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Optimal control of the generalized Kuramoto-Sivashinsky equation with energy- and entropy-based objectives
Phys. Rev. E 114, 034204 – Published 4 September, 2026
DOI: https://doi.org/10.1103/b2h7-b2qs
Abstract
We conduct numerical simulations of a noisy generalized Kuramoto-Sivashinsky system under optimal control. The cost functions are kinetic energy and permutation entropy, which are designed to reduce the kinetic energy and the permutation entropy, respectively. The results demonstrate that kinetic-energy-based control strongly suppresses the structures and drives the system into a trivial state. In contrast, the permutation-entropy-based control preserves nontrivial structures, although the reduction in kinetic energy is smaller and requires only slight actuation energy. These findings provide insight into designing control strategies for complex systems where both efficiency and functional richness are desired.
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