Exponential cone approach to joint chance constraints in stochastic model predictive control
Stochastic model predictive control addresses uncertainties by incorporating the probabilistic description of the disturbances into joint chance constraints. Yet, the classic methods for handling this class of constraints are often computationally inefficient and overly conservative. To overcome thi...
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| Published in | International journal of control pp. 1 - 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
2025
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Stochastic model predictive control addresses uncertainties by incorporating the probabilistic description of the disturbances into joint chance constraints. Yet, the classic methods for handling this class of constraints are often computationally inefficient and overly conservative. To overcome this, we propose to replace the nonconvex inverse cumulative distribution function of the standard normal distribution in the deterministic counterpart of these constraints with a highly accurate, exponential cone-representable approximation. This allows the constraints to be formulated as exponential cone functions, and the problem is solved as an exponential cone optimization with risk allocation as decision variables. The main advantage of the proposed approach is that the optimization problem is efficiently solved with off-the-shelf software, and with reduced conservativeness. Moreover, it applies to any problem with linear joint chance constraints subject to normally distributed disturbances. We validate our method with numerical examples of stochastic model predictive control applications. |
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| AbstractList | Stochastic model predictive control addresses uncertainties by incorporating the probabilistic description of the disturbances into joint chance constraints. Yet, the classic methods for handling this class of constraints are often computationally inefficient and overly conservative. To overcome this, we propose to replace the nonconvex inverse cumulative distribution function of the standard normal distribution in the deterministic counterpart of these constraints with a highly accurate, exponential cone-representable approximation. This allows the constraints to be formulated as exponential cone functions, and the problem is solved as an exponential cone optimization with risk allocation as decision variables. The main advantage of the proposed approach is that the optimization problem is efficiently solved with off-the-shelf software, and with reduced conservativeness. Moreover, it applies to any problem with linear joint chance constraints subject to normally distributed disturbances. We validate our method with numerical examples of stochastic model predictive control applications. |
| Author | Löfberg, Johan Marques Barbosa, Filipe |
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| Cites_doi | 10.1016/j.jprocont.2016.03.005 10.1109/TAES.2021.3086956 10.1007/s10957-006-9084-x 10.1007/s10957-016-0892-3 10.1007/s10107-005-0677-1 10.1109/CDC.2003.1272813 10.1007/s002080010009 10.23919/ACC53348.2022.9867816 10.1137/050622328 10.1080/00207179.2022.2084163 10.1109/TRO.2011.2161160 10.1007/BFb0109870 10.1137/15M1049415 10.1016/j.automatica.2005.08.023 10.1109/TAC.2021.3124750 10.1007/s10107-021-01631-4 10.1016/j.arcontrol.2009.07.001 10.1080/00207179.2017.1323351 10.1287/moor.22.1.1 10.2514/6.2009-5876 10.1109/TCST.2023.3291570 10.1016/j.automatica.2003.08.009 10.1109/CDC.2011.6160721 10.1137/S1052623495290209 10.1201/9781003456285 10.1109/CACSD.2004.1393890 10.1016/j.compchemeng.2017.10.026 10.1137/080734510 |
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