<p>This review focuses on the boundary control research of fractional-order reaction–diffusion systems (FRDSs). As an important research direction in the field of complex system modeling and control, FRDSs based on the nonlocal calculus characteristics have demonstrated significant advantages in describing complex phenomena such as anomalous diffusion, multi-scale spatiotemporal coupling, and delayed reactions. The specific memory characteristics of this type of system bring new challenges to the traditional control theory. Especially, although breakthroughs have been achieved in the theory of whole domain control strategies, their engineering applications are restricted due to the realization mode relying on high-density actuators. Against this background, boundary control methods with non-invasive regulation characteristics have emerged as a research focus. This paper first introduces the research background and significance of boundary control for FRDSs, and then systematically reviews the related research progress. Subsequently, the design and analysis methods of boundary control scheme are introduced and compared, and the problems that need to be solved to improve the effectiveness and applicability of current results are further discussed.</p>

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A review on boundary control of fractional-order reaction–diffusion systems

  • Cheng Zhang,
  • Guo-Jian Ren,
  • Wei Chen,
  • Yong-Guang Yu,
  • Yang-Quan Chen

摘要

This review focuses on the boundary control research of fractional-order reaction–diffusion systems (FRDSs). As an important research direction in the field of complex system modeling and control, FRDSs based on the nonlocal calculus characteristics have demonstrated significant advantages in describing complex phenomena such as anomalous diffusion, multi-scale spatiotemporal coupling, and delayed reactions. The specific memory characteristics of this type of system bring new challenges to the traditional control theory. Especially, although breakthroughs have been achieved in the theory of whole domain control strategies, their engineering applications are restricted due to the realization mode relying on high-density actuators. Against this background, boundary control methods with non-invasive regulation characteristics have emerged as a research focus. This paper first introduces the research background and significance of boundary control for FRDSs, and then systematically reviews the related research progress. Subsequently, the design and analysis methods of boundary control scheme are introduced and compared, and the problems that need to be solved to improve the effectiveness and applicability of current results are further discussed.