Application of fractional derivative in control functions

Application of fractional derivative in control problems such as sliding surface design in sliding mode control, training of MLP in neural networks, and parameters updating in model reference adaptive control is studied in this paper. Use of the fractional derivative increases possibility of improving the control performance by reducing the convergence time in the mentioned control problems. This gain is attained due to the higher degree of freedom exist in the fractional dynamical systems. We study such control problems by replacing the integer order derivative with the fractional order derivative. The performance of the proposed methods is illustrated through computer simulations of gyro and ball and beams systems.