A Hamilton-Jacobi setup for constrained neural network control

In this paper, we derive nonlinear state feedback controllers for constrained systems with and without disturbances via Hamilton-Jacobi equations. In the former case, we show how to formulate the associated Hamilton-Jacobi-Bellman (HJB) equation using nonquadratic functionals then solve it using successive iterations between the control and the cost function. The type of constraints considered in this case are input saturation, constrained states, and minimum-time control. Later in the paper, we include disturbance into the controller design for constrained input systems only. We show how to formulate the associated Hamilton-Jacobi-Isaac (HJI) equation using special nonquadratic supply rates to obtain the nonlinear state feedback H/sub /spl infin// control. In both Hamilton-Jacobi equations, the solution is carried over a compact set of the asymptotic stability region of an initial stabilizing control. We show through an example for the HJB case how this method enlarges the region of asymptotic stability (RAS). This is an important feature when considering constrained input systems.