Indirect model reference adaptive control for a class of fractional order systems

This article focuses on the indirect model reference adaptive control problem for fractional order systems. A constrained gradient estimation method was established firstly, since parameter estimation is part and parcel of the whole control problem. Then a novel adaptive control law is designed, from which the two problems, i.e., parameter estimation and reference tracking, can be unified perfectly. On these basis, an effective control scheme is established. The stability of the resulting closed-loop system is analyzed rigorously via indirect Lyapunov method and frequency distributed model. Finally, a careful simulation study is reported to illustrate the effectiveness of the proposed scheme.