A Distributionally Robust Optimization Based Method for Stochastic Model Predictive Control

• Published in: IEEE transactions on automatic control Vol. 67; no. 11; pp. 5762 - 5776
• Main Authors: Li, Bin, Tan, Yuan, Wu, Ai-Guo, Duan, Guang-Ren
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Chance constraints; Chebyshev approximation; Computational complexity; Convergence; distributionally robust optimization (DRO); Linear systems; Optimization; Prediction algorithms; Predictive control; Robust control; stochastic model predictive control (SMPC); Stochastic models; Stochastic processes
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3124750

Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms.