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

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.