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arXiv · 1805.07145

Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets

Lukas Hewing·Melanie N. Zeilinger
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Abstract

In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.

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BibTeXRIS

Lukas Hewing, Melanie N. Zeilinger. 2018-05-18. Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets. https://doi.org/10.1109/cdc.2018.8619554

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