Robust Tracking Error Feedback Control for a One-Dimensional Schrodinger Equation
Liu, Jun-Jun1; Guo, Bao-Zhu2,3
AbstractIn this article, we consider robust output tracking for a Schrodinger equation with external disturbances in all possible channels. The challenge of the problem comes from the fact that the observation operator is unbounded and the regulated output and the control are noncollocated. An observer-based approach is adopted in investigation. We first select specially some coefficients of the disturbances to obtain a nominal system, which is a coupled PDE+ODE system. For this nominal system, we design a feedforward control by solving related regulator equation. An observer is then designed for the nominal system in terms of the tracking error only. As a result, an error feedback control is, thus, designed by replacing the state and disturbances in the feedforward control with their estimates obtained from the observer. We show that this observer based error feedback control is robust to disturbances in all possible channels and system uncertainty. The stability of the closed loop and convergence are established by the Riesz basis approach. Some numerical simulations are presented to validate the results.
KeywordMathematical model Feedback control Regulation Observers Feedforward systems Eigenvalues and eigenfunctions Convergence Internal model principle output tracking robust control Schrodinger equation
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[61873260] ; China Postdoctoral Science Foundation[2020M680919]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000761219400007
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Document Type期刊论文
Corresponding AuthorGuo, Bao-Zhu
Affiliation1.Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Peoples R China
2.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China
3.Acad Sinica, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Liu, Jun-Jun,Guo, Bao-Zhu. Robust Tracking Error Feedback Control for a One-Dimensional Schrodinger Equation[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2022,67(3):1120-1134.
APA Liu, Jun-Jun,&Guo, Bao-Zhu.(2022).Robust Tracking Error Feedback Control for a One-Dimensional Schrodinger Equation.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,67(3),1120-1134.
MLA Liu, Jun-Jun,et al."Robust Tracking Error Feedback Control for a One-Dimensional Schrodinger Equation".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 67.3(2022):1120-1134.
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