Research On Iterative Learning Control Algorithms For Singular Systems

Singular systems are a class of more general dynamical systems,widely existing in complex power grid systems and decision systems.Compared with normal systems,singular systems can better describe the physical characteristics of the system.Iterative learning control(ILC)is an important branch in the field of intelligent control,which is suitable for periodically controlled objects.Iterative learning control consists of two processes: time process and iterative process.The two-dimensional system theory(also called 2-D system theory)can simultaneously express the dynamic process of the time domain and the learning process of space.The application of the 2-D system theory to the iterative learning control is called the 2-D method.In the research results of iterative learning control,most of them are concerned with the normal system.The main work of this article is as follows:1.For a class of linear discrete singular systems,an iterative learning control algorithm is proposed.The linear discrete Rosser model of the system is established by using the 2-D system theory.The convergence analysis of the proposed algorithm is completed.The numerical example simulation shows the effectiveness of the algorithm.2.We study the output convergence of the linear discrete singular system when the initial state of the initial value changes in the bounded neighborhood of the expected initial value.A discrete iterative learning control algorithm is designed by using the 2-D linear discrete system theory and the sufficient necessary conditions for the convergence of the algorithm are given.Finally,the effectiveness of the algorithm is verified by numerical simulation.3.For linear discrete singular systems with state delay,the robustness of the system output under given learning law is studied on the basis of 2-D system theory.The numerical simulation proves that the actual output of the system converges to the ideal output under the action of the algorithm.4.The convergence speed of iterative learning control for singular systems is studied.Based on the principle of the equivalent type decomposition and the compression mapping of the generalized system,the sufficient conditions for the convergence of the first order iterative learning control algorithm and the two order iterative learning control algorithm are discussed respectively.With the help of Q factor,the convergence rate of the first order learning law and the two order learning law is compared.The magnitude of the convergence rate of the first order learning law and the two order learning law depends on the different combinations of the learning gain.Numerical simulations verify the effectiveness of the two algorithms and the relationship between the speed of convergence and the different values of learning gains.