Analysis On Iterative Learning Control Algorithm For Several Kinds Of Singular Systems

Singular system,also known as generalized state space,is a natural representation of objective system which widely applied in many actual system model.It can be used to describe more performance characteristics of the system.Singular system is an important tool to deal with multi-objective,multidimensional and multi-level large-scale complex systems.Compared with normal system,singular system is more complex in structure,more challenging in research,and more universal.It has been extensively applied in many fields,such as,circuit systems,econometrics,decision theory and electrical network,etc.Learning is one of the intelligent behaviors of human beings,iterative learning control(ILC)is another relatively significant control scheme with memory characteristics and correction strategies in control theory.It doesn't depend on the systems' s accurate dynamic mathematical model and it is applicable for repetitive controlled system,such as industrial robot.The task of the iterative learning control is improving the current response of the system.By fully utilizing the past control experience to update the unsatisfied control signal such that the tracking performance of the system improved.However,there are little researches focus on the issue of iterative learning control for singular systems and only focus on singular continuous time systems.In this paper,we mainly discussed iterative learning control issue and related problems for several kinds of singular systems.The innovations are as follows :1.It's well known that the development of normal control theory for singular discrete time systems is becoming more and more complete.In our paper,on account of the widely application of the discrete singular systems and the basic iterative learning control knowledge of singular continuous systems,the iterative learning control issue for discrete singular systems is investigated.We consider a class of PD-type iterative learning control scheme such that the system state output can track the desired output trajectory on finite time interval.The convergence conditions and theoretical analysis of the PD-type algorithm are presented in detail.Illustrative example supported the theoretical results and the effectiveness of the algorithm is shown at the end of the paper.Theory of iterative learning control for singular systems is enormously enriched and developed.2.Impulsive control system is extensively used in modern technology.At present,there are lots of researches about the existence,stability and periodicity of the solutions for the impulsive control system.From the point view of impulsive differential equations,iterative learning control is an effective and feasible control strategy.Based on the studies for such systems,we discussed the iterative learning control issue for a class of singular impulsive systems.Furthermore,appropriate iterative learning control schemes are presented to guarantee the system output converges to the desired one.And the sufficient conditions for the algorithm convergence are obtained.3.Fractional differential equation generalized the traditional integer order differential equations into fractional order even complex field.As a result,the conception of traditional differential systems are extremely expanded.Based on the existence and uniqueness of the solutions for fractional order systems,we discussed the iterative learning control issue for a class of singular fractional systems.Fractional order iterative learning control algorithm is investigated to improve the tracking performance.Then the sufficient convergence conditions of the system output error are derived through rigorous theoretical analysis.And the validity of the results is verified by numerical simulations.4.Nonlinear problem exits in practical engineering process and it is inevitable.In a degree,nonlinear phenomenon reflect the essence of the operation for a class of nonlinear systems.In general,the method of equivalent linearization is used to analyse nonlinear systems with relatively low nonlinearization.The essential of linearization is simplify the nonlinear problem to linear case,then to solve the linearized systems.In our dissertation,we discussed the iterative learning control issue for a class of nonlinear singular impulsive system and nonlinear singular fractional order system.The sufficient conditions of the convergence for the system output errors are proposed.Then,the effectiveness of the algorithm is validated by numerical examples.Finally,the full work is summarized and the further research direction is pointed out.