Conference paper
A Mean-Variance Criterion for Economic Model Predictive Control of Stochastic Linear Systems
Department of Applied Mathematics and Computer Science, Technical University of Denmark1
Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark2
Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3
Center for Energy Resources Engineering, Centers, Technical University of Denmark4
CITIES - Centre for IT-Intelligent Energy Systems, Centers, Technical University of Denmark5
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.
Language: | English |
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Publisher: | IEEE |
Year: | 2014 |
Pages: | 5907-5914 |
Proceedings: | 53rd IEEE Conference on Decision and Control (CDC 2014)IEEE Conference on Decision and Control |
ISBN: | 1467360899 , 1467360902 , 1479977462 , 9781467360890 , 9781467360906 , 9781479977468 , 1479977454 and 9781479977451 |
Types: | Conference paper |
DOI: | 10.1109/CDC.2014.7040314 |
ORCIDs: | Dammann, Bernd , Madsen, Henrik and Jørgensen, John Bagterp |
Cost function EMPC Economics Monte Carlo methods Monte-Carlo approach Noise Standards Stochastic processes Trajectory certainty equivalence strategy convex programming convex relaxation economic model predictive control linear systems mean-variance criterion open loop systems open-loop simulations optimal control optimal control problem power management predictive control stochastic linear systems stochastic systems