Interior point methods in optimal control problems of affine systems: Convergence results and solving algorithms

TL;DR

This paper develops an interior point method for affine optimal control problems, providing convergence analysis and algorithms, demonstrated through a complex numerical example.

Contribution

It introduces a novel interior point approach with proven convergence for affine control problems, including primal and primal-dual algorithms.

Findings

Convergence of primal and dual variables established.

Algorithms successfully solve a challenging numerical example.

Method applicable to pure-state and mixed-constrained problems.

Abstract

This paper presents an interior point method for pure-state and mixed-constrained optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of two-point boundary value problems of differential and algebraic equations. This paper establishes a convergence result for primal and dual variables of the optimal control problem. A primal and a primal-dual solving algorithm are presented, and a challenging numerical example is treated for illustration. Accepted for publication at SIAM SICON 2023