Control of piecewise-affine hybrid systems (Extended abstract)

P.J. Collins, L.C.G.J.M. Habets, M. Petreczky, J.H. Schuppen, van

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    Abstract

    The character of this paper is an extended abstract of the approach developed by the authors for control of piecewise-affine hybrid systems. Control of hybrid systems is a wide ranging research topic with many theoretical problems. The authors have therefore decided early on to restrict attention to piecewise-affine hybrid systems on polytopes. The approach developed includes for affine systems on polytopes sufficient conditions for the problems (1) leaving the polytope in finite time through a prespecified set of facets; (2) remaining inside a particular polytope forever; and (3) converging to a fixed state inside a particular polytope. For piecewise-affine hybrid system on polytopes a procedure for reachability and control synthesis is proposed consisting of (1) for each discrete state the computation of all possible exit facets and exit events; (2) abstraction of the continuous dynamics to an automaton; and (3) the search of a path in the automaton from an initial discrete state to a target discrete state. Open research issues for control of hybrid systems are stated.
    Original languageEnglish
    Title of host publicationProceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems (Zaragoza, Spain, September 16-18, 2009)
    EditorsA. Giua, C. Mahulea, M. Silva, J. Zatoon
    PublisherIFAC
    Pages234-237
    Publication statusPublished - 2009

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