Static and dynamic stabilizing neural controllers, applicable to transition between equilibrium points

A design method for stabilization of nonlinear systems by feedforward and recurrent neural networks is proposed, applicable to transition between equilibrium points with local stabilization at the endpoint. Both static and dynamic state and output feedback stabilizing neural control are discussed. The link with linear controller design techniques is explained by linearizing the model around the target equilibrium point and incorporating the linear controller design results in the neural controller. The weights are learned o -line and are the solution to a nonlinear optimization problem through simulation of the system. The method is illustrated with the example of swinging up the pole of an inverted pendulum system with local stabilization at the upper equilibrium point, both by a feedforward and a recurrent neural network.