A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedback

Oldewurtel, Frauke; Jones, Colin N.; Morari, Manfred

doi:10.1109/cdc.2008.4738806

Cited by 142 publications

(107 citation statements)

References 17 publications

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“…Problem 4 can be solved as a standard QP, see [12]. Theorem 2 (ADF With BDS): For Problem 4, the following statements hold: (1) Problem 4 is a conservative approximation of Problem 2 in the sense that the level of constraint violation is strictly smaller than α.…”

Section: Problem 4 (Adf With Bds)mentioning

confidence: 99%

“…It can also be seen from the fact that linear constraints are used for inner approximations of SOC constraints. 2) BDS (x 0 ) is convex (see [12]). This together with the cost function of Problem 4 being convex according to Proposition 1 establishes the assertion.…”

Section: (2) Problem 4 Is Convexmentioning

confidence: 99%

“…By using affine disturbance feedback and by exploiting the fact that comfort violations are allowed from time to time with the chance constraints, the conservatism of traditional robust solutions is reduced. The presented material is an extension to the ideas proposed in [12] and offers a comparison and analysis of different formulations. The chosen formulation is assessed on a large-scale building example from the OptiControl project and shown to outperform current control practice.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Model Predictive Control for Building Climate Control

Oldewurtel

Jones

Parisio

et al. 2014

IEEE Trans. Contr. Syst. Technol.

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121

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Abstract-In this brief paper, a Stochastic Model PredictiveControl formulation tractable for large-scale systems is developed. The proposed formulation combines the use of Affine Disturbance Feedback, a formulation successfully applied in robust control, with a deterministic reformulation of chance constraints. A novel approximation of the resulting stochastic finite horizon optimal control problem targeted at building climate control is introduced to ensure computational tractability. This work provides a systematic approach toward finding a control formulation which is shown to be useful for the application domain of building climate control. The analysis follows two steps: 1) a small-scale example reflecting the basic behavior of a building, but being simple enough for providing insight into the behavior of the considered approaches, is used to choose a suitable formulation; and 2) the chosen formulation is then further analyzed on a large-scale example from the project OptiControl, where people from industry and other research institutions worked together to create building models for realistic controller comparison. The proposed Stochastic Model Predictive Control formulation is compared with a theoretical benchmark and shown to outperform current control practice for buildings.

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Section: Problem 4 (Adf With Bds)mentioning

confidence: 99%

Section: (2) Problem 4 Is Convexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Model Predictive Control for Building Climate Control

Oldewurtel

Jones

Parisio

et al. 2014

IEEE Trans. Contr. Syst. Technol.

Self Cite

121

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“…The main benefit of using this affine disturbance feedback formulation is that the resulting optimization problem can be formulated as a convex problem, so that it can be solved using common commercial codes while providing a very good performance [17,18].…”

Section: Stochastic Mpc (Smpc)mentioning

confidence: 99%

Use of model predictive control and weather forecasts for energy efficient building climate control

Oldewurtel

Parisio

Jones

et al. 2012

Energy and Buildings

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1,004

501

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a b s t r a c tThis paper presents an investigation of how Model Predictive Control (MPC) and weather predictions can increase the energy efficiency in Integrated Room Automation (IRA) while respecting occupant comfort. IRA deals with the simultaneous control of heating, ventilation and air conditioning (HVAC) as well as blind positioning and electric lighting of a building zone such that the room temperature as well as CO 2 and luminance levels stay within given comfort ranges. MPC is an advanced control technique which, when applied to buildings, employs a model of the building dynamics and solves an optimization problem to determine the optimal control inputs. In this paper it is reported on the development and analysis of a Stochastic Model Predictive Control (SMPC) strategy for building climate control that takes into account the uncertainty due to the use of weather predictions.As first step the potential of MPC was assessed by means of a large-scale factorial simulation study that considered different types of buildings and HVAC systems at four representative European sites. Then for selected representative cases the control performance of SMPC, the impact of the accuracy of weather predictions, as well as the tunability of SMPC were investigated. The findings suggest that SMPC outperforms current control practice.

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“…This approach is different from the previous ones in that it approximates the probability constraints using linear inequalities and the value function is also a certainty equivalent version [33]. We summarize a slightly…”

Section: A Tractable Approximation Of Probability Constrained Stochasmentioning

confidence: 99%

Stochastic LQ Control with Probabilistic Constraints

Zhou¹

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In this thesis we focus on stochastic LQ control problems with probabilistic constraints. We will briefly review the history of LQ control and the related classical results for constrained and unconstrained cases. Then we formulate the problem studied, where the system has linear dynamics and a quadratic cost, and states are required to satisfy a probabilistic constraint. We sample the most recent techniques for such probability constrained control problems and propose our own approach. We consider two types of probability constraints:all-stage and per-stage. In the first case, there is a joint probabilistic constraint on all the system states over the whole predicting horizon while in the second one the states are restricted by individual probability constraints at each stage. The contribution of this thesis has two parts: first we develop a recursive state feedback control algorithm for a special class of state constrained stochastic LQR, and a disturbance feedback controller for the general case using quadratic programming for the all-stage problems. Second, we design a recursive algorithm for the per-stage problem based on sub-gradient method. We also implement a practical Model Predictive Control algorithm for such problems. The control algorithm is tested on a simple temperature control problem for analysis.ii The last but not the least I am grateful to the staff members at the International Student Office and the language development center. As an international student I feel at home with their help.Four years can change much about a person, I sincerely thank you all for being part of this crucial change of my life.

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A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedback

Cited by 142 publications

References 17 publications

Stochastic Model Predictive Control for Building Climate Control

Stochastic Model Predictive Control for Building Climate Control

Use of model predictive control and weather forecasts for energy efficient building climate control

Stochastic LQ Control with Probabilistic Constraints

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