Numerical Computations on Feedback Control and State Estimation of the Kuramoto-Sivashinsky Equation


Valentine Blez L. Lampayan1, Christian Victor L. Arellano2, Jose Ernie C. Lope2,
and Ricardo C.H. del Rosario*2

1Division of Natural Sciences and Mathematics,
University of the Philippines in the Visayas, Tacloban College
Magsaysay Blvd., Tacloban City
2Institute of Mathematics, University of the Philippines Diliman
C.P. Garcia St., U.P. Campus, Quezon City

corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.



We considered the problem of minimizing the fluctuations of thin film flow which was modeled by the Kuramoto-Sivashinsky equation, a scalar nonlinear partial differential equation. We specifically addressed the problems of determining the optimal locations of the sensors and actuators, estimating the state from partial state observations and formulating a feedback control method. The control methodology was based on the LQR/LQG theory and its extension to nonlinear problems. In the numerical implementation of the feedback control methods, we considered systems with different viscosities, and we compared the performance of feedback controls based on the linear and nonlinear systems. Our results showed that the control and state estimation strategies based on the linear system performed as well as the strategies based on the nonlinear system. This result is useful for real-time applications where the computation time for the feedback coefficients is crucial.



The simulation and control of fluid flow has been studied for decades but it remains an active research area until today as it produces interesting results due to the complexity of its dynamics. The fundamental description of fluid flow is given by the Navier-Stokes equation but its numerical approximation is still too complicated even with the most powerful computers and most advanced numerical methods. The Kuramoto-Sivashinsky Equation (KSE) is a simplification of the Navier-Stokes equation which retains the most important . . . . . . . . . . . . . .





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