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 necessary. 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 disturbances 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 dictated 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 is obtained by solving an infinite sequence of finite horizon problems each of which may violate its constraints with a finite probability? This talk will outline these challenges and propose solutions for some. The resulting stochastic MPC methods will be illustrated on benchmark problems and compared with alternatives.