Reachability Analysis for Controlled Discrete Time Stochastic Hybrid Systems
A model for discrete time stochastic hybrid systems whose evolution can be influenced by some control input is proposed in this paper. With reference to the introduced class of systems, a methodology for probabilistic reachability analysis is developed that is relevant to safety verification. This methodology is based on the interpretation of the safety verification problem as an optimal control problem for a certain controlled Markov process. In particular, this allows to characterize through some optimal cost function the set of initial conditions for the system such that safety is guaranteed with sufficiently high probability. The proposed methodology is applied to the problem of regulating the average temperature in a room by a thermostat controlling a heater.
KeywordsOptimal Control Problem Control Input Discrete State Reachability Analysis Safe Policy
Unable to display preview. Download preview PDF.
- 2.Hu, J., Prandini, M., Sastry, S.: Probabilistic safety analysis in three-dimensional aircraft flight. In: Proc. of the IEEE Conf. on Decision and Control (2003)Google Scholar
- 3.Prajna, S., Jadbabaie, A., Pappas, G.: Stochastic safety verification using barrier certificates. In: Proc. of the IEEE Conf. on Decision and Control (2004)Google Scholar
- 8.Lygeros, J., Watkins, O.: Stochastic reachability for discrete time systems: an application to aircraft collision avoidance. In: Proc. of the IEEE Conf. on Decision and Control (2003)Google Scholar
- 9.Bujorianu, M., Lygeros, J.: General stochastic hybrid systems: Modelling and optimal control. In: Proc. of the IEEE Conf. on Decision and Control (2004)Google Scholar
- 11.Bertsekas, D.P., Shreve, S.E.: Stochastic optimal control: the discrete-time case. Athena Scientific (1996)Google Scholar