Name
Title | ||
|---|---|---|
A mean-variance criterion for economic model predictive control of stochastic linear systems |
Abstract | ||
|---|---|---|
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. Open-loop 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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1109/CDC.2014.7040314 | Decision and Control |
Keywords | Field | DocType |
Monte Carlo methods,convex programming,linear systems,open loop systems,optimal control,predictive control,stochastic systems,EMPC,Monte-Carlo approach,certainty equivalence strategy,convex relaxation,economic model predictive control,mean-variance criterion,open-loop simulations,optimal control problem,power management,stochastic linear systems | Variance Criterion,Power management,Mathematical optimization,Optimal control,Linear system,Control theory,Computer science,Heuristics,Economic model predictive control,Expected cost,Operating cost | Conference |
ISSN | Citations | PageRank |
0743-1546 | 1 | 0.35 |
References | Authors | |
18 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Leo Emil Sokoler | 1 | 1 | 0.35 |
| Bernd Dammann | 2 | 40 | 2.46 |
| H. Madsen | 3 | 4 | 0.99 |
| John Bagterp Jørgensen | 4 | 11 | 2.83 |