Boundary and distributed control of the viscous Burgers equation
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摘要
In this paper, the dynamics of the forced Burgers equation: ut=νuxx-uux+f(x), subject to both Neumann boundary conditions and periodic boundary conditions using boundary and distributed control is analyzed. For the boundary control problem, we show that the controlled unforced Burgers equation (i.e., the closed loop system) is exponentially stable when the viscosity ν is known, and globally asymptotically stable when ν is unknown. As for the distributed control problem, we apply Karhunen–Loéve decomposition on the dynamics of the forced Burgers equation to generate a low dimensional dynamical system whose dynamics is similar to that of Burgers equation. Then, a feedback linearization control is used on the reduced system to exponentially stabilize the dynamics of the equation. Numerical simulations for the boundary and distributed controls are presented to support the analytical results.
论文关键词:34H05,35B37,35Q53,93D15,Boundary and distributed control,Forced Burgers equation,Stabilization
论文评审过程:Received 6 June 2004, Available online 21 January 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2004.10.020