# Sufficient Conditions for Strong Local Optimality with Applications to Biomedical Problems

Abstract : We consider optimal control problems over a fixed interval for multi-input bilinear dynamical systems with both $L_1$ and $L_2$-type objectives in the presence of control constraints. Problems of this type arise as mathematical models for cancer chemotherapy over an a priori specified fixed therapy horizon. The extremals resulting from an application of the Pontryagin maximum principle are analyzed. Conditions are given that allow to embed extremals into a field of broken extremals leading to easily verifiable sufficient conditions for strong local optimality. In the case of an $L_1$-type objective, flows of extremal bang-bang trajectories arise for which a simple algorithmic procedure to verify local optimality will be formulated. In the case of an $L_2$-type objective, sufficient conditions for strong local optimality that are based on the existence of a bounded solution to a matrix Riccati differential equation will be formulated. The theory is illustrated with a $3$-compartment model for multi-drug cancer chemotherapy with cytotoxic and cytostatic agents.
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https://hal.inria.fr/hal-01024597
Contributor : Hasnaa Zidani <>
Submitted on : Wednesday, July 16, 2014 - 1:21:34 PM
Last modification on : Monday, March 21, 2016 - 5:44:24 PM
Long-term archiving on: : Monday, November 24, 2014 - 4:16:52 PM

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• HAL Id : hal-01024597, version 1

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Urszula Ledzewicz. Sufficient Conditions for Strong Local Optimality with Applications to Biomedical Problems. NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France. ⟨hal-01024597⟩

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