We consider the problem of designing a disturbance compensator for a discrete time linear system, so as to optimize a performance index while satisfying probabilistic state and input constraints in steady-state conditions. The problem is formulated as a chance-constrained program that depends on the compensator parameters through the state and input stationary distributions. In this paper, we focus on the Gaussian noise case and provide an analytic expression of the stationary state distribution as a function of the compensator parameters. This expression can be used in the chance-constrained program, which can then be tackled via the scenario approach. Some useful extensions of the set-up are also discussed to further broaden the applicability of the approach. Performance of the proposed design methodology is shown on a building energy management problem where cyclostationary disturbances are compensated, thus providing a stochastic periodic control solution.

Optimal steady-state disturbance compensation for constrained linear systems: the Gaussian noise case

Falsone A.;Deori L.;Ioli D.;Garatti S.;Prandini M.
2022-01-01

Abstract

We consider the problem of designing a disturbance compensator for a discrete time linear system, so as to optimize a performance index while satisfying probabilistic state and input constraints in steady-state conditions. The problem is formulated as a chance-constrained program that depends on the compensator parameters through the state and input stationary distributions. In this paper, we focus on the Gaussian noise case and provide an analytic expression of the stationary state distribution as a function of the compensator parameters. This expression can be used in the chance-constrained program, which can then be tackled via the scenario approach. Some useful extensions of the set-up are also discussed to further broaden the applicability of the approach. Performance of the proposed design methodology is shown on a building energy management problem where cyclostationary disturbances are compensated, thus providing a stochastic periodic control solution.
2022
Buildings
Covariance matrices
Disturbance compensation
Gaussian noise
Linear systems
optimal constrained control
Probabilistic logic
Stationary state
Steady-state
stochastic linear systems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1205221
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