Advances in modeling and control of nonlinear distributed parameter systems and their applications: A review

Numerous processes in various fields including engineering, physics, and chemistry, etc., belong to distributed parameter systems (DPSs). These systems are strongly spatiotemporal coupled, possessing complex time-varying dynamics and infinite-dimensional spatial distribution characteristics. Additionally, there are unknown initial/ boundary conditions and parameter variation during the interaction of information or energy exchange, especially in complex application scenarios (i.e., large operation range, large spatial region, etc.). These factors make the modeling, prediction and control of spatiotemporal dynamics extremely difficult and challenging. With the enrichment of computational resources and data-driven/ intelligent methods, many new frameworks and strategies are designed and applied for nonlinear DPSs, which promotes the research diversity and maturity of DPS theory. Meanwhile, the development also gives rise to new problems. From the perspective of review, this paper starts from the practical modeling and control problems in combination with several application cases of nonlinear DPSs, and summarizes the research and application progress, including traditional methods, data-driven methods, intelligent modeling methods etc., and looks forward to the future development trends, providing guidance for related research and practical problem-solving of nonlinear DPSs.