An analytic approximate solution of the matrix Riccati differential equation arising from the LQ optimal control problems

Abstract

Approximate analytical solution of the matrix Riccati differential equation related to the linear quadratic optimal control problems, is the main goal of this paper which has a specific importance in the optimal control theory. To this end, a modification of the parametric iteration method is used. This modification, reduces the time consuming repeated calculations and improves the convergence rate of the iterational algorithm. Comparison with the existent solutions and also with the numerical Runge-Kutta (RK78) method confirms the high accuracy of the method, whilst accessibility to the analytical solutions is the preference of the new technique.