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Some Recent Developments in Systems and Control Theory on Infinite Dimensional Banach Space: Part 2

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Optimization and Control Techniques and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 86))

Abstract

The objective of this chapter is to present some recent developments in systems and control theory on infinite dimensional spaces. In part 1, we considered evolution equations with mild solutions and presented some results on optimal control. This is part 2 and here we consider evolution equations which do not admit mild solutions but have measure solutions. We introduce and use the notion of measure valued solutions for both deterministic and stochastic systems. Following this we consider the question of existence of optimal feedback controls and formulate several interesting control problems on the space of measures. This is then applied to stochastic Navier–Stokes equations and its optimal feedback control and nonlinear filtering problem aimed at finding from an admissible class the best operator modeling the observation equation. In the final section we consider hybrid systems driven by vector measures and operator valued measures which include impulsive systems as special cases and present some results asserting existence of optimal measure valued controls.

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Author information

Authors and Affiliations

  1. EECS, University of Ottawa, Ottawa, ON, Canada

    N. U. Ahmed

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  1. N. U. Ahmed
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Correspondence to N. U. Ahmed .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University, Perth, West Australia, Australia

    Honglei Xu

  2. Department of Mathematics and Statistics, Curtin Univeristy, Perth, Australia

    Kok Lay Teo

  3. Department of Mathematics, China University of Petroleum, Beijing, China

    Yi Zhang

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Ahmed, N. (2014). Some Recent Developments in Systems and Control Theory on Infinite Dimensional Banach Space: Part 2. In: Xu, H., Teo, K., Zhang, Y. (eds) Optimization and Control Techniques and Applications. Springer Proceedings in Mathematics & Statistics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43404-8_2

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