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Stochastic Model Predictive Control Using a Combination of Randomized and Robust Optimization


X. Zhang, K. Margellos, P.J. Goulart, J. Lygeros

IEEE Conference on Decision and Control, Florence, Italy, pp. 7740 - 7745

In this paper, we focus on Stochastic Model Predictive Control (SMPC) problems for systems with linear dynamics and additive uncertainty. One way to address such problems, in which one must satisfy probabilistic constraint satisfaction guarantees without imposing any assumptions on the probability distribution of the uncertainty, is by means of randomized algorithms. Typically these algorithms require substituting the chance constraint of the SMPC problem with a finite number of hard constraints corresponding to samples of the uncertainty. However, earlier approaches toward this direction lead to problems that are computationally very expensive, and for which the resulting solution is very conservative in terms of cost. To address these limitations we follow an alternative methodology based on a combination of randomized and robust optimization, and show that our approach can offer significant advantages in terms of both cost and computation time. We consider both open-loop (i.e. optimizing over input sequences) and closed-loop (i.e optimizing over policies) MPC problems, and demonstrate the efficacy of ours relative to standard randomized techniques on a building control problem.


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% Autogenerated BibTeX entry
@InProceedings { ZhaEtal:2013:IFA_4479,
    author={X. Zhang and K. Margellos and P.J. Goulart and J. Lygeros},
    title={{Stochastic Model Predictive Control Using a Combination of
	  Randomized and Robust Optimization}},
    booktitle={IEEE Conference on Decision and Control},
    pages={7740 -- 7745},
    address={Florence, Italy},
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