Diffusing-Horizon Model Predictive Control

• 成果类型: Article
• 署名作者: Shin, Sungho; Zavala, Victor M. M.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3137100
• 发表日期: 2023
• 页码: 188-201
• 关键词: Discrete-time systems; linear programming; optimal control; Predictive control

摘要

We analyze a time-coarsening strategy for model predictive control (MPC) that we call diffusing-horizon MPC. This strategy seeks to overcome the computational challenges associated with optimal control problems that span multiple timescales. The coarsening approach uses a time discretization grid that becomes exponentially more sparse as one moves forward in time. This design is motivated by a recently established property of optimal control problems that is known as exponential decay of sensitivity (EDS). This property states that the impact of a parametric perturbation at a future time decays exponentially as one moves backward in time. We establish conditions under which this property holds for a constrained MPC formulation with linear dynamics and costs. Moreover, we show that the proposed coarsening scheme can be cast as a parametric perturbation of the MPC problem and, thus, the exponential decay condition holds. We use a HVAC plant case study with real data to demonstrate the proposed approach. Specifically, we show that computational times can be reduced by two orders of magnitude while increasing the closed-loop cost by only 3%.