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Multitime Controllability, Observability and Bang-Bang Principle

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Abstract

Control problems for multitime first-order PDE arise in many different contexts and ways. The obstruction of complete integrability conditions (path independent curvilinear integrals) has determined the mathematicians to study such problems only in the discrete context, though thus they loose the geometrical character which is proper to the continuous approach.

In this paper, we study controllability, observability and bang-bang properties of multitime completely integrable autonomous linear PDE systems, overcoming the existent mathematical prejudices regarding the importance of a multitime evolution of m-flow type. Our geometrical arguments show that each basic theorem has a correspondent in the case of a single-time linear controlled ODE system.

The main results include controllability criteria, equivalence between controllability of a PDE system and observability of the dual PDE system, geometry of the control set, extremality and multitime bang-bang principle. All of these show that the passing from controlled single-time evolution (1-flow) to the controlled multitime evolution (m-flow) is not trivial. Changing the geometrical language, the case of nonholonomic evolution can be recovered easily from our theory.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Applied Sciences, Polytechnic University of Bucharest, Splaiul Independentei 313, Bucharest, 060042, Romania

    C. Udrişte

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  1. C. Udrişte
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Correspondence to C. Udrişte.

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Communicated by Franco Giannessi.

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Udrişte, C. Multitime Controllability, Observability and Bang-Bang Principle. J Optim Theory Appl 139, 141–157 (2008). https://doi.org/10.1007/s10957-008-9430-2

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  • DOI: https://doi.org/10.1007/s10957-008-9430-2

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