Polynomial approximation on subintervals for the solution of optimal control problems

In this document, we present a novel approach for approximating analytical solutions to differential equations, referred to as the Polynomial Approximation on Subintervals (PAS) method. We demonstrate the method’s effectiveness when applied to optimal control problems. To begin, the original optimal control problem is transformed into a variational problem. Subsequently, we solve the corresponding Euler-Lagrange Equation and obtain an approximate analytical solution utilizing the innovative PAS method. To evaluate its performance, we provide a numerical example that includes a comparative analysis between the outcomes obtained with PAS and those achieved by other researchers who employed various approximation techniques.