Adaptive Actor-Critic Based Optimal Regulation for Drift-Free Nonlinear Systems

In this paper, a continuous-time adaptive actor-critic reinforcement learning (RL) controller is developed for drift-free uncertain nonlinear systems. Practical examples of such systems are image-based visual servoing (IBVS) and wheeled mobile robots (WMR), where the system dynamics include a parametric uncertainty in the control effectiveness matrix with no drift term. The uncertainty in the input term poses a challenge when developing a continuous-time RL controller using existing methods. This paper presents an actor-critic/synchronous policy iteration (PI)-based RL controller with a newly derived constrained concurrent learning (CCL)-based parameter update law for estimating the unknown parameters of the linearly parametrized control effectiveness matrix. The parameter update law ensures that the parameters do not converge to $zero$, avoiding possible loss of stabilization. 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 in the presence of noise validate the proposed theory using IBVS and WMR examples.