Application of Statistical Learning Control to
the Design of a Fixed-Order Controller for a
M. Ariola, V. Koltchinskii, C.T. Abdallah
This paper shows how probabilistic methods and statistical learning theory can provide approximate solutions to "dif-
ficult" control problems. The paper also introduces bootstrap learning methods to drastically reduce the bound on the
number of samples required to achieve a performance level. These results are then applied to obtain more efficient algo-
rithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems.
The paper includes examples of the applications of these methods.
Statistical Learning, Radamacher bootstrap, Robust Control, Sample Complexity, NP-hard problems, Decidability
M. Ariola is with the Dipartimento di Informatica e Sistemistica, Universit`a degli Studi di Napoli Federico II, Napoli,
Italy. E-mail:firstname.lastname@example.org. His research is partially supported by the MURST.
V. Koltchinskii is with the Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131,
USA. E-mail: email@example.com. His research is partially supported by NSA Grant MDA904-99-1-0031.
Corresponding Author: C.T. Abdallah is with the Electrical & Computer Engineering Department, University of
Tennessee at Knoxville, 401 Ferris Hall Knoxville, TN 37996-2100, Usa. Phone: (865)974-0927, Fax: (865)974-5483 (Fax),