On Optimal Control of Stochastic Linear Hybrid Systems
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Cyber-physical systems are often hybrid consisting of both discrete and continuous subsystems. The continuous dynamics in cyber-physical systems could be noisy and the environment in which these stochastic hybrid systems operate can also be uncertain. We focus on multimodal hybrid systems in which the switching from one mode to another is determined by a schedule and the optimal finite horizon control problem is to discover the switching schedule as well as the control inputs to be applied in each mode such that some cost metric is minimized over the given horizon. We consider discrete-time control in this paper. We present a two step approach to solve this problem with respect to convex cost objectives and probabilistic safety properties. Our approach uses a combination of sample average approximation and convex programming. We demonstrate the effectiveness of our approach on case studies from temperature-control in buildings and motion planning.