Robust and stochastic economic model predictive control

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Model predictive control (MPC), also called receding horizon control, is a control strategy which consists of repeatedly solving (online) a finite horizon optimal control problem and then applying the first part of the corresponding solution to the considered system. Its main advantages and reasons for its widespread success include the possibility to explicitly incorporate state and input constraints as well as some performance criterion into the controller design. Most of the results available in the literature consider stabilizing MPC schemes, where the control objective is the stabilization of some a priori given setpoint (or more general reference signal). On the other hand, in recent years economic MPC schemes have received an increasing amount of attention, where the control objective is the optimization of some general performance criterion, which need not be related to a specific steady-state as in stabilizing MPC. Such economic MPC schemes are of importance in many different applications, and they require different analysis methods and concepts than stabilizing MPC due to the more general control objective. As in most practical applications modeling uncertainties as well as disturbances are present, it is of intrinsic importance to develop MPC schemes for which closed-loop guarantees such as constraint satisfaction and performance estimates can be established despite the presence of these disturbances. In the context of stabilizing MPC, various different solution methods to this problem are available both in a robust and stochastic setting. On the other hand, for economic MPC, this is to a very large extent an open problem and only very few first attempts in this direction were made so far. The main goal of the proposed project is to contribute to this open research area. In particular, we aim at developing economic MPC schemes for uncertain systems for which desired closed-loop guarantees such as recursive feasibility, constraint satisfaction and (average) performance guarantees can be rigorously proven. We consider both the cases where no further information on the disturbances is known (i.e., robust economic MPC schemes) as well as cases where additional (stochastic) information on the disturbance is available, which can be used for performance improvement (i.e., stochastic economic MPC schemes). To this end, the project examines whether and how certain approaches from stabilizing robust and stochastic MPC can be extended and transferred to an economic setting, and develops novel methods and concepts which are needed due to the more general nature of the problem.