Iterative Learning Control For Second-Order Hyperbolic Impulsive Distributed Parameter Systems

Second-order hyperbolic impulsive distributed parameter systems accurately reflect the sudden change phenomena of the system while taking into account the two-dimensional variables of time and space,and have a wide range of background applications in fields such as materials chemistry,rehabilitation medicine and aerospace.However,second-order hyperbolic impulsive distributed parameter systems have infinite dimensional degrees of freedom and transient steps can cause discontinuities in the system,leading to a more complex study of its control problems.Iterative learning control is an intelligent algorithm that imitates the human ’learning’ process,constantly updating the learning strategy in a repeatedly running system to achieve complete tracking of the desired output.It is suitable for solving control problems of second-order hyperbolic impulsive distributed parameter systems due to its simplicity,ease of implementation and less a priori knowledge required.At present,research on iterative learning control of impulsive systems is mainly focused on ordinary differential systems,but research on impulsive distributed parameter systems described by partial differential equations is rare.In particular,no research has been reported on the iterative learning control of second-order hyperbolic impulsive distributed parameter systems.This dissertation addresses issues related to the iterative learning control of secondorder hyperbolic impulsive distributed parameter.The main research work of the paper is as follows:(1)Firstly,the problem of convergence analysis of a second-order linear hyperbolic impulsive distributed parameter system is investigated.Two iterative learning control algorithms,open-loop and closed-loop,are designed and analysed rigorously by using mathematical tools such as the impulsive Gronwall inequality,a mild solution based on operator semigroup theory,and the contraction mapping method,so that the actual output of the system completely tracks the desired output trajectory.The results obtained show that the tracking error of the system over a finite time interval can converge to zero along the iterative axis when a finite number of impulses is involved.The validity of the theoretical results is verified by two numerical simulation examples.(2)Secondly,the complete tracking problem is investigated for two second-order nonlinear hyperbolic impulsive distributed parameter system with different state initial value cases.When the initial value of the state is fixed,a P-type distributed iterative learning control algorithm is used to establish sufficient conditions for the convergence of the tracking error.For the case in which the initial value of the state is offset,an initial state iterative learning control algorithm is designed to ensure the tracking performance of the system output.The simulation results verify the effectiveness of the proposed iterative learning control algorithms.(3)Finally,an open-loop iterative learning consensus control protocol containing network topology information and information about adjacent agents is proposed for the consensus control problem of second-order nonlinear hyperbolic impulsive distributed parameter multi-agent systems.A convergence analysis of the consensus error is given.Based on this,an open-closed-loop consensus control protocol is proposed in order to improve the convergence speed of the system.Theoretical results show that the consensus error between any two agents converges to zero as the number of iterations increases under the given conditions.The effectiveness of its iterative learning control protocol is verified by two numerical simulations.