Research On Iterative Learning Control Algorithm For Singular Systems Based On Lebesgue-p Norm

Iterative learning control(ILC)is applied to systems which has repetitive motion.Because ILC has simple control,small computation and full tracking of the desired trajectory,it is especially suitable for nonlinear,strongly coupled and difficult modeling systems.Singular system is also called as generalized system,which is more general than general system in description.There are many singular system in real system such as aerospace system,power system,economic systems,decision-making processes and so on.Convergence and convergence speed are key point of singular system ILC.Convergence is the most important guarantee of algorithm effectiveness,and convergence speed is also an important index to measure the quality of iterative learning algorithm.However,Most of the existing findings are likely to be analysed with lambda norm,which bring in negative exponential weighting to compress the error,potentially leading to misjudged in convergence.Lebesgue-p norm takes the whole system interval error into consideration,so it can reflect the performance of the system function more reasonably.In this paper,Lebesgue-p norm is used to analyze the convergence and convergence speed of iterative learning algorithm in singular systems.The main work of this paper is as follows:1.For a class of linear continuous singular systems with regular Conditions,a closed-loop D-type algorithm is proposed.Lebesgue-p norm is introduced to analyze convergence conditions.Comparing it with convergence conditions under lambda norm,the feature of the two norms are analyzed.Then numerical simulation is carried out,results show that it is a better choice to use Lebesgue-p norm to discuss the convergence of iterative learning control.2.For a class of linear continuous singular systems,based on singular value decomposition,first-order and second-order open-loop P-type algorithm are proposed.Using Lebesgue-p norm to analyze convergence and then get the convergence condition.Q_p factor are introduced to compared the convergence speed between the first order P-type algorithm and the second order P-type algorithm.The results show that the order of ILC algorithm,system coefficient matrix and learning rate gain all affect the convergence speed.3.The state tracking problem of a class of singular systems is studied by using iterative learning control method,Based on singular value decomposition,open-loop and open-closed loop Hybrid PD-type algorithm are proposed.Using Lebesgue-p norm to analyze convergence and then get the convergence condition.Q_p factor are introduced to compared the convergence speed of the open PD-type algorithm and the open-closed loop PD-typeorder.The results show that the speed of convergence is affected by the closed-loop part,and the convergence can be accelerated by selecting reasonable closed-loop part parameters.