Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

This article proposes a novel distributionally robust optimization (DRO)‐based soft‐constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state‐space system. Without a priori knowledge of the exact uncertainty distribution, this fra...

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Bibliographic Details
Published in:AIChE journal 2020-10, Vol.66 (10), p.n/a
Main Authors: Lu, Shuwen, Lee, Jay H., You, Fengqi
Format: Article
Language:English
Subjects:
Computer applications
conic duality
Constraints
Control systems
distributionally robust optimization
Feasibility
Learning algorithms
linear cost function
Machine learning
model predictive control
Motion control
Optimization
Predictive control
principal component analysis
Robustness
stability under uncertainty
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Summary:This article proposes a novel distributionally robust optimization (DRO)‐based soft‐constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state‐space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first‐order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO‐based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi‐stage scenario based stochastic MPC.
ISSN:0001-1541
1547-5905
DOI:10.1002/aic.16546