A Lyapunov approach to exponential stabilization of nonholonomic systems in power form

Abstract

this note a continuous feedback control law with time-periodic terms is derived for the control of nonholonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector elds are homogeneous of degree zero.

Backstepping based nonlinear adaptive control for the extended nonholonomic double integrator

“…The reason for this is primarily threefold: i) Mechanical systems such as wheeled mobile robots, robot manipulators, space robots and underwater vehicles have non integrable constraints; ii) the formation of control law for systems which cannot be easily transformable into linear control problem in a meaningful way is quiet challenging and iii) these systems cannot be stabilized by static time invariant state feedback laws as pointed out by Brockett [6]. Different control strategies have been presented for the stabilization of nonholnomic systems to overcome the limitations of the Brockett result like: discontinuous time-invariant stabilization [4,10,12,14], smooth time-varying stabilization [13,15], adaptive techniques [9,19] and sliding mode control [1,5,17].…”

Dipole-like fields for stabilization of systems with Pfaffian constraints

“…The majority of these approaches, [4]- [7], [10], [11], provide stabilizing controllers for drift-free, kinematic nonholonomic systems, which are either in chained or in power form. The so-called dynamic nonholonomic systems arise either from the dynamic extension of nonholonomic kinematic systems [9], or from the modeling of underactuated mechanical systems, which induces second-order nonholonomic constraints.…”

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

“…[4] that studied exponential stabilization using Lyapunov approach, and [12] in which exponential stabilization for homogeneous systems was thoroughly investigated.…”