A derivative-free approach to optimal control problems with piecewise constant Mayer cost function

TL;DR

This paper introduces a hybrid numerical method combining derivative-free and smooth optimization techniques to effectively solve optimal control problems with piecewise constant Mayer cost functions, which are challenging for standard methods.

Contribution

A novel hybrid approach is proposed that addresses the discontinuities in piecewise constant Mayer cost functions, improving solution efficiency over traditional methods.

Findings

The hybrid method outperforms standard techniques in numerical simulations.

NOMAD and IPOPT effectively solve different parts of the problem.

The approach handles discontinuities in the cost function successfully.

Abstract

A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having its own Mayer cost value. In such a context, the standard numerical methods used in optimal control theory naturally fail, due to the discontinuities and the null gradients associated with the Mayer cost function. In this paper an hybrid numerical method, based on both derivative-free optimization and smooth optimization techniques, is proposed to solve this class of problems. Numerical simulations are performed on some standard control systems to show the efficiency of the hybrid method, where NOMAD and IPOPT are used as, respectively, derivative-free optimization and smooth optimization solvers.