Abstract
We consider the problem of constructing a “controller” for a hybrid system which will solve the viability problem that all points of plant trajectories stay inside a given “viability set”. Here, a “controller” is a network of three successive devices, a digital to analog converter, a digital program (a computer together with its control software), and an analog to digital converter. We model a controller as an input-output automaton, which we call a “control automaton”. We give a necessary and sufficient condition that must be satisfied in order that a finite state control automaton solves a viability problem. Our results apply to plants modelled by vector differential equations with control and disturbance parameters, or to plants modelled by differential inclusions with a control parameter. We represent imprecise sensing of plant state. The main restrictions on the range of applicability of our results are that the set of admissible control laws is finite, and that we can neglect delays when control laws are reset. The latter restriction seems to be inessential.
Supported in part by Army Research Office contract DAAL03-91-C-0027
Supported in part by Army Research Office contract DAAL03-91-C-0027 and NSF grant DMS-9306427
Supported by DARPA-US ARMY AMCCOM (Picatinny Arsenal, N. J.) contract DAAA21-92-C-0013 to ORA Corp.
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Nerode, A., Remmel, J.B., Yakhnis, A. (1995). Controllers as fixed points of set-valued operators. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems II. HS 1994. Lecture Notes in Computer Science, vol 999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60472-3_17
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DOI: https://doi.org/10.1007/3-540-60472-3_17
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