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Point Stabilization of the Kuramoto-Sivashinsky Equation by Linear Quadratic Regulation
PDE and Applied Math Seminar| Speaker: | Arthur J. Krener, Naval Postgraduate School |
| Location: | Zoom |
| Start time: | Thu, Mar 7 2024, 4:10PM |
We consider the nonlinear Kuramoto-Sivashinsky equation and its linear part on a finite interval subject to periodic boundary conditions. The linear part can have a finite number of unstable eigenvalues so we assume there are point actuators that allow a linear feedback to move all the unstable eigenvalues into the open left half plane. Such a linear feedback law is found by the well-known technique of Linear Quadratic Regulation (LQR). The resulting linear feedback moves all the unstable eigenvalues into the open left half plane but has little effect on the open loop eigenvalues that were already in the open left half plane. This linear feedback locally stabilizes the nonlinear Kuramoto-Sivashinsky equation but Nonlinear Nonquadratic Regulation (NNR) can be used to find a cubic feedback that stabilizes it faster.