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Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

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Abstract

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem, an invertible transformation is first introduced to change the system into an observer canonical form, from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Xia Li, Yungang Liu & Zaihua Xu

  2. School of Mathematics and Information Science, Yantai University, Yantai, 264005, China

    Jian Li

Authors
  1. Xia Li
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  2. Yungang Liu
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  3. Jian Li
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  4. Zaihua Xu
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Corresponding author

Correspondence to Yungang Liu.

Additional information

This work was supported by the National Natural Science Foundations of China under Grant Nos. 61821004, 61873146 and 61773332, and the Special Fund of Postdoctoral Innovation Projects in Shandong Province under Grant No. 201703012.

This paper was recommended for publication by Editor HU Xiaoming.

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Li, X., Liu, Y., Li, J. et al. Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter. J Syst Sci Complex 34, 298–313 (2021). https://doi.org/10.1007/s11424-020-9159-z

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  • DOI: https://doi.org/10.1007/s11424-020-9159-z

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