On robust feedback for systems with multidimensional control

TL;DR

This paper develops a robust feedback control method for multidimensional control systems with unknown bounded disturbances, ensuring finite-time stabilization and providing bounds on perturbation ranges, demonstrated on coupled pendulums.

Contribution

It introduces a new feedback synthesis approach using Korobov's controllability function for systems with multidimensional control and unknown disturbances.

Findings

Constructed a bounded control for finite-time stabilization.

Derived bounds for perturbation ranges.

Applied method to coupled pendulums example.

Abstract

The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an arbitrary initial point to the origin in some finite time; an estimate from above for the time of motion is given. We have found the range of a segment where the perturbations can vary. As an example we consider the problem of stopping the oscillations of the system of two coupled pendulums.