Convergence of the shooting algorithm for singular optimal control problems

TL;DR

This paper introduces a shooting algorithm for singular optimal control problems with affine control systems, demonstrating local quadratic convergence under certain conditions and validating it through a numerical example.

Contribution

It proposes a new shooting algorithm tailored for singular optimal control problems with affine controls, with proven local quadratic convergence.

Findings

The algorithm converges quadratically under second order sufficient conditions.

Numerical example confirms the theoretical convergence rate.

The method effectively handles boundary constraints in control problems.

Abstract

In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We recall a second order sufficient condition for weak optimality, and show that it guarantees the local quadratic convergence of the algorithm. We show an example and solve it numerically.