A novel MRAC-based fractional adaptive control design for a class of fractional order linear systems

This paper proposes a new model reference adaptive control design for a class of fractional order linear systems with unknown model parameters. The objective of the synthesized adaptive controller is to force the controlled plant to track the desired reference model dynamics. Using the Lyapunov stability theorem, we show that the closed loop system is stabilized with this control action and that the parameter estimation error converges to zero. Two numerical simulation examples results verify the desired fractional adaptive control system stability and tracking performance.