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Introduction to optimal control theory. (English) Zbl 0624.49009

We will show several formulations of the optimal control of a dynamical system described by ordinary differential equations. Then, we will present briefly two main aspects of optimal control: Pontryagin’s maximum principle (which generalizes the calculus of variations) and Bellman’s dynamic programming. After that, an example of optimal control in pharmacology will present one of the many applications, and one of the many mathematical techniques employed in solving control problems.
Some important aspects of optimal control will not be treated here among them, the study of stochastic systems and adaptive (or self-organizing) control, and the study of systems governed by partial differential equations.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49L20 Dynamic programming in optimal control and differential games
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
92Cxx Physiological, cellular and medical topics
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References:

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