Iterative Learning Control For Bilinear Control Systems

Bilinear control system is the nonlinear control system with simple structure and closest to the linear system.The main characteristic of bilinear control system is the product of the state variable and the control variable.Although they are respective linear about the state as well as control variables,bilinear control systems is the nonlinear system on the whole.Although the state variables,control variables are linear.Because of these significant advantages,bilinear control systems become one of the topical issues in the field of control research.Iterative learning control(ILC)is a typical intelligent control method with strict mathematical description.ILC has been an important and effective technique in dealing with the repetitive control problem for dynamic systems with complex modeling,strong nonlinear coupling and uncertainties.Iterative learning control algorithm is designed which based on several different types of bilinear control systems in this paper.The relevant of the theory is analyzed and simulations are studied finally.This paper consists of the following five parts:1.The opening chapter shows an introduction to the research background and significance for bilinear control systems,the mathematical model and the research present situations.Meanwhile,iterative learning control,which summarizes the basic principles and the research present situations for iterative learning control.Finally,it lists the main work of this article is given.2.For a class of continuous bilinear control systems,we construct the D-type iterative learning control law and derive the convergence condition of iterative learning error.Through logarithmic error approach,it is shown a rigorous proof that guarantees the convergence of learning error.Also example simulation validates the effectiveness of the algorithm.3.We consider a class of homogeneous input discrete bilinear control systems,which constructs the logarithmic error approach and the exponential iterative learning law.Furthermore,the sufficient conditions is deduced for the convergence of learning error.The rigorous mathematical proof is given for the algorithm.Finally,under the example simulation,it is verified the effectiveness of the iterative learning control algorithm of the bilinear control systems.4.The problem of bilinear control systems for first order hyperbolic distribution parameters,We design a closed-loop P-type iterative learning controller,that compares with the simulation results of open-loop iterative learning.Closed-loop iterative learning control law has a faster convergence rate.Finally,it summarizes the research results,and the future development prospects which need to be studied are proposed.