Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint

TL;DR

This paper analyzes the well-posedness of a shooting algorithm designed for control-affine problems with scalar control and state constraints, providing convergence conditions and illustrating the theory with an example.

Contribution

It introduces a sufficient condition for the local convergence of a shooting algorithm applied to control-affine problems with scalar state constraints.

Findings

Provided a sufficient condition for local convergence.

Illustrated the theory with a concrete example.

Addressed well-posedness issues in control-affine shooting algorithms.

Abstract

We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a sufficient condition for its local convergence. We exhibit an example that illustrates the theory.