Research On Initial Value Problems Of Several Singular Iterative Learning Control Systems

As an intelligent control method,iterative learning control is suitable for the complex system which repeatedly operates and is difficult to model.It improves the controlled system by iteratively modifying the control input within a limited time interval,and finally enables the iterative output of the system to track the expected output asymptotically along the direction of the iterative axis.The initial value problem of iterative learning control refers to the relationship between the initial state value of the system and the convergence of the iterative learning control algorithm.The singular system,also known as the generalized state space system,is a relatively accurate description of a class of systems that actually exist in the the real life.It is widely used in many fields such as economy,electric power,and aerospace.This thesis will focus on the initial value problems of several types of singular iterative learning control systems,which is of great significance to further enrich and improve the iterative learning control theory of singular systems.The main contents are shown as follows:For the fixed initial value problem of iterative learning control for continuous singular systems,two different forms of iterative learning control algorithms are considered.Firstly,a closed-loop PD-type iterative learning algorithm is proposed and proved that under the convergence condition the output of the system is uniformly convergent to a signal,which has a fixed deviation compared with the expected output of the system.Then,an initial state error correction strategy is proposed to solve the deviation problem of the closed-loop PD-type learning algorithm.It is theoretically proved that this strategy can correct the fixed initial deviation formed by each initial state.Finally,the influence of the fixed deviation will be effectively eliminated and the effectiveness of the strategy is proved by numerical simulation.For continuous singular systems with state time-delay,two different iterative learning control algorithms with initial state learning are studied in the case of arbitrary initial state.The corresponding theoretical proofs and simulation analyses are given respectively.The results show that both algorithms can make the iterative output of the system converge to its expected output.For the initial value problem of iterative learning control for discrete singular systems with control time-delay,two initial conditions are considered,which are initial state of bounded disturbance and arbitrary initial state respectively.Under the two different initial states conditions,iterative learning control algorithms are studied before and after.Combinedwith theoretical analysis and simulation experiments,the effectiveness of the algorithms in two different situations are proved.