Iterative learning control of linear continuous systems with variable initial states based on 2-D system theory

Author(s):  
Wei Guan ◽  
Qiao Zhu ◽  
Xu-Dong Wang ◽  
Xu-Hui Liu
2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Wei Guan ◽  
Qiao Zhu ◽  
Xu-Dong Wang ◽  
Xu-Hui Liu

This paper is concerned with the variable initial states problem in iterative learning control (ILC) for linear continuous systems. Firstly, the properties of the trajectory of 2-D continuous-discrete Roesser model are analyzed by using Lyapunov's method. Then, for any variable initial states which absolutely converge to the desired initial state, some ILC design criteria in the form of linear matrix inequalities (LMI) are given to ensure the convergence of the PD-type ILC rules. The convergence for variable initial states implies that the ILC rules can be used to achieve the perfect tacking for variable initial states, even if the system dynamic is unknown. Finally, the micropropulsion system is considered to illustrate efficiency of the proposed ILC design criteria.


2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Zhang Qunli

An iterative learning control problem for nonlinear systems with delays is studied in detail in this paper. By introducing theλ-norm and being inspired by retarded Gronwall-like inequality, the novel sufficient conditions for robust convergence of the tracking error, whose initial states are not zero, with time delays are obtained. Finally, simulation example is given to illustrate the effectiveness of the proposed method.


2019 ◽  
Vol 42 (5) ◽  
pp. 981-996
Author(s):  
Fateme Afsharnia ◽  
Ali Madady ◽  
Mohammad Bagher Menhaj

This paper presents a novel model reference adaptive iterative learning control (ILC) for unknown continuous-time linear time-varying systems. The unknown time-varying parameters of the system are neither required to vary slowly nor to have known bounds. The system is not required to be minimum-phase, stable, controllable or observable. The input of the system is determined by a differentiator-free control law. The used reference model is time-invariant and first order and thus choosing its parameters is easily possible, even though, the system under control is high order and time variant. Almost all of the components of the system initial condition can be iteration variant. By introducing a novel kind of Lyapunov function the convergence of the proposed adaptive ILC (AILC) and achieving asymptotic tracking are proved. Also, by rigorous mathematical analysis and with the help of some mathematical key techniques such as Bellman-Gronwall lemma, it is shown that all signals and quantities in the closed-loop system are bounded in the sense of at least one norm. Finally, the effectiveness of the proposed method is verified by two simulation examples.


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