One of the challenges encountered in the application of classical reinforcement learning methods to real-control problems is the curse of dimensiality. In order to overcome this difficulty, hybrid algorithms that combine reinforcement learning with various Function approximators have attracted many research interests. In this paper, a novel Neural Reinforcement Learning (NRL) scheme which is based on Sarsa learning and Radial Basis Function (RBF) network is proposed. The RBF network is used to approximate the Action Value Function (AVF) on-line. The inputs of RBF network are state-action pairs of system and its outputs are corresponding approximated AVF. As the necessary condition for the convergence ofNSL to the optimal task performance, the existence of stationary points for NSL which coincide with the fixed points of Approximate Action Value Iteration (AAVI) are proved. The validity of the proposed algorithmis tested through simulation examples: mountain car control task, and acrobot problem. Overall results demonstrate that our algorithm can effectively improve convergence speed and the efficiency of experience exploitation.

In this paper, we propose a new method for solving the stochastic advection-diffusion equation of Ito type. In this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit Milstein scheme for the resulting linear stochastic system of differential equation. The main purpose of this paper is the stability investigation of the applied method. Finally, some numerical examples are provided to show the accuracy and efficiency of the proposed technique.

In the present work we deal with the approximation properties of certain linear polynomial operators in rearrangement invariant quasi Banach Function spaces. We obtain some Jackson type direct theorem and sharp converse theorem of trigonometric approximation with respect to fractional positive order moduli of smoothness in these spaces.

This paper is concerned with the problem of designing a robust adaptive controller for flexible joint robots (FJR). Under the assumption of weak joint elasticity, FJR is firstly modeled and converted into singular perturbation form. The control law consists of a FAT-based adaptive control strategy and a simple correction term. The first term of the controller is used to stability of the slow dynamics, and the second term is used to damp out the elastic oscillations of the joints. The stability analysis is provided according to the Lyapunov direct method. Simulation results on a single-link FJR demonstrate suitable performance of the proposed control schemes.

Among all statistical distributions, standard normal distribution has been the most important and practical distribution in which calculation of area under probability density Function and cumulative distribution Function are required. Unfortunately, the cumulative distribution Function of this is, in general, expressed as a definite integral with no closed form or analytical solution. Consequently, it has to be approximated. In this paper, attempts have been made for Winitzki's approximation to be proved by a new approach. Then, the approximation is improved with some modifications and shown that the maximum error resulted from this is less than 0.0000584. Finally, an inverse Function for computation of normal distribution quantiles has been derived.