Optimization of nonlocal time-delayed feedback controllers

Peter Nestler (), Eckehard Schöll () and Fredi Tröltzsch ()
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Peter Nestler: Technische Universität Berlin
Eckehard Schöll: Technische Universität Berlin
Fredi Tröltzsch: Technische Universität Berlin

Computational Optimization and Applications, 2016, vol. 64, issue 1, No 10, 265-294

Abstract: Abstract A class of Pyragas type nonlocal feedback controllers with time-delay is investigated for the Schlögl model. The main goal is to find an optimal kernel in the controller such that the associated solution of the controlled equation is as close as possible to a desired spatio-temporal pattern. An optimal kernel is the solution to a nonlinear optimal control problem with the kernel taken as control function. The well-posedness of the optimal control problem and necessary optimality conditions are discussed for different types of kernels. Special emphasis is laid on time-periodic functions as desired patterns. Here, the cross correlation between the state and the desired pattern is invoked to set up an associated objective functional that is to be minimized. Numerical examples are presented for the 1D Schlögl model and a class of simple step functions for the kernel.

Keywords: Schlögl model; Nagumo equation; Pyragas type feedback control; Nonlocal delay; Controller optimization; Numerical method (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9809-6

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