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 -