Optimal control of convective FitzHugh-Nagumo equation

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Uzunca M., Kucukseyhan T., YÜCEL H., KARASÖZEN B.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.73, no.9, pp.2151-2169, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 9
  • Publication Date: 2017
  • Doi Number: 10.1016/j.camwa.2017.02.028
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2151-2169
  • Keywords: FitzHugh-Nagumo equation, Traveling waves, Sparse controls, Second order optimality conditions, Discontinuous Galerkin method, DISCONTINUOUS GALERKIN METHODS, OPTIMAL BOUNDARY CONTROL, SPARSE OPTIMAL-CONTROL, DIFFUSION EQUATIONS, ERROR ANALYSIS, CONTROL CONSTRAINTS, BLOOD-COAGULATION, ELLIPTIC PROBLEMS, SIPG METHOD, MODEL
  • Middle East Technical University Affiliated: Yes

Abstract

We investigate smooth and sparse optimal control problems for convective FitzHugh Nagumo equation with traveling wave solutions in moving excitable media. The cost function includes distributed space time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several numerical results are presented for the control of the traveling waves. We also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing Tikhonov regularization parameter. Further, we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced Hessian. (C) 2017 Elsevier Ltd. All rights reserved.