A Riccati-equation-based algorithm for nonlinear optimal control problems

In this paper, we propose an iterative method for numerical solutions of unconstrained nonlinear optimal control problems, which is essentially based on the closed loop solutions of the linear quadratic optimal control problems. We also prove that accumulation points generated by the algorithm, if they exist, satisfy the weak necessary conditions for optimality. Moreover, we illustrate the numerical effectiveness of the present algorithm through five examples by simulation.