Further Results on Optimal Tracking Control for Nonlinear Systems With Nonzero Equilibrium via Adaptive Dynamic Programming

This article develops a novel cost function (performance index function) to overcome the obstacles in solving the optimal tracking control problem for a class of nonlinear systems with known system dynamics via adaptive dynamic programming (ADP) technique. For the traditional optimal control problems, the assumption that the controlled system has zero equilibrium is generally required to guarantee the finiteness of an infinite horizon cost function and a unique solution. In order to solve the optimal tracking control problem of nonlinear systems with nonzero equilibrium, a specific cost function related to tracking errors and their derivatives is designed in this article, in which the aforementioned assumption and related obstacles are removed and the controller design process is simplified. Finally, comparative simulations are conducted on an inverted pendulum system to illustrate the effectiveness and advantages of the proposed optimal tracking control strategy.