Solving Riccati differential equations with multilayer neural networks

The tangential linearisation along the solution curve in a state space has been proposed for solving the feedback stabilisation of a nonlinear system. With the technique a nonlinear control problem can be transferred into a linear time-varying one. However, the Riccati differential equation for the optimal control of the linearised system is not only time dependent, but also the state and input-signal dependent. Therefore, one can not obtain the solution with a general method. In this paper we propose to train multilayer neural networks to get an approximate solution for the Riccati differential equation. An example shows that this method can lead to a good result.