NUMERICAL APPROXIMATION OF OPTIMAL CONTROL PROBLEMS CONSTRAINED BY DYNAMIC EQUATIONS VIA GALERKIN METHOD

Matthew Folorunsho  Akinmuyise; AKINWUMI  SHARIMAKIN; ILESANMI  FAKUNLE

Matthew Folorunsho Akinmuyise Department of Mathematics, Adeyemi University of Education, Ondo, Ondo State, Nigeria
AKINWUMI SHARIMAKIN Department of Economics, Adeyemi University of Education, Ondo, Ondo State, Nigeria
ILESANMI FAKUNLE Department of Mathematics, Adeyemi University of Education, Ondo, Ondo State, Nigeria

Keywords: Unconstrained problem, orthogonal vector, Hamiltonian, System of equations, Galerkin method, Tolerance

Abstract

The research investigates the application of the Galerkin method to optimal control problems constrained by coupled dynamic equations. These
constrained problems are reformulated into unconstrained ones using the Hamiltonian approach, which facilitates the determination of boundary conditions
for both the state and costate variables. By assuming a polynomial solution, the weighted and residual functions were derived. The Orthogonality of the
product of these functions leads to the formation of a system of linear equations. Solving these equations provides the solution for the boundary condi-
tions through direct substitution. This scheme was developed for the Lagrange form of optimal control problems to assess its accuracy in approximating exact
solutions. Several optimal control problems with known exact solutions were solved using the proposed scheme, and the results were compared to evaluate
its eectiveness.

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