Asymptotic optimal control of uncertain nonlinear Euler–Lagrange systems |
| |
Authors: | Keith Dupree Parag M Patre Zachary D Wilcox Warren E Dixon [Author vitae] |
| |
Affiliation: | aDepartment of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA |
| |
Abstract: | 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 system is challenging. For an optimal control problem when a cost function is provided a priori, 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 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 semi-global 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. An extension is included to illustrate how a NN can be combined with the previous results. Experimental results are given to demonstrate the proposed controllers. |
| |
Keywords: | Optimal control Neural networks RISE Nonlinear control Lyapunov-based control |
本文献已被 ScienceDirect 等数据库收录! |
|