Abstract
In this paper, we propose a fractional order adaptive backstepping control solution to the saturation problem of incommensurate fractional order system with uncertainty and non-linearity. A model transformation is introduced to make the system appropriate to backstepping scheme, and the virtual signals are generated to compensate saturation via the construction of fractional order auxiliary system. By indirect Lyapunov method, the backstepping procedure is applied to fractional order systems with input saturation for the first time, which achieves the goals of stabilization and tracking. Finally, the effectiveness of the proposed fractional order backstepping is demonstrated in several examples.
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