Boundary Control of Multidimensional Discrete-Velocity Kinetic Models

• 成果类型: Article
• 署名作者: Yang, Haitian; Yong, Wen-An
• 署名单位: Tsinghua University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3555944
• 发表日期: 2025
• 页码: 6183-6190
• 关键词: mathematical models; vectors; Structural engineering; steady-state; Numerical models; Null space; Symmetric matrices; Kinetic theory; Boundary conditions; Boltzmann equation; Boundary stabilization; control laws; discrete velocity models; hyperbolic relaxation systems; structural stability condition

摘要

This technical note is concerned with boundary stabilization of multidimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive feasible control laws so that the corresponding solutions decay exponentially in time. The result is illustrated with an application to the 2-D coplanar model in a square container. The effectiveness of the derived control laws is confirmed by numerical simulations.