Optimal control of uncertain nonlinear systems using a neural network and RISE feedback

A sufficient condition to solve an optimal control problem is to solve the Hamilton-Jacobi-Bellman (HJB) equation. However, finding a value function that satisfies the HJB equation for a nonlinear systems is challenging. Previous efforts have utilized feedback linearization methods which assume exact model knowledge, or have developed neural network (NN) approximations of the HJB value function. The current effort builds on our previous efforts to illustrate how a NN can be combined with a recent robust feedback method to asymptotically minimize a given quadratic performance index as the generalized coordinates of a nonlinear Euler-Lagrange system asymptotically track a desired time-varying trajectory despite general uncertainty in the dynamics. A Lyapunov analysis is provided to examine the stability of the developed optimal controller.