Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation

Abstract

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.

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Cited by in corpus (4)

• Feedback control of surface roughness in a one-dimensional KPZ growth process
• Variational Optimization Based Reinforcement Learning for Infinite Dimensional Stochastic Systems
• The role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar--Parisi--Zhang growth process
• Variational Inference for Stochastic Control of Infinite Dimensional Systems