Optimal control of uncertain nonlinear systems using RISE feedback

Abstract

A Hamilton-Jacobi-Bellman optimization scheme is used along with a RISE feedback structure to minimize a quadratic performance index while the generalized coordinates of a nonlinear Euler-Lagrange system asymptotically track a desired time-varying trajectory despite general uncertainty in the dynamics, such as additive bounded disturbances and parametric uncertainty. Motivated by recent previous results that use a neural network structure to approximate the dynamics (i.e., the state space model is approximated with a residual function reconstruction error), the result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semiglobal asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. Simulation results are included to demonstrate the performance of the developed controller. © 2008 IEEE.