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Integral reinforcement learning (IRL) was proposed in literature to obviatethe 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 stabilizingcontroller and dual-approximator structure could be obviated by using amodified gradient descent-based update law containing a stabilizing term withcritic-only structure. To the best of the authors' knowledge, there has been nostudy on leveraging such stabilizing term in IRL algorithm framework to solveoptimal trajectory tracking problems for continuous time nonlinear systems withactuator constraints. To this end a novel update law leveraging the stabilizingterm along with variable gain gradient descent in IRL framework is presented inthis paper. With these modifications, the IRL tracking controller can beimplemented using only critic NN, while no initial stabilizing controller isrequired. Another salient feature of the presented update law is its variablelearning rate, which scales the pace of learning based on instantaneousHamilton-Jacobi-Bellman error and rate of variation of Lyapunov function alongthe system trajectories. The augmented system states and NN weight errors areshown to possess uniform ultimate boundedness (UUB) stability under thepresented update law and achieve a tighter residual set. This update law isvalidated on a full 6-DoF nonlinear model of UAV for attitude control.

Critic-Only Integral Reinforcement Learning Driven by Variable Gain Gradient Descent for Optimal Tracking Control