Optimal disturbance compensation for constrained linear systems operating in stationary conditions: A scenario-based approach

We consider the problem of optimizing the stationary performance of a discrete time linear system affected by a disturbance and subject to probabilistic input and state constraints. More precisely, the goal is to design a disturbance compensator which optimally shapes the stationary state distribution so as to best satisfy the given control specifications. To this purpose, we formulate a chance-constrained program with the compensator parametrization as optimization vector. Chance-constrained programs are generally hard to solve and a possible way to tackle them is to resort to the so-called scenario approach. In our set-up, however, the scenario approach is not directly applicable since the stationary state process depends on disturbance realizations of infinite extent. Our contribution is then to provide a new scenario-based methodology, where the stationary state process is approximated and constraints are suitably tightened so as to retain the chance-constrained feasibility guarantees of the scenario solution. Design of a periodic compensator of a cyclostationary disturbance can be embedded in our framework, as illustrated in an energy management numerical example. (C) 2019 Elsevier Ltd. All rights reserved.