Properties of Receding Horizon Controllers for Some Hybrid Systems with Event Uncertainties

Abstract

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 in prior work 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 derive additional properties, 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.