Sakawa-Shindo algorithm for optimal control of time-delay systems, with applications to epidemiology

TL;DR

This paper extends the Sakawa-Shindo algorithm to handle optimal control problems with multiple discrete delays, proving its convergence and applying it to epidemic intervention planning.

Contribution

The paper introduces a generalized Sakawa-Shindo algorithm for delayed systems and demonstrates its effectiveness in epidemic control applications.

Findings

Algorithm guarantees finite termination.

Generated controls are asymptotically first-order optimal.

Applied to epidemic models with delays in incubation and vaccination.

Abstract

We extend the Sakawa-Shindo algorithm to solve optimal control problems where the system dynamics involve an arbitrary number of discrete state delays. We prove that the algorithm guarantees termination in a finite number of steps, asymptotic first-order optimality of the generated control sequence and convergence of a subsequence to a control satisfying first-order optimality, and we apply it to the optimal design of non-pharmaceutical interventions and vaccination plans for epidemic models with delays associated with incubation period and vaccination.