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

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  • Novak, Andrej

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.

Suggested Citation

  • Novak, Andrej, 2023. "A nonlinear optimal control problem with an application to optimal dosing of cytotoxic drugs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923012031
    DOI: 10.1016/j.chaos.2023.114301
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    References listed on IDEAS

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    1. Jasmina Djordjevic & Sanja Konjik & Darko Mitrović & Andrej Novak, 2021. "Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 316-338, July.
    2. Avram, Florin & Freddi, Lorenzo & Goreac, Dan, 2022. "Optimal control of a SIR epidemic with ICU constraints and target objectives," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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