A Study Of Iterative Learning Control Synchronization Of Complex Dynamical Network

In this paper, we studied three aspects of the theory of adaptive iterative learning control which contained adaptive iteration learning control synchronization problem for complex dynamic network of non-uniform nodes, complex dynamical network with unknown control gain synchronous control problem and problem of complex dynamic network with unknown control direction synchronous control. The main contributions of this paper are as following.Firstly, for complex dynamic network of non-coincident nodes and unknown time-varying coupling strength, we present a new adaptive iterative learning control strategy in which use the saturation function to estimate the unknown time-varying coupling by studying of synchronization controlling problem of uncertain complex dynamic network. Based on the stability of Lyapunov method, we have overcome the difficulty of the design of unknown nonlinear time-varying coupling parameters adaptive law and proved the convergence of synchronization error of the parameters, and boundedness of all the signals in the closed-loop system as well. We verify the feasibility and effectiveness of the method through computer simulation examples at last.Secondly, for complex dynamical network with unknown control gain synchronous control problem, we have proposed a new adaptive iterative learning control method and designed the adaptive iterative learning controller in which we use the projection operator to estimate unknown variables. By using the Lyapunov function and the parameters of recombinant principle, we overcome the difficulties with unknown control gain and proved that the synchronization error converges to zero. By the design of a Lyapounov-krasovskii-like function, it is proved that all the signals in the closed-loop system are uniformly bounded. And we then verify the effectiveness of the method through computer simulation examples.Finally, we have designed a new controller by using the method of adaptive iterative learning control design for the complex dynamic network for the unknown control direction and the unknown time-varying strength. In the controller, the unknowntime-varying coupling strength is adaptively estimated by using saturation function. By constructing a Nussbaum function, complex dynamical network with unknown control directions are solved. We have proved the convergence of synchronous error in the limited time based on Lyapunov stability theorem and the re-parameterization method. Through a new Lyapounov-Krasovskii function, it is proved that all the signals in the closed-loop system are globally uniformly bounded. And at last simulations are given to confirm the feasibility and effectiveness of the proposed method.