Composite observer-based backstepping tracking control of fractional-order chaotic systems

An observer-based backstepping strategy is constructed for fractional-order chaotic systems. A disturbance observer and a state observer are simultaneously constructed to gain the estimations of uncertain disturbances and unmeasurable states, respectively, and an auxiliary system is developed to connect the two observers. Then, a fractional-order command filter is used to avoid tedious derivatives of virtual signals so as to reduce computational burden. A coupling backstepping controller, which ensures the convergence of tracking error and the boundedness of closed-loop signals, is constructed. Finally, two simulation examples are given to verify the effectiveness of theoretical analysis.