes it impossible to deal with the problem with the method used in [12]. To the best of our knowledge, there is still no design tool for this problem.…”