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Boundary control of discrete repetitive processes with smoothing: controllability, observability and disturbance attenuation

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Abstract

In this paper, we proffer an explicit representation of solutions for a specific class of linear repetitive processes with smoothing. This representation is used to obtain direct controllability and observability criteria of this same class of discrete time 2-D systems. Not only classical controllability properties are considered, where control of the system is obtained by choosing its inhomogeneity appropriately, but also controllability of the system by steering it through boundary data control. From the point of view of technical applications, for instance in high pressure gas network modelling (see Azevedo-Perdicoúlis and Jank in Proceedings of n-DS, international workshop on multidimensional systems, Thessaloniki. 2009), it seems to be more reliable to consider boundary data controls. Therefore, in this paper we emphasise boundary data control properties of the system. A disturbed optimal boundary control problem with a quadratic criterion is also solved.

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References

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Acknowledgments

We would like to thank the reviewers for their careful reading and helpful comments and the editors of the Multidimensional Systems and Signal Processing that led to a significant improvement of this manuscript.

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Authors and Affiliations

  1. ISR, Coimbra, Portugal

    Teresa Paula Azevedo-Perdicoúlis

  2. Departamento de Matemática, UTAD, 5001-801 , Vila Real, Portugal

    Teresa Paula Azevedo-Perdicoúlis

  3. Department II of Mathematics, RWTH, University of Technology, 52056 , Aachen, Germany

    Gerhard Jank

  4. FEUP, 4200-465 , Porto, Portugal

    Paulo Lopes dos Santos

Authors
  1. Teresa Paula Azevedo-Perdicoúlis
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  2. Gerhard Jank
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  3. Paulo Lopes dos Santos
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Corresponding author

Correspondence to Teresa Paula Azevedo-Perdicoúlis.

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Azevedo-Perdicoúlis, T.P., Jank, G. & Lopes dos Santos, P. Boundary control of discrete repetitive processes with smoothing: controllability, observability and disturbance attenuation. Multidim Syst Sign Process 26, 145–158 (2015). https://doi.org/10.1007/s11045-013-0241-8

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  • DOI: https://doi.org/10.1007/s11045-013-0241-8

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