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.

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

Falsone A.;Deori L.;Ioli D.;Garatti S.;Prandini M.
2019-01-01

Abstract

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.
2019
Disturbance compensation; Optimal constrained control; Stochastic linear systems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1119938
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