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The method of characteristics is utilized to investigate the value function of an optimal control problem with a smooth control near singularities of the corresponding flow of extremals. A direct generalization of the classical concept of envelopes from the calculus of variations to the optimal control problem is formulated. As a simple illustration it is shown that the local geometric properties...
A mathematical model for the scheduling of a combination of anti-angiogenic and chemotherapeutic agents is considered as a multi-input optimal control problem. Numerical results that are based on an explicit equation for a singular control confirm as optimal a structure of protocols that administer the anti-angiogenic agent according to the optimal monotherapy control and the cytotoxic agent at maximum...
A mathematical model for the scheduling of angiogenic inhibitors that includes a pharmacokinetic equation is considered as an optimal control problem. When dosage and concentration of the inhibitor are identified, there exists an optimal singular arc of order 1 that forms the core of a synthesis of optimal controls. Under the standard pharmacokinetic linear model for the concentration this singular...
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