Research On Iterative Learning Control Algorithms For Several Classes Of Singular Systems

Iterative learning control(ILC)is an effective control technique for repetitive dynamic systems,over a finite time interval,that can achieve the tracking accuracy for the given desired trajectory by correcting the tracking error.In this dissertation,the problems of ILC algorithms are studied for several classes of singular systems.Meanwhile,the fixed initial shift problem,the non-repetitive desired trajectory tracking problem,and the consensus problem of singular multi-agent systems are also considered.Main works of this dissertation are summarized as follows:1.The ILC problem for linear singular systems is discussed.Based on the equivalent restrict decomposition form of singular systems,a mixed PD-type learning algorithm is proposed and applied to a class of discrete singular time-delay systems.Furthermore,a closed-loop PD-type learning algorithm is constructed,which has the ability to eliminate the non-causality of discrete-time singular systems.The convergence conditions of the proposed algorithms are given and the effectiveness of the algorithms are verified by numerical examples.2.The state tracking problem for discrete singular systems with fixed initial shift is studied.According to the characteristics of the singular systems,a new closed-loop learning algorithm is designed and the corresponding state limiting trajectory is presented.It is shown that the algorithm can guarantee the system's state asymptotically tracks the desired trajectory.Then the initial rectifying strategy is introduced to the discrete singular systems for eliminating the effect of the fixed initial shift.By using the initial rectifying strategy,the system's state can converge to the desired trajectory within the pre-specified finite time interval.3.The ILC problem for a class of one-sided Lipschitz nonlinear singular systems is considered.In order to track the given desired trajectory,a closed-loop D-type learning algorithm is proposed for such nonlinear singular systems.Then,the convergence result is derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions.Finally,the effectiveness of the theoretical result is verified by numerical simulations.4.The design of ILC algorithms for singular switched systems is investigated.Firstly,based on the singular value decomposition method,the switched generalized system is transformed into the switched differential-algebra system and a new learning algorithm composed of D-type and P-type learning algorithms is constructed.Secondly,the closedloop D-type learning algorithm is used to study the ILC for a class of singular switched time-delay systems.Finally,the ILC for discrete singular switched systems with arbitrary switching rules is considered.According to the characteristics of the singular system,two types of iterative learning algorithms are proposed.5.By using internal mode principle,the high-order internal model-based P-type learning algorithm is constructed to deal with the non-repetitive desired trajectory tracking problem for a class of linear singular systems,where the variation of the desired trajectory in the iteration domain is described by a high-order internal model.Then,the convergence theorems of the presented algorithm are established.It is shown that the algorithm can ensure the output trajectory tracks the iteration-varying desired trajectory.6.The consensus tracking problem of singular multi-agent systems is studied through ILC approach.Here,the communication among the followers is described by a directed graph,and only a portion of the followers can receive the leader's information.For such singular multi-agent systems,a unified iterative learning algorithm is proposed in both continuous-time and discrete-time domains.It is shown that the algorithm can guarantee the outputs of the followers converge to the leader's trajectory on a finite time interval.