Finitely additive stochastic games with Borel measurable payoffs
International Journal of Game Theory
Discrete-time control for rectangular hybrid automata
Theoretical Computer Science
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Compositional Analysis of Multi-mode Systems
ECRTS '10 Proceedings of the 2010 22nd Euromicro Conference on Real-Time Systems
Optimal scheduling for constant-rate multi-mode systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Green scheduling: Scheduling of control systems for peak power reduction
IGCC '11 Proceedings of the 2011 International Green Computing Conference and Workshops
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
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Bounded-rate multi-mode systems (BMS) are hybrid systems that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. The schedulability problem for BMS is defined as an infinite-round game between two players---the scheduler and the environment---where in each round the scheduler proposes a time and a mode while the environment chooses an allowable rate for that mode, and the state of the system changes linearly in the direction of the rate vector. The goal of the scheduler is to keep the state of the system within a pre-specified safe set using a non-Zeno schedule, while the goal of the environment is the opposite. Green scheduling under uncertainty is a paradigmatic example of BMS where a winning strategy of the scheduler corresponds to a robust energy-optimal policy. We present an algorithm to decide whether the scheduler has a winning strategy from an arbitrary starting state, and give an algorithm to compute such a winning strategy, if it exists. We show that the schedulability problem for BMS is co-NP complete in general, but for two variables it is in PTIME. We also study the discrete schedulability problem where the environment has only finitely many choices of rate vectors in each mode and the scheduler can make decisions only at multiples of a given clock period, and show it to be EXPTIME-complete.