Statistical Learning Control of Uncertain Systems: It is Better Than It Seems

Technical ReportRecently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to \diÆcult" control problems. Unfortunately, the number of samples required in order to guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap learning methods and the concept of stopping times to drastically reduce the bound on the number of samples required to achieve a performance level. We then apply these results to obtain more eÆcient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems.The research of V. Koltchinskii is partially supported by NSA Grant MDA904-99-1-0031. The research of C.T.Abdallah is partially supported by Boeing Computer Services Grant 3-48181, and by NSF INT-9818312