A nonlinear optimal control problem with an application to optimal dosing of cytotoxic drugs

Andrej Novak

Chaos, Solitons & Fractals, 2023, vol. 177, issue C

Abstract: We consider the problem of minimizing a quadratic cost functional, subject to quasilinear systems of ordinary differential equations. By employing a fixed-point theorem argument, we characterize the optimal control via the associated Riccati equation in a manner analogous to the linear version of the problem. Additionally, we introduce a novel numerical method to approximate the solution and validate it within the context of a quasilinear quadratic cancer therapy model. This general methodology provides both theoretical and practical tools for addressing optimal control problems across various fields.

Keywords: Quasilinear optimal control problems; Riccati equation; Fixed point theorem; Dosing of cytotoxic drugs (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923012031

DOI: 10.1016/j.chaos.2023.114301

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