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Models for hybrid systems: Automata, topologies, controllability, observability

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Hybrid Systems (HS 1992, HS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 736))

Abstract

By a “hybrid system” we mean a system of continuous plants, subject to disturbances, interacting with sequential automata in a network. “Hybrid Control” is the name we give to control of continuous plants by digital sequential control automata, that is, by control programs implemented on sequential automata. We associate, without using any approximations, sequential automata with continuous plants, and use this to bring sequential control automata and continuous plants into automata networks which themselves are sequential automata modelling hybrid systems. To be useful, the control automaton's ability to control plant trajectories in a hybrid system should be maintained under small changes in control laws, disturbance, trajectory, measurement, etc. We formalize this notion of controllability and observability for hybrid systems by continuity of system functions, including the input-output function of the control automaton, in non-Hausdorff subtopologies of the usual topologies on spaces of controls, sensor data, plants, disturbances, target sets, etc. These subtopologies arise from the limited ability of digital programs to discriminate between continuous inputs. These notions are appropriate for any knowledge or rule based system where automated deduction interacts in real time with the external world. This topological approach was announced in [46]. (What we call “controllability and observability” here is what we called “stability” in [46] in order to correspond somewhat more closely to usage in the literature [3].)

Research supported by ORA Corp., DARPA-US ARMY AMCCOM (Picatinny Arsenal,NJ) contract DAAA21-92-C-0013, the U. S. Army Research Office contract DAAL03-91-C-0027.

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Authors and Affiliations

  1. Mathematical Sciences Institute, Cornell Uniyersity, 14850, Ithaca, New York

    Anil Nerode

  2. Intermetrics Corporation, Bellevue, Washington

    Wolf Kohn

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  1. Anil Nerode
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  2. Wolf Kohn
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Robert L. Grossman Anil Nerode Anders P. Ravn Hans Rischel

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© 1993 Springer-Verlag Berlin Heidelberg

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Nerode, A., Kohn, W. (1993). Models for hybrid systems: Automata, topologies, controllability, observability. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds) Hybrid Systems. HS HS 1992 1991. Lecture Notes in Computer Science, vol 736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57318-6_35

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  • DOI: https://doi.org/10.1007/3-540-57318-6_35

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