Abstract
This paper considers dynamical systems under feedback with control actions limited to switching. The authors wish to understand the closed-loop systems as approximating multi-scale problems in which the implementation of switching merely acts on a fast scale. Such hybrid dynamical systems are extensively studied in the literature, but not much so far for feedback with partial state observation. This becomes in particular relevant when the dynamical systems are governed by partial differential equations. The authors introduce an augmented BV setting which permits recognition of certain fast scale effects and give a corresponding well-posedness result for observations with such minimal regularity. As an application for this setting, the authors show existence of solutions for systems of semilinear hyperbolic equations under such feedback with pointwise observations.
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The authors acknowledge the support of the Elite Network of Bavaria under the grant #K-NW-2004-143 and dedicated this paper to David Russell in recognition of his 70th birthday and in gratitude for his many contributions to the control theory of partial differential equations.
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Hante, F.M., Leugering, G. & Seidman, T.I. An augmented BV setting for feedback switching control. J Syst Sci Complex 23, 456–466 (2010). https://doi.org/10.1007/s11424-010-0140-0
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DOI: https://doi.org/10.1007/s11424-010-0140-0