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A comparison of control problems for timed and hybrid systems. (English) Zbl 1044.93518
Tomlin, Claire J. (ed.) et al., Hybrid systems: computation and control. 5th international workshop, HSCC 2002, Stanford, CA, USA, March 25–27, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43321-X). Lect. Notes Comput. Sci. 2289, 134-148 (2002).
Summary: In the literature, we find several formulations of the control problem for timed and hybrid systems. We argue that formulations where a controller can cause an action at any point in dense (rational or real) time are problematic, by presenting an example where the controller must act faster and faster, yet causes no Zeno effects (say, the control actions are at times $$0,\frac{1}{2},1,1\frac{1}{4},2,2\frac{1}{8},3,3\frac{1}{16},\ldots$$). Such a controller is, of course, not implementable in software. Such controllers are avoided by formulations where the controller can cause actions only at discrete (integer) points in time. While the resulting control problem is well-understood if the time unit, or “sampling rate” of the controller, is fixed a priori, we define a novel, stronger formulation: the discrete-time control problem with unknown sampling rate asks if a sampling controller exists for some sampling rate. We prove that this problem is undecidable even in the special case of timed automata.
For the entire collection see [Zbl 0989.00055].

##### MSC:
 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 68Q45 Formal languages and automata
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