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The Discrete-Time Linear Quadratic Regulator Problem

In: State Space and Input-Output Linear Systems

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  • David F. Delchamps

    (Cornell University, School of Electrical Engineering)

Abstract

In this section and the next, we discuss what might be construed as one of the great triumphs of modern linear system theory. There is no doubt that the linear quadratic regulator problem has spawned a vast quantity of research, both theoretical and applied; the simplicity of its formulation, the elegance of its solution, and its evident relevance to applications in a variety of contexts make it the heart of perhaps the most widely understood and heavily applied body of system theoretic results. Moreover, the problem illustrates in a beautiful way the manner in which properties of a system such as reachability and observability manifest themselves as intuitively appealing and mathematically transparent sufficient conditions for the unraveling of a problem whose solution is by no means obvious at first glance.

Suggested Citation

  • David F. Delchamps, 1998. "The Discrete-Time Linear Quadratic Regulator Problem," Springer Books, in: State Space and Input-Output Linear Systems, chapter 26, pages 393-405, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3816-4_27
    DOI: 10.1007/978-1-4612-3816-4_27
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