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RESEARCH PRODUCT

Adaptive dual control in one biomedical problem

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In this paper, the following biomedical problem is considered. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which an individual patient will have toxicity level that does not cross the allowable limit. We discuss sequential procedures for searching the optimal dosage, which are based on the concept of dual control and the principle of optimality. According to the dual control theory, the control has two purposes that might be conflicting: one is to help learning about unknown parameters and/or the state of the system (estimation); the other is to achieve the control objective. Thus the resulting control sequence exhibits the closed‐loop property, i.e. it anticipates how future learning will be accomplished and how it can be fully utilized. Thus, in addition to being adaptive, this control also plans its future learning according to the control objective. Results are obtained for a priori uniform distribution of the unknown dosage. Because answers can be obtained analytically without approximation, the optimum policy can be compared with the non‐optimum policy of optimizing stage by stage. An illustrative example is given.