Bridging Direct and Indirect Data-Driven Control Formulations via Regularizations and Relaxations

• 成果类型: Article
• 署名作者: Dorfler, Florian; Coulson, Jeremy; Markovsky, Ivan
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; ICREA; Universitat Politecnica de Catalunya; Centre Internacional de Metodes Numerics en Enginyeria (CIMNE)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3148374
• 发表日期: 2023
• 页码: 883-897
• 关键词: trajectory; Linear systems; Predictive control; data models; Aerospace electronics; optimization; Complexity theory; optimal control; Pareto optimization; System identification

摘要

In this article, we discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal decision compatible with recorded data assembled in a Hankel matrix and robustified through suitable regularizations. We formulate these two problems in the language of behavioral systems theory and parametric mathematical programs, and we bridge them through a multicriteria formulation trading off system identification and control objectives. We illustrate our results with two methods from subspace identification and control: namely, subspace predictive control and low-rank approximation, which constrain trajectories to be consistent with a nonparametric predictor derived from (respectively, the column span of) a data Hankel matrix. In both cases, we conclude that direct and regularized data-driven control can be derived as convex relaxation of the indirect approach, and the regularizations account for an implicit identification step. Our analysis further reveals a novel regularizer and a plausible hypothesis explaining the remarkable empirical performance of direct methods on nonlinear systems.