A class of integrable riccati equations and applications to optimal control

In this paper, based on the theory of Lie group and the Hamilton-Jacobi Theorem, the solution of the second-order linear homogeneous equations which can be obtained from a class of Riccati equations by transformation are considered. By solving the corresponding Hamilton-Jacobi equations, a class of integrable Riccati differential equations is obtained. Finally, the classical optimal control problem with finite time be considered, and a class of systems for the optimal control problem is solved by using the proposed method to solving the corresponding Riccati equations.