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In this paper, we utilize fractional calculus, theory of semigroup and fixed point approach to prove existence and approximate controllability results for a class of fractional differential equations (FDEs) with noninstantaneous impulses by constructing a suitable composite control function, imposing that the associated linear problem is approximately controllable on the terminal subinterval and dividing our global task into many subtasks on each subinterval. Next, we apply P-type iterative learning control (ILC) updating law to generate a sequence of control functions to find a desired control function to guarantee the error between the output and the desired reference trajectories tending to zero via a suitable norm in the sense of uniform convergence. As a result, the limit of the sequence of control functions is the required control to guarantee the above problem is approximately controllable. In addition, a numerical example is illustrated to demonstrate ILC scheme to solve approximate controllability of time fractional impulsive PDEs via tracking the given continuous and discontinuous trajectory. [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]