About Robustness of Control Systems Embedding an Internal Model

• 成果类型: Article
• 署名作者: Bin, Michelangelo; Astolfi, Daniele; Marconi, Lorenzo
• 署名单位: Imperial College London; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Engineering & Systems Sciences (INSIS); Universite Claude Bernard Lyon 1; University of Bologna
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3151574
• 发表日期: 2023
• 页码: 1306-1320
• 关键词: Internal model; nonlinear control; output regulation; Robustness

摘要

Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired reference signals in spite of external disturbances and parametric uncertainties. This result is commonly known as the internal model principle. A complete extension of such linear result to general nonlinear systems is still an open problem, exacerbated by the large number of alternative definitions of uncertainty and desired control goals that are possible in a nonlinear setting. In this article, we develop a general framework in which all these different notions can be formally characterized in a unifying way. Classical results are reinterpreted in the proposed setting, and new results and insights are presented with a focus on robust rejection/tracking of arbitrary harmonic content. Moreover, we show by counterexample that, in the relevant case of continuous unstructured uncertainties, there are problems for which no smooth finite-dimensional robust regulator exists ensuring exact regulation.