Optimization problems involving chance constraints, i.e. constraints on decision variables that are required to hold with given probability, occur in numerous engineering contexts, but have in particular contributed to developments in robust control design over the past decade. This talk will provide a new perspective on randomized methods for solving chance-constrained programming problems based on samples of uncertain parameters, and presents a theoretical framework for sampled convex programming that encompasses analyses of constraint discarding approaches and sequential sampling approaches. We show that tight bounds on the confidence of the solution of a sampled problem meeting chance constraints apply if a randomized sample discarding strategy is employed. This suggests a solution methodology which is both computationally convenient, being based on the solutions of convex sampled optimization problems, and efficient, requiring the solution of smaller numbers of problems than existing constraint discarding and sequential methods. We illustrate the method with examples from stochastic model predictive control design.

Bio. Mark Cannon obtained the degrees of MEng in Engineering Science in 1993 and D.Phil. in Control Engineering in 1998, both from Oxford University, and SM in Mechanical Engineering in 1995 from Massachusetts Institute of Technology. He is currently Associate Professor of Engineering Science, Oxford University, and an Official Fellow of St John's College. His research interests are in robust constrained control and stochastic model predictive control, specifically: issues relating to optimization and controller design, closed loop stability and constraint satisfaction, and applications to power management in electric vehicles.