2015/11/20 by Rafael Vázquez, Miroslav Krstić, Vazquez, Rafael +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Electrical engineering #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1511.06641
openalex publication_date 2015/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An explicit output-feedback boundary feedback law is introduced that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only measurements from the boundary. The backstepping method is used to design both the control law and a boundary observer. To apply backstepping the system is reduced to an infinite sequence of 1-D systems using spherical harmonics. Well-posedness and stability are proved in the H1 space. The resulting control and output injection gain kernels are the product of the backstepping kernel used in control of one-dimensional reaction-diffusion equations and a function closely related to the Poisson kernel in the n-ball.