  In this paper, a continuous-time adaptive actor-critic reinforcement learning
(RL) controller is developed for drift-free nonlinear systems. Practical
examples of such systems are image-based visual servoing (IBVS) and wheeled
mobile robots (WMR), where the system dynamics includes a parametric
uncertainty in the control effectiveness matrix with no drift term. The
uncertainty in the input term poses a challenge for developing a
continuous-time RL controller using existing methods. In this paper, an
actor-critic or synchronous policy iteration (PI)-based RL controller is
presented with a concurrent learning (CL)-based parameter update law for
estimating the unknown parameters of the control effectiveness matrix. An
infinite-horizon value function minimization objective is achieved by
regulating the current states to the desired with near-optimal control efforts.
The proposed controller guarantees closed-loop stability and simulation results
validate the proposed theory using IBVS and WMR examples.
