  Integral reinforcement learning (IRL) was proposed in literature to obviate
the requirement of drift dynamics in adaptive dynamic programming framework.
Most of the online IRL schemes in literature require two sets of neural network
(NNs), known as actor-critic NN and an initial stabilizing controller.
Recently, for RL-based robust tracking this requirement of initial stabilizing
controller and dual-approximator structure could be obviated by using a
modified gradient descent-based update law containing a stabilizing term with
critic-only structure. To the best of the authors' knowledge, there has been no
study on leveraging such stabilizing term in IRL algorithm framework to solve
optimal trajectory tracking problems for continuous time nonlinear systems with
actuator constraints. To this end a novel update law leveraging the stabilizing
term along with variable gain gradient descent in IRL framework is presented in
this paper. With these modifications, the IRL tracking controller can be
implemented using only critic NN, while no initial stabilizing controller is
required. Another salient feature of the presented update law is its variable
learning rate, which scales the pace of learning based on instantaneous
Hamilton-Jacobi-Bellman error and rate of variation of Lyapunov function along
the system trajectories. The augmented system states and NN weight errors are
shown to possess uniform ultimate boundedness (UUB) stability under the
presented update law and achieve a tighter residual set. This update law is
validated on a full 6-DoF nonlinear model of UAV for attitude control.
