Numerical solutions of optimal control problems constrained by PDEs with time-dependent coefficients

Document Type : Original Article

Author

Department of Mathematics, University of Qom, Qom, Iran.

Abstract

This paper develops a numerical approach to solve an optimal‎‎ control problem‎, ‎which is governed by a‎‎ parabolic partial differential equation (PDE) with time-dependent coefficients‎. ‎First‎, ‎by‎ considering the PDEs and using the HDMR method‎, ‎the‎‎ time-dependent coefficients are approximated and the PDE is transformed into a set of PDEs with constant coefficients‎.‎ In the next step‎, ‎these PDE problems are transformed‎‎ to high-dimensional nonhomogeneous ordinary differential equation system (ODES)‎. ‎Then‎, ‎the homogeneous parts of these ODEs are solved using semigroup theory‎.‎ In the rest of the paper‎, ‎the original optimal‎‎ control problem is solved by utilizing the solution of the homogeneous‎‎ part.‎ ‎Finally‎, ‎numerical results are presented.

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