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Linear Control Systems in Sequence Spaces

In: Functional Analysis and Evolution Equations

Author

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  • Hector O. Fattorini

    (University of California, Department of Mathematics)

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.

Suggested Citation

  • Hector O. Fattorini, 2007. "Linear Control Systems in Sequence Spaces," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 273-290, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_18
    DOI: 10.1007/978-3-7643-7794-6_18
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