Stochastic model predictive control with joint chance constraints

This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The...

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Bibliographic Details
Published inInternational journal of control Vol. 93; no. 1; pp. 126 - 139
Main Authors Paulson, Joel A., Buehler, Edward A., Braatz, Richard D., Mesbah, Ali
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2020
Taylor & Francis Ltd
Subjects
Acetone
Algorithms
Butanol
Chebyshev approximation
Constraint modelling
disturbance feedback parametrization
Disturbances
Ethanol
Fermentation
Linear systems
Predictive control
Risk allocation
Stochastic models
Stochastic systems
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Summary:This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The Cantelli-Chebyshev inequality is used in combination with risk allocation to obtain computationally tractable but accurate surrogates for the joint state chance constraints when only the mean and variance of the arbitrary disturbance distributions are known. An algorithm is presented for determining the optimal feedback gain and optimal risk allocation by iteratively solving a series of convex programs. The proposed stochastic MPC approach is demonstrated on a continuous acetone-butanol-ethanol fermentation process, which is used in the production of biofuels.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2017.1323351