Soft-constrained model predictive control based on data-driven distributionally robust optimization |
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Authors: | Shuwen Lu Jay H Lee Fengqi You |
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Affiliation: | 1. Systems Engineering, College of Engineering, Cornell University, New York, New York, USA;2. Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea |
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Abstract: | 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. |
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Keywords: | conic duality distributionally robust optimization linear cost function model predictive control principal component analysis stability under uncertainty |
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