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Control of rare intense events in spatiotemporally chaotic systems

University of Maryland, College Park, Maryland 20742, USA

Phys. Rev. E 76, 066206 – Published 18 December, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.066206

Abstract

We address the problem of using feedback control for the purpose of suppressing rare intense events in spatially extended systems. As an example, we investigate the use of control to suppress turbulent spikes in the complex Ginzburg-Landau equation in the limit of small dissipation. We explore how information obtained by forecasting can be used to implement spatially and temporally localized control parameter changes and how control strength and cost are related to effectiveness in this framework. The effects of model error and imperfect state measurement are also considered.

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In addition to control by modifying an intrinsic parameter of the system (e.g., our discussion of changing the parameter $α$ ), one might also envision adding an externally applied “control force” $f (x, t)$ to the right-hand side of Eq. (1) with the intrinsic system unchanged. We note, however, that our changing of $α$ can also be viewed as an external force control with $f (x, t)$ chosen to be $i α (α^{'} (x, t) - α) {| u |}^{2} u$ . Other choices for the control force $f (x, t)$ might, e.g., utilize an added nonlinear dissipation [such as $- m (x, t) {| u |}^{σ} u$ with $σ = 2, 3, \dots$ ] or an added dispersion [such as $i p (x, t) \nabla^{2 n} u$ with $n = 1, 2, \dots$ ]. We have tried some of these alternative forms for the control and found that they can also perform well when used in our forecast driven control scenario illustrated in Fig. 5.
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Control of rare intense events in spatiotemporally chaotic systems

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