28 research outputs found
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
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