A Warm Start Method for Solving Chance Constrained Optimal Control Problems

TL;DR

This paper introduces a warm start method that enhances the efficiency of solving complex chance constrained optimal control problems by tuning kernel density estimators, switching kernels, and incrementally increasing sample sizes during mesh refinement.

Contribution

The paper presents a novel warm start approach combining parameter tuning, kernel switching, and incremental sampling to improve computational efficiency in solving chance constrained optimal control problems.

Findings

Successfully applied to two challenging problems

Improves computational efficiency significantly

Effectively integrates kernel tuning and mesh refinement

Abstract

A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished by tuning a parameter of the kernel density estimator, as well as implementing a kernel switch as part of the solution process. Additionally, the number of samples for the biased kernel density estimator is set to incrementally increase through a series of mesh refinement iterations. Thus, the warm start method is a combination of tuning a parameter, a kernel switch, and an incremental increase in sample size. This warm start method is successfully applied to solve two challenging chance constrained optimal control problems in a computationally efficient manner using biased kernel density estimators and Legendre-Gauss-Radau collocation.