Group for Research in Decision Analysis

Worst-Case and Probabilistic Models of Uncertainty: Benefits and Pitfalls

Roberto Tempo Politecnico di Torino, Italy

In this lecture, we study benefits and pitfalls of worst-case and probabilistic models of uncertainty using the methodology of randomized algorithms. This methodology leads to powerful tools systematically utilized in various research areas, including computer science and numerical analysis. On the other hand, randomization appears only in a rather scattered fashion within systems and control. Simulation techniques are largely based on Monte Carlo methods, but these techniques are often used with the sole objective of testing a specific system's performance, and not for deriving results applicable to broad classes of systems.

Recently, we have seen a first attempt to rigorously develop efficient randomized algorithms for complex systems with uncertainty, with the goal of reducing the complexity of feedback. To this end, worst-case and probabilistic models of uncertainty are merged assigning a given probability measure to the uncertainty set provided by robust control.

In this lecture, we address these issues and study some specific problems, such as the computation of bounds on the number of required random systems, the connections between randomized algorithms, learning theory and stochastic approximation methods, the generation of random samples in norm-bounded sets, and other probabilistic-based problems.


Roberto Tempo was born in Cuorgne', Italy, in 1956. In 1980 he graduated in Electrical Engineering at Politecnico di Torino, Italy. After a period spent at the Dipartimento di Automatica e Informatica, Politecnico di Torino, he joined the National Research Council of Italy (CNR) at the research institute IEIIT, Torino, where he is a Director of Research of Systems and Computer Engineering since 1991. He has held visiting and research positions at Kyoto University, University of Illinois at Urbana-Champaign, German Aerospace Research Organization in Oberpfaffenhofen and Columbia University in New York.

Dr. Tempo's research activities are mainly focused on complex systems with uncertainty, and related applications. On these topics he has given plenary and semi-plenary lectures at various conferences and workshops, including the Robust Control Workshop, Delft, The Netherlands, 2005. He has been an invited speaker at the NATO Lecture Series on “Robust Integrated Control System Design Methods,” Universita' di Bologna, Forli', Italy, Escola Superior de Tecnologia de Setubal, Portugal and University of Southern California, Los Angeles, 2003.

Dr. Tempo is author or co-author of more than 130 research papers published in international journals, books and conferences. He is also a co-author of the book “Randomized Algorithms for Analysis and Control of Uncertain Systems,” Springer-Verlag, London, 2005. He is a recipient of the "Outstanding Paper Prize Award" from the International Federation of Automatic Control (IFAC) for a paper published in Automatica, and of the “Distinguished Member Award” from the IEEE Control Systems Society. He is a Fellow of the IEEE for “Contributions to Robust Identification and Control of Uncertain Systems.”

Dr. Tempo is currently an Editor and Deputy Editor-in-Chief of Automatica. He is also Editor for Technical Notes and Correspondence of the IEEE Transactions on Automatic Control. He has served as member of the program committee of several IEEE, IEE, IFAC and EUCA (European Union Control Association) conferences, and Program Chair of the first joint IEEE Conference on Decision and Control and European Control Conference, Seville, Spain, 2005. He has been Vice-President for Conference Activities of the IEEE Control Systems Society during the period 2002-2003 and a member of the EUCA Council in 1998-2003.