Numerical methods based on Gaussian quadrature and continuous Runge-Kutta integration for optimal control problems

This paper provides a numerical approach for solving optimal control problems governed by ordinary differential equations. Continuous extension of an explicit, fixed step-size Runge-Kutta scheme is used in order to approximate state variables; moreover, the objective function is discretized by means of Gaussian quadrature rules. The resulting scheme represents a nonlinear programming problem, which can be solved by optimization algorithms. With the aim to test the proposed method, it is applied to different problems.