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The Maximum Principle: Discrete Time

In: Optimal Control Theory

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  • Suresh P. Sethi

    (University of Texas at Dallas)

Abstract

For many purposes it is convenient to assume that time is discrete and not continuous. This is particularly true when we wish to solve a large control theory problem using a computer. It is also desirable, even when solving small problems that have state or adjoint differential equations whose solutions cannot be expressed in closed form, to formulate them as discrete problems and solve them on a computer in a stepwise manner. This chapter is devoted to deriving a discrete-time maximum principle by using the necessary Kuhn-Tucker conditions for optimizing nonlinear programming problems along with a brief discussion of the required constraint qualifications. To follow this procedure, we must make some simplifying assumptions and hence obtain only a restricted form of the discrete maximum principle. In Sect. 8.3, we state without proof a more general form of the discrete maximum principle. There are many exercises at the end of the chapter.

Suggested Citation

  • Suresh P. Sethi, 2021. "The Maximum Principle: Discrete Time," Springer Texts in Business and Economics, in: Optimal Control Theory, edition 4, chapter 8, pages 239-260, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-91745-6_8
    DOI: 10.1007/978-3-030-91745-6_8
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