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Data-Driven Iterative Learning Control for Nonlinear Discrete-Time Systems Based on Full-Form Dynamic Linearization
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DOI：10.1109/TASE.2025.3639940.png)
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Abstract
En 中文
In this study, a standardized controller design and analytical framework is put forward for nonlinear systems that meet the requirements within the framework of full-form iterative dynamic linearization (FFIDL). A discrete data-driven, two-dimensional theoretical analysis method is introduced. This method comprehensively covers both controller and stability analysis under compact form iterative dynamic linearization (CFIDL) and partial form iterative dynamic linearization (PFIDL). Compared with traditional methods, this analysis approach provides a more intuitive and structurally clearer interpretation of the system’s convergence properties. Different from the contraction mapping approach, when excess data tail terms exist, the contraction mapping may readily impede the establishment of closed-loop analysis, thus overlooking valuable data information. In data-based two-dimensional systems, the bounded-input bounded-output (BIBO) properties of contraction mappings are analyzed by using inequalities of two-dimensional expansion in combination with time-weighted functions. Moreover, the limitations related to the full-form dynamic linearization model-free adaptive control (FFDL-MFAC) in the process of tracking constant expectations are addressed. These theoretical and experimental solutions have been verified through simulation results. Note to Practitioners—The escalating complexity of industrial systems and the challenges associated with modeling nonlinear dynamics have spurred the adoption of data-driven control (DDC) methodologies. To the best of the authors’ knowledge, traditional model-free adaptive control (MFAC) approaches encounter limitations when dealing with systems featuring repetitive operations. The aim of this paper is to devise a novel data-driven iterative learning control (DDILC) method by leveraging FFIDL. This method enhances the tracking capabilities for time-varying reference trajectories, thereby overcoming the limitation of traditional FFDL-MFAC, which confines reference signals to constant values. Subsequently, a controller design and the corresponding stability proof are presented in this paper. Numerical simulations are carried out to validate the effectiveness of the proposed approach.
Keywords:
Data-driven
iterative learning control
model-free adaptive control
dynamic linearization
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