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

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 Hamil-

tonian 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 equa-

tions. 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 e ectiveness.