Neural network H/sub /spl infin// state feedback control with actuator saturation: the nonlinear benchmark problem

In this paper, we describe a constrained H/sub /spl infin// state feedback controller to stabilize the Rotational/Translational Actuator (RTAC) benchmark problem with L/sub 2/ disturbance attenuation. The design method requires formulating the corresponding Hamilton-Jacobi-Isaacs equation (HJI) by encoding the input constraints via a quasinorm, and performing quasi L/sub 2/-gain analysis of the corresponding closed-loop nonlinear system. An iterative solution technique based on the game theoretic interpretation of the HJI equation is presented. It is shown that the derived constrained state feedback control law has the largest region of definition than any other controller with the same attenuation gain. A computational offline algorithm is given to successively solve the HJI equation using neural networks. The result is a closed-loop neural network constrained state feedback controller that guarantees closed loop stability and L/sub 2/-gain boundedness of disturbances over a certain predefined region of the state space.