On inf-convolution-based robust practical stabilization under computational uncertainty

TL;DR

This paper develops a robust inf-convolution-based control method for nonlinear systems that maintains stability despite computational uncertainties, measurement noise, and actuator disturbances, demonstrated through a robotic case study.

Contribution

It introduces a modified control approach that ensures robustness of the stabilization technique against noise and computational errors, applicable to systems with non-smooth control Lyapunov functions.

Findings

The modified control is robust to measurement noise and computational uncertainty.

Numerical experiments on a three-wheel robot validate the effectiveness of the approach.

The method applies to piece-wise smooth control Lyapunov functions.

Abstract

This work is concerned with practical stabilization of nonlinear systems by means of inf-convolution-based sample-and-hold control. It is a fairly general stabilization technique based on a generic non-smooth control Lyapunov function (CLF) and robust to actuator uncertainty, measurement noise, etc. The stabilization technique itself involves computation of descent directions of the CLF. It turns out that non-exact realization of this computation leads not just to a quantitative, but also qualitative obstruction in the sense that the result of the computation might fail to be a descent direction altogether and there is also no straightforward way to relate it to a descent direction. Disturbance, primarily measurement noise, complicate the described issue even more. This work suggests a modified inf-convolution-based control that is robust w. r. t. system and measurement noise, as well as computational uncertainty. The assumptions on the CLF are mild, as, e. g., any piece-wise smooth function, which often results from a numerical LF/CLF construction, satisfies them. A computational study with a three-wheel robot with dynamical steering and throttle under various tolerances w. r. t. computational uncertainty demonstrates the relevance of the addressed issue and the necessity of modifying the used stabilization technique. Similar analyses may be extended to other methods which involve optimization, such as Dini aiming or steepest descent.