Research On Iterative Learning Control Problem Of Impulsive Differential Systems

As a kind of mathematical model to describe the mutation phenomenon, impulsive differential systems have been widely used in industrial and economic fields. Iterative learning control technology, as a solution for a class of tracking problems, has been widely used in equipment manufacturing, machine operation and other industrial fields. In order to solve some finite time interval tracking problems with instantaneous mutation trajectory, this paper mainly studies the iterative learning control problem of Impulsive differential systems. The contents are follows:First, in order to extend the classical method and the results of the continuous trajectory tracking to the discontinuous trajectory, we have done the following work for nonlinear impulsive systems:We designed the open-loop and closed-loop P-type learning law with initial learning. Based on the impulsive Gronwall inequality and Holder inequal-ity, we give a sufficient condition for the convergence of the initial state deviation case in the sense of L2-norm. Numerical examples are presented to demonstrate effectiveness of the proposed theory results.Second, considering the D-type controller has the characteristics of prospective and forecast, we designed the open-loop and closed-loop PD-type learning law with initial learning. We give a sufficient condition for the convergence of the initial state devi-ation case in the sense of A-norm. Numerical examples are presented to demonstrate effectiveness of the proposed theory results.Finally, to make the controller more flexible control means, we designed the open-loop and closed-loop PDDa-type learning law with initial learning. Based on the formula of integration by parts with fractional order calculus, we give a sufficient condition for the convergence of the initial state deviation case in the sense of A-norm. By numerical examples, we also proved the effectiveness of the proposed theory results. To show the PDDa-type learning law is superior to the P-type learning law and the P_D-type learning law in terms of the iteration speed and convergence precision, it is applied to the speed control of a robotic fish.