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Spatially Discrete Control of Scalar Linear Distributed Plants of Parabolic and Hyperbolic Types

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Abstract

A spatially discrete control law is proposed for a class of systems described by scalar linear differential equations of parabolic and hyperbolic types with unknown parameters and disturbances. A finite set of discrete measurements (with respect to the spatial variable) of the plant state is available. The control law depends on a function that depends on the spatial variable and on a finite set of measurements of the plant state. Examples of this function, which allows realizing the control signal only at certain intervals in the spatial variable and providing lower control costs than some other analogs, are given. The exponential stability of the closed-loop system and robustness with respect to interval uncertain parameters of the plant and exogenous bounded disturbances are proved. Numerical modeling examples confirm the results of calculations and show the efficiency of the algorithm compared with some existing analogs.

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Funding

The results in Sec. 3 were produced with support from the Russian Science Foundation, project no. 18-79-10104, at the Institute for Problems in Mechanical Engineering, Russian Academy of Sciences (IPME RAS). The results in Secs. 4 and 5 were produced with support from the Russian Foundation for Basic Research, project no. 19-08-00246, at IPME RAS. The results in Secs. 6 and 7 were supported by a grant from the President of the Russian Federation, project no. MD-1054.2020.8, at IPME RAS.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia

    I. B. Furtat

  2. Gubkin University, Moscow, 119991, Russia

    P. A. Gushchin

Authors
  1. I. B. Furtat
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  2. P. A. Gushchin
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Corresponding authors

Correspondence to I. B. Furtat or P. A. Gushchin.

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Translated by V. Potapchouck

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Furtat, I.B., Gushchin, P.A. Spatially Discrete Control of Scalar Linear Distributed Plants of Parabolic and Hyperbolic Types. Autom Remote Control 82, 433–448 (2021). https://doi.org/10.1134/S0005117921030048

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  • DOI: https://doi.org/10.1134/S0005117921030048

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