Approximation of reachable sets using optimal control and support vector machines

TL;DR

This paper introduces a novel computational approach combining optimal control and support vector machines to approximate reachable sets in nonlinear control systems, with demonstrated convergence through numerical examples.

Contribution

It extends existing optimal control methods by integrating support vector machines for set approximation in a reproducing kernel Hilbert space.

Findings

Method successfully approximates reachable sets for nonlinear systems.

Numerical examples confirm convergence of the proposed approach.

Supports potential for efficient set computation in control applications.

Abstract

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for several examples.