TY - GEN

T1 - A comparison of control problems for timed and hybrid systems

AU - Cassez, Franck

AU - Henzinger, Thomas A.

AU - Raskin, Jean François

PY - 2002

Y1 - 2002

N2 - 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 (formula presented). 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 wellunderstood 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.

AB - 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 (formula presented). 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 wellunderstood 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.

UR - http://www.scopus.com/inward/record.url?scp=84958173226&partnerID=8YFLogxK

U2 - 10.1007/3-540-45873-5_13

DO - 10.1007/3-540-45873-5_13

M3 - Conference proceeding contribution

AN - SCOPUS:84958173226

SN - 354043321X

SN - 9783540433217

VL - 2289

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 134

EP - 148

BT - Hybrid Systems: Computation and Control

A2 - Tomlin, C

A2 - Greenstreet, M

PB - Springer, Springer Nature

CY - Berlin; Heidelberg

T2 - 5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002

Y2 - 25 March 2002 through 27 March 2002

ER -