Research On Stochastic Iterative Learning Control Algorithms For A Class Of Singular Systems

As an intelligent control method,iterative learning control(ILC)is suitable for the controlled systems with repetitive movement.It mainly relies on input and output information to gradually correct the control signal to reduce the errors,which makes it has small calculation amount and easy to implement.It can realize complete tracking of the target trajectories in a limited time without the accurate models of the controlled systems.The singular systems are more general than the normal systems and have a wide range of applications in the actual engineering system models.However,due to the existence of various stochastic factors in the actual projects,the controlled systems are difficult to meet the strict repeatability requirements of the iterative learning control.There may be randomly varying trial lengths,different initial states from expected initial states,and stochastic noise interference.This paper studies the problem of stochastic iterative control for a class of singular systems,and it is of great significance to further enrich the iterative learning control theory of singular systems.The main research work of this dissertation is as follows:For the state tracking problem of a class of discrete singular systems with randomly varying trial lengths,two iterative learning control algorithms are proposed based on the restricted equivalence decomposition of singular systems.One is the PD-type algorithm with a stochastic variable.The convergence condition is given through theoretical analysis and it proves that the complete tracking of the expected state can be achieved under the algorithm.The other is the higher-order iterative learning with an average operator.The convergence condition of the algorithm is also given through theoretical analysis and its convergence is proved.The numerical simulations are used to illustrate the effectiveness of the two algorithms.The initial state problem of a class of singular systems with randomly varying trial length is discussed.For the case where the initial state error is bounded,a PD-type algorithm with forgetting factor is proposed.It is proved that the tracking error of the system converges to a small range related to the boundary of the initial state error,and the effectiveness of the algorithm is verified by a numerical simulation.For arbitrary initial state,the control scheme of learning input and initial state simultaneously is used.The convergence of the algorithm is proved theoretically,and the simulation shows that as the number of iterations increases,the actual output of the system can achieve full tracking of the desired output.The iterative learning control problem for a class of linear discrete singular systems with stochastic measurement noise is studied.A P-type iterative learning control algorithm is used,and the Roessor model of the system is established using 2-D linear discrete system theory.The recursive algorithm of learning gain matrix is given.The mean square convergence of the algorithm is proved and the effectiveness of the algorithm is verified by numerical simulation.