Linear Control Systems in Sequence Spaces

Hector O. Fattorini ()
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Hector O. Fattorini: University of California, Department of Mathematics

A chapter in Functional Analysis and Evolution Equations, 2007, pp 273-290 from Springer

Abstract: Abstract Pontryagin’s maximum principle in its infinite-dimensional version provides (separate) necessary and sufficient conditions for both time and norm optimality for the system y′ = Ay + u (A an infinitesimal generator). The question whether targets in D(A) guarantee a smooth costate has been open. We show the answer is “no” by means of a counterexample involving an analytic semigroup. Another analytic semigroup sheds some light on other subjects such as the existence of hypersingular time optimal controls (thus answering another open question) and the characterization of the reachable space and of singular functionals in its dual.

Keywords: Linear control systems in Banach spaces; norm optimal problem; time optimal problem; costate (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_18

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DOI: 10.1007/978-3-7643-7794-6_18

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