A novel algorithm on adaptive backstepping control of fractional order systems

This article presents a new method of designing the adaptive backstepping controller for triangular fractional order systems with non-commensurate orders. The fractional order indirect Lyapunov method is available for the 0<α<1 case, by introducing the appropriate transformations of frequency distributed model. Meanwhile, based on the semigroup property of fractional order derivative and the fractional order tracking differentiator, we extend the result to the 1<α<2 case. The case of controlling fractional order systems with unknown control input coefficient is also investigated. Simulation examples are given to demonstrate the effectiveness of the proposed controllers.