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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Document associé à des manifestations scientifiques
NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France
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https://hal.inria.fr/hal-01024597
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Dernière modification le : lundi 21 mars 2016 - 17:44:24
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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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