L1 Adaptive Control for Fractional-Order Systems

Abstract

Fractional-order calculus has attracted the attention of scholars in the areas of control and system analysis.However, despite its notable advantages, ℒ1 adaptive control technique remains unexplored in this field.This thesis introduces an extension of this technique to fractional-order systems. Firstly, a new fractional-order ℒ1 adaptive controller is proposed for a class of fractional-order systems with matched uncertaintiesand external disturbances. Then, the controller is generalized to the case of multiple-input multiple-outputincommensurate systems. The extension of the methodology is possible thanks to the use of a fractional-order sliding surface, simplifying the control architecture and facilitating stability analysis. In the pursuitof enhancing the developed controller, neural networks are employed to handle time-varying input gainand unmodeled dynamics. Additionally, fuzzy logic systems are implemented to tackle various sources ofuncertainty within the system. These include unknown input nonlinearities, unmodeled system dynamics,and external disturbances. The analysis of the obtained theoretical and simulation results confirms thatthe developed strategies guarantee closed-loop stability maintaining the key features of the ℒ1adaptivecontroller.