A Distributionally Robust Optimization Approach to Two-Sided Chance-Constrained Stochastic Model Predictive Control With Unknown Noise Distribution

• 成果类型: Article
• 署名作者: Tan, Yuan; Yang, Jun; Chen, Wen-Hua; Li, Shihua
• 署名单位: Southeast University - China; Loughborough University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3273775
• 发表日期: 2024
• 页码: 574-581
• 关键词: distributionally robust optimization; second-order cone; stochastic model predictive control (SMPC); two-sided chance constraints

摘要

In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of multiple two-sided chance constrained discrete-time linear systems corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying Bool's inequality. In this proposed DR-SMPC framework, an exact second-order cone approach is adopted to abstract the multiple two-sided chance constraints by considering the first and second moments of the noise. With the proposed DR-SMPC algorithm, the worst-case probability of violating safety constraints is guaranteed to be within a prespecified maximum value. By flexibly adjusting this prespecified maximum probability, the feasible region of the initial state can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are rigorously established by introducing a binary initialization strategy for the nominal state. A simulation study of a single spring and double mass system was conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.