Exponential stabilization of driftless nonlinear control systems using homogeneous feedback
- 1 May 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 42 (5) , 614-628
- https://doi.org/10.1109/9.580865
Abstract
This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.Keywords
This publication has 30 references indexed in Scilit:
- Experiments in exponential stabilization of a mobile robot towing a trailerPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Stabilization of multiple input chained form control systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Nonholonomic systems and exponential convergence: some analysis toolsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- A Hamiltonian approach to stabilization of nonholonomic mechanical systemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Closed loop steering of unicycle like vehicles via Lyapunov techniquesIEEE Robotics & Automation Magazine, 1995
- Nonholonomic Control and Gauge TheoryPublished by Springer Nature ,1993
- Nilpotent and High-Order Approximations of Vector Field SystemsSIAM Review, 1991
- Asymptotically Stabilizing Feedback Controls and the Nonlinear Regulator ProblemSIAM Journal on Control and Optimization, 1991
- Nonlinear Control SystemsPublished by Springer Nature ,1989
- Nilpotent Approximations of Control Systems and DistributionsSIAM Journal on Control and Optimization, 1986