A Riccati-equation-based algorithm for continuous-time optimal control problems

In this paper we consider continuous-time unconstrained optimal control problems. We propose a computational method which is essentially based on the closed-loop solutions of the linear quadratic optimal control problems. In the proposed algorithm, Riccati differential equations play an important role. We prove that accumulation points generated by the present algorithm, if they exist, satisfy the weak necessary conditions for optimality, under some assumptions including Kalman's sufficient conditions for the bounded Riccati solutions. In addition, we also propose the simple but effective technique to guarantee the boundedness of the solutions of Riccati equations. Lastly, we illustrate the usefulness of the present algorithm through simulation experiences.