Adaptive Fuzzy Control for Fractional-Order Interconnected Systems With Unknown Control Directions

Abstract

This article concentrates on the study of the decentralized fuzzy control method for a class of fractional-order interconnected systems with unknown control directions. To overcome the difficulties caused by the multiple unknown control directions in fractional-order systems, a novel fractional-order Nussbaum function technique is proposed. This technique is much more general than those of existing works since it not only handles single/multiple unknown control directions but is also suitable for fractional-/integer-order single/interconnected systems. Based on this technique, a new decentralized adaptive fuzzy control method is proposed for fractional-order interconnected systems with unknown strong interconnections among subsystems. Furthermore, fuzzy logic systems are utilized to approximate unknown nonlinearities. It is proven that the designed controller can guarantee the boundedness of all signals in interconnected systems and the convergence of tracking errors. Two examples are given to show the validity of the proposed method.