  This paper presents a novel method of global adaptive dynamic programming
(ADP) for the adaptive optimal control of nonlinear polynomial systems. The
strategy consists of relaxing the problem of solving the
Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is
solved via a new policy iteration method. The proposed method distinguishes
from previously known nonlinear ADP methods in that the neural network
approximation is avoided, giving rise to significant computational improvement.
Instead of semiglobally or locally stabilizing, the resultant control policy is
globally stabilizing for a general class of nonlinear polynomial systems.
Furthermore, in the absence of the a priori knowledge of the system dynamics,
an online learning method is devised to implement the proposed policy iteration
technique by generalizing the current ADP theory. Finally, three numerical
examples are provided to validate the effectiveness of the proposed method.
