№2, 2011

APPLICATION OF ARTIFICIAL NEURAL NETWORK IN OPTIMAL PURSUIT PROBLEM WITH RESPECT TO DOMAIN

Kambiz Majidzadeh

In the present paper, the convex domain’s space is constructed and a scalar product is introduced. The derivative of a domain function in this space is defined. Using this approach, a method is proposed to investigate an optimal control pursuit problem with respect to domain. Unlike the traditional problem, here the controller and trajectory are a domain at each moment of time. In other words, controller and trajectory are a domain function. At first we show the existence of the solution of Cauchy problem where the process is described, and then prove the maximum principle for the considered optimal control problem. Using the obtained results, we offer an algorithm for its numerical solution and train it to neural network. (p. 38-48)

Keywords: support function, optimal pursuit, artificial neural network, network training.
References
  • Sokolowski, J.-P.Zolesio, Introduction to shape optimization // Shape Sensitivity Analysis, Springer, Heidelberg, 1992.
  • J. Haslinger, R.A.E.Makinen, Introduction to shape optimization // theory, approximationand computation, SIAM, Philadelphia, 2003.
  • A.A. Niftiyev, C.I.Zeynalov, H.C.Efendiyeva, Optimal control problem relatively to domain evolution // International Journal of Applied Mathematics (IJAM). 2010, v.23, no.3, pp. 527-538.
  • V.F. Demyanov, A.M.Rubinov, Bases of non-smooth analysis and quasidifferential calculus, M.: “Nauka”, 1990.
  • Y.S.Gasimov, A. Nashaoui, A.A. Niftiyev, Nonlinear eigenvalue problems for p-laplacian // Optimization Letters, 2010, no.4, pp.67-84.
  • A.Niftiyev, E.R.Akhmadov, Variational statement of an inverse problem for a domain // Journal Differential equation, 2007, v.43, no.10, pp.1410-1416.
  • K. Majidzadeh, Application of neural networks to the problems on finding the form in dynamic processes // Transaction of Azerbaijan Nat. Acad. of Sciences, Information Technology, Baku, 2011, no.3, pp. 141-147.
  • R.M.Aliguliyev, K.Majidzadeh , Y.Ghasemi, Application of neural networks to finding optimal form // Problems of Information Technology, Baku, 2010, no.2, pp. 47-51.
  • F.P. Vasilyev, Optimization methodsMoscow, “Factorial Press”, 2002, 824 p.
  • Ward Cheney, Will Light A., Course in Approximation Theory. Brooks/Cole,
  • R.M. Alguliev, R.M. Aliguliyev, R.K. Alekperov, An approach to optimal task assignment in a distributed system // Journal Automation and Information Sciences, 2004, v.36, no.10, pp.51-55.