Receding horizon optimal control for some stochastic hybrid systems

We consider optimal control problems for a class of hybrid systems with switches dependent on an external event process. In the case where all event times in this process are fully known, the solution to such problems was obtained in prior work. When event times are uncertain or unknown, we have proposed a receding horizon (RH) control scheme in which only some future event information is available within a time window of length T and have obtained several properties of this scheme. In this paper, we provide a full set of properties for this scheme, including the fact that the error due to lack of future event information is monotonically decreasing under certain conditions and may be zero for segments of the sample path, depending on the window length T. This enables the use of a controller based on limited knowledge of future events with limited loss of optimality properties. We further explore the case where T = 0, i.e., allowing no lookahead capability in the controller, as well as the cases of estimating some future event times.