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Generalized Duality Theory. The Increasing and Decreasing Lagrangian Scales

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Dynamic Programming for Impulse Feedback and Fast Controls

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 468))

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Abstract

The problems of optimal impulse control under state constraints may be posed in different functional spaces leading to solutions of dual problems, which are presented accordingly in terms of respective conjugate spaces. These arrays of problems form a scale discussed in the present chapter. A similar situation arises in the problem of dynamic state estimation. In this section, we consider stationary systems.

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Notes

  1. 1.

    Considered in detail in present Sect. 10.2 is the problem of minimizing the norm of \(\mathsf {U}(\cdot )\)—the function that generated \(U(\cdot )\) through a k-times multiple integration. When dealing with duality, we restrict the discussion to minimization of \(U(\cdot )\).

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    Alexander B. Kurzhanski

  2. Google Research, Zürich, Switzerland

    Alexander N. Daryin

Authors
  1. Alexander B. Kurzhanski
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  2. Alexander N. Daryin
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Correspondence to Alexander B. Kurzhanski .

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Kurzhanski, A.B., Daryin, A.N. (2020). Generalized Duality Theory. The Increasing and Decreasing Lagrangian Scales. In: Dynamic Programming for Impulse Feedback and Fast Controls. Lecture Notes in Control and Information Sciences, vol 468. Springer, London. https://doi.org/10.1007/978-1-4471-7437-0_10

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