Robust Data-Driven Control of Discrete-Time Linear Systems With Errors in Variables

• 成果类型: Article
• 署名作者: Miller, Jared; Dai, Tianyu; Sznaier, Mario
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Northeastern University; MathWorks
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3447809
• 发表日期: 2025
• 页码: 947-962
• 关键词: NOISE; Symmetric matrices; POLYNOMIALS; Noise measurement; Linear matrix inequalities; PROCESS CONTROL; Linear systems; Data-driven control (DDC); linear matrix inequality (LMI); optimization; Robust control; sum of squares (SOS)

摘要

This article presents a sum of squares (SOS)-based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by & ell;(infinity )bounded input, measurement, and process noise (error in variable setting). Certificates of full-state-feedback robust performance, superstabilization or quadratic stabilization of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true worst-case optimal & ell;(infinity) (extended) superstabilizing controllers. With some conservatism, quadratically stabilizing controllers with certified H-2 performance bounds can also be found. The performance of this SOS method is improved through the application of a Theorem of Alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H-2 control costs.