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

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.