A Mean-Variance Criterion for Economic Model Predictive Control of Stochastic Linear Systems

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Stochastic linear systems arise in a large number of control applications. This paper presents a mean-variance criterion for economic model predictive control (EMPC) of such systems. The system operating cost and its variance is approximated based on a Monte-Carlo approach. Using convex relaxation, the tractability of the resulting optimal control problem is addressed. We use a power management case study to compare different variations of the mean-variance strategy with EMPC based on the certainty equivalence principle. The certainty equivalence strategy is much more computationally efficient than the mean-variance strategies, but it does not account for the variance of the uncertain parameters. Openloop simulations suggest that a single-stage mean-variance approach yields a significantly lower operating cost than the certainty equivalence strategy. In closed-loop, the single-stage formulation is overly conservative, which results in a high operating cost. For this case, a two-stage extension of the mean-variance approach provides the best trade-off between the expected cost and its variance. It is demonstrated that by using a constraint back-off technique in the specific case study, certainty equivalence EMPC can be modified to perform almost as well as the two-stage mean-variance formulation. Nevertheless, we argue that the mean-variance approach can be used both as a strategy for evaluating less computational demanding methods such as the certainty equivalence method, and as an individual control strategy when heuristics such as constraint back-off do not perform well.
Original languageEnglish
Title of host publicationProceedings of the 53rd IEEE Conference on Decision and Control
Number of pages8
Publication date2014
Pages5907 - 5914
ISBN (Print)978-1-4799-7746-8
Publication statusPublished - 2014
Event53rd IEEE Conference on Decision and Control (CDC 2014) - Los Angeles, United States
Duration: 15 Dec 201417 Dec 2014


Conference53rd IEEE Conference on Decision and Control (CDC 2014)
Country/TerritoryUnited States
CityLos Angeles
Internet address


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