Nonsmooth stabilization and its computational aspects

This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with smooth and nonsmooth stabilization is provided, followed by a concise summary of basic tools and techniques, including general stabilization, sliding-mode control and nonsmooth backstepping. Their presentation is accompanied with examples. The survey is concluded with some remarks on computational aspects related to determination of sampling times and control actions.Comment: Submitted to IFAC 202

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

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.Comment: Accepted for publication in IEEE TRANSACTIONS ON AUTOMATIC CONTROL; 8 pages, 3 figure