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<p>In the stability framework of model predictive control (MPC), the size of the stabilizable set (also known as the region of attraction) is dependent on the terminal constraint region. This article aims to investigate the optimization of the terminal region for predictive control of a class of systems with multiplicative uncertainty, aiming to expand the attraction region in MPC. By utilizing a coordinate transformation, we initially develop a structured design for terminal ingredients while considering uncertainties in parameters. Subsequently, we propose novel methods to convert the original nonlinear problem into a linear matrix inequality (LMI) problem with minimal conservatism in the formulation. We propose an iterative learning optimization approach to compute the polytopic terminal region, and its incremental volume is theoretically proven. The effectiveness of the proposed approaches is demonstrated using a benchmark academic example and vehicle lateral dynamics. Through real-time simulation experiments, we demonstrate that the proposed approach can enlarge the domain of attraction as well as reduce the computational complexity of robust MPC systems under parameter uncertainty.</p>

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Characterization of terminal region for MPC with multiplicative uncertainty: an iterative learning optimization approach

  • 期刊论文

  • 发表日期：

    2025年7月21日

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  • Yang Sun,
  • Wenchao Xue,
  • Jizhen Liu,
  • Hui Deng

摘要

In the stability framework of model predictive control (MPC), the size of the stabilizable set (also known as the region of attraction) is dependent on the terminal constraint region. This article aims to investigate the optimization of the terminal region for predictive control of a class of systems with multiplicative uncertainty, aiming to expand the attraction region in MPC. By utilizing a coordinate transformation, we initially develop a structured design for terminal ingredients while considering uncertainties in parameters. Subsequently, we propose novel methods to convert the original nonlinear problem into a linear matrix inequality (LMI) problem with minimal conservatism in the formulation. We propose an iterative learning optimization approach to compute the polytopic terminal region, and its incremental volume is theoretically proven. The effectiveness of the proposed approaches is demonstrated using a benchmark academic example and vehicle lateral dynamics. Through real-time simulation experiments, we demonstrate that the proposed approach can enlarge the domain of attraction as well as reduce the computational complexity of robust MPC systems under parameter uncertainty.