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An important issue in the area of multi-operation systems is the observation of a discontinuous trajectory. In order to track a discontinuous output trajectory, we choose impulsive differential systems to generate a series of local continuous state trajectories, which become a set of output trajectories via the action of the output functions. Concerning impulsive differential control systems, we design proportional–derivative (PD-type) and proportional plus one order derivative and fractional order derivative (PDDα-type) iterative learning control laws with initial state learning. In particular, the PDDα-type law is more flexible due to the impact of a certain fractional order factor α. Thereafter, we give the associated convergence characteristics by establishing sufficient conditions on open-loop and closed-loop iterative learning schemes in the sense of λ-norm under mild assumptions. Finally, several numerical examples, including an application to robotic fish, are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we design learning law with high-order internal models for fractional order differential equations to track the varying reference accurately by adopting a few iterations in a finite time interval. We establish sufficient conditions of convergence for the P-type and PD-type updating law for different fractional order differential equations. Finally, we give some numerical examples to demonstrate the validity of the designed method. [ABSTRACT FROM AUTHOR]

In order to track the discontinuous reference trajectory accurately using a few iterations in a finite time interval, we design a P-type iterative learning control law with initial state learning for a noninstantaneous impulsive fractional-order system. The convergent sufficient conditions of open-loop and closed-loop iterative learning schemes are established. Finally, two numerical examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]