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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Spring 2010 Seminar Series
Stochastic Model Predictive Control: Tractability and
Constraint Satisfaction
John Lygeros, ETH Zurich
Wednesday, April 7, 2010, 11:00 12:00pm HFH 4164
Abstract: Exploiting advances in optimization, especially convex and multi-parametric optimization, model predictive
control (MPC) for deterministic systems has matured into a powerful methodology with a wide range of applications. Recent
activity in robust optimization has also enabled the formulation and solution of robust MPC problems for systems subject to
various kinds of worst case uncertainty. For systems subject to stochastic uncertainty, however, the formulation and solution
of MPC problems still poses fundamental conceptual challenges. Optimization over open loop controls, for example, tends
to lead to excessively conservative solutions, so optimization over an appropriate class of feedback policies is often neces-
sary. As in the case of robust MPC, the selection of policies one considers is crucial and represents a trade-off between the
tractability of the optimization problem and the optimality of the solution. Moreover, in the presence of stochastic disturbanc-
es hard state and input constraints need to be re-interpreted as chance constraints, or integrated chance constraints, which
may be violated with a certain tolerance. This interpretation, however, makes it difficult to enforce hard input constraints dic-
tated by the capabilities of the system and the actuators, especially if one considers desirable classes of feedback policies
such as affine policies. And what guarantees can one provide in the infinite horizon case, given that the system evolution


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics