Adaptive Actor-Critic with Integral Sliding Manifold for Learning Control of Robots

Abstract

The synthesis of reinforcement learning techniques, as adaptive actor-critic method, has provided sound techniques to learn a robot’s action, generally using recurrent neural networks that approximate the unknown functionals without prior training. On the other hand, invariant manifolds have been studied to yield dimensionality reduction for efficient learning. In this paper, inspired by both schemes and the seminal approach of Campos and Lewis, we propose an integral manifold as a dynamical performance evaluator, PE, to drive an adaptive critic-action scheme. It is shown that an integral sliding mode is enforced; thus, the learning is driven by an invariant manifold. Thus, an exponential error convergence with closed-loop stability in the Lyapunov sense is guarantee together with smooth control action. Simulations show the numerical behavior for a nonlinear dynamical robot learning to follow a time varying trajectory.