Abstract
AbstractThis article presents a result of stabilization of a coupled partial differential equation (PDE) and ordinary differential equation (ODE) system through boundary control. The PDE is the Burgers' equation, which is a widely considered nonlinear PDE, partially due to its low order and partially due to its structure analogous to the Navier–Stokes equation, which describes fluid dynamics. The controller we employ for stabilizing this system was first developed from the boundary control problem of the corresponding linearized system, based on an infinite‐dimensional backstepping transformation. The stabilization result is achieved using only one boundary measurement and one boundary control. Numerical simulations show the boundary control law can be used to stabilize the system.
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