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Volume 10 Issue 10
Oct.  2023

IEEE/CAA Journal of Automatica Sinica

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D. Y. Meng and  J. Y. Zhang,  “Fundamental trackability problems for iterative learning control,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 10, pp. 1933–1950, Oct. 2023. doi: 10.1109/JAS.2023.123312
Citation: D. Y. Meng and  J. Y. Zhang,  “Fundamental trackability problems for iterative learning control,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 10, pp. 1933–1950, Oct. 2023. doi: 10.1109/JAS.2023.123312

Fundamental Trackability Problems for Iterative Learning Control

doi: 10.1109/JAS.2023.123312
Funds:  This work was supported in part by the National Natural Science Foundation of China (62273018) and in part by the Science and Technology on Space Intelligent Control Laboratory (HTKJ2022KL502006)
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  • Generally, the classic iterative learning control (ILC) methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory, whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence (FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.

     

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    Highlights

    • This paper addresses the fundamental trackability problem of continuous-time iterative learning control (ILC). A definition of trackability is formally introduced for any specified trajectory in ILC by resorting to the frequency-domain algebraic equations. Furthermore, the trackability criteria are explored for ILC systems by taking advantage of the polynomial matrix properties. It is shown that both the system relative degree and the initial alignment condition have great influences on whether the specified trajectory is trackable in ILC. This actually provides a strong explanation about why the system relative degree and the initial alignment condition are two fundamentally required assumptions in classic ILC from the trackability viewpoint of the specified trajectory
    • A general feedback-based design method is proposed for ILC updating laws in the presence of any tracking tasks. Under the trackability premise of the specified trajectory, the proposed method closely connects the design of ILC updating laws with a class of state feedbacks constructed in the iteration domain. This is thanks to generalizing the state feedbacks from the static form to the dynamical form with the frequency-domain methods, which also narrows the gap between the design of classic continuous-time ILC and that of feedback-based control methods. In particular, the proposed design method collapses into providing PID-type ILC updating laws with appropriate selections of the gain function matrix
    • A convergence analysis method of ILC is developed by resorting to properties of the functional Cauchy sequence (FCS). This helps to arrive at a unified design condition to achieve the ILC convergence from the perspectives of both output and input, regardless of multiple-input multiple-output controlled systems. It is shown that the steady-state input obtained after an ILC process depends heavily on the initial input. Moreover, the relationship between the trackability of a trajectory specified for ILC and the accomplishment of the resulting perfect tracking objective is bridged. With the FCS-based method, it is actually revealed that regardless of whether the controlled systems are over-actuated or under-actuated, the perfect tracking objectives for ILC can be accomplished under certain ILC updating laws if and only if the specified trajectories are trackable in ILC

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