Feedback semiglobal stabilization to trajectories for the Kuramoto-Sivashinsky equation
S\'ergio S. Rodrigues, Dagmawi A. Seifu
TL;DR
This paper demonstrates that an oblique projection-based feedback control can stabilize the Kuramoto-Sivashinsky equation's state to a desired trajectory using finite actuators, with simulations confirming effectiveness in 1D.
Contribution
It introduces a novel feedback control method employing oblique projections for stabilizing the Kuramoto-Sivashinsky equation to time-dependent trajectories.
Findings
Feedback control successfully stabilizes the equation in simulations.
Finite number of actuators effectively control the system.
Method applicable to rectangular domains with finite actuators.
Abstract
It is shown that an oblique projection based feedback control is able to stabilize the state of the Kuramoto-Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The number of actuators is finite and consists of a finite number of indicator functions supported in small subdomains. Simulations are presented, in the one-dimensional case, showing the stabilizing performance of the feedback control.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Stability and Controllability of Differential Equations