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Optimal Control

In: Mathematical Methods in Dynamic Economics

Author

Listed:
  • András Simonovits

    (Hungarian Academy of Sciences)

Abstract

After discussing discrete-time optimal systems in Chapters 7 and 8, we turn to continuous-time optimal systems. We are given a control system (see Section 5.4), that is, a system of differential equations, describing the dynamics of the state vector as a function of a control vector. For a given control path, the state space equation determines the state path. In the theory of Optimal Control, the equations are time-variant and we are given a scalar-valued function, called reward function of time, of the state vector and of the control vector. We are looking for that control path which maximizes the time integral of the reward function. Section 9.1 outlines the solution of the basic problem. Section 9.2 presents an important special case of optimal control, namely, the Calculus of Variations. Section 9.3 contains additional material, including sufficient conditions, the isoperimetric problem and the present value problem. We shall rely on Kamien and Schwartz (1981) (see also Chiang, 1992). For a more demanding treatment, see Pontryagin et al. (1961) and Gelfand and Fomin (1962).

Suggested Citation

  • András Simonovits, 2000. "Optimal Control," Palgrave Macmillan Books, in: Mathematical Methods in Dynamic Economics, chapter 9, pages 191-207, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-0-230-51353-2_10
    DOI: 10.1057/9780230513532_10
    as

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