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Performance Output Tracking for an ODE Cascaded with Schrödinger Equation Subject to Disturbances

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Abstract

In this paper, we are concerned with the performance output tracking for a Schrödinger PDE-ODE cascaded system with external disturbances enter in all possible channels. The main challenge of the problem is the fact that the disturbances are non-collocated to the controller. By proper trajectory planning approach, this difficulty can be overcome by converting non-collocated configurations into the collocated ones. Then a state observer is designed in terms of the tracking errors. Finally, the feedback control is proposed by applying the backstepping technique. The stability of the closed-loop system and the exponential convergence of the regulation error are proved. Some numerical simulations illustrate that the proposed approach is very effective.

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Funding

This work was supported by the Basic Research Program of Shanxi Province (Free Exploration) Project under Grant: 20210302123181, 20210302124688, the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi under Grant STIP2021L416, and the Youth fund of Shanxi University of Finance and Economics (Grant No. QN-2019024).

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, China

    Yi-Jing Li & Jun-Jun Liu

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  1. Yi-Jing Li
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  2. Jun-Jun Liu
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Correspondence to Jun-Jun Liu.

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Li, YJ., Liu, JJ. Performance Output Tracking for an ODE Cascaded with Schrödinger Equation Subject to Disturbances. J Dyn Control Syst 29, 901–917 (2023). https://doi.org/10.1007/s10883-022-09631-z

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  • DOI: https://doi.org/10.1007/s10883-022-09631-z

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