Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

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

Convergence Rates for Nonholonomic Systems in Power Form

This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of controllers exhibiting exponential convergence is included

Convergence Rates for Nonholonomic Systems in Power Form

This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of controllers exhibiting exponential convergence is included

Exponential Stabilization of Driftless Nonlinear Control Systems using Homogeneous Feedback

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 non-standard dilation that is compatible with the algebraic structure of the control Lie algebra. Using this structure, we show that any continuous, time-varying controller that achieves exponential stabilization 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