Numerical optimal control for distributed delay differential equations: A simultaneous approach based on linearization of the delayed variables

TL;DR

This paper presents a numerical optimal control method for distributed delay differential equations by linearizing delayed variables and discretizing with Euler's implicit method, transforming the problem into a nonlinear program solved in MATLAB.

Contribution

It introduces a simultaneous approach that linearizes delayed variables and discretizes the equations, enabling efficient numerical optimal control of delay differential equations.

Findings

Effective control of a molten salt nuclear reactor model

Transformation of infinite-dimensional problems into finite nonlinear programs

Demonstrated numerical efficiency and accuracy

Abstract

Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach for numerical optimal control of delay differential equations with distributed time delays. Specifically, we linearize the delayed variables around the current time, and we discretize the resulting implicit differential equations using Euler's implicit method. Furthermore, we transcribe the infinite-dimensional optimal control problem into a finite-dimensional nonlinear program, which we solve using Matlab's fmincon. Finally, we demonstrate the efficacy of the approach using a numerical example involving a molten salt nuclear fission reactor.