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Control of oscillations by control of invariants in quasi-polynomial nonlinear systems

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Abstract

An approach to control of invariant sets of quasi-polynomial nonlinear systems in the presence and absence of bounded uncertainty (disturbances) in the model is proposed. The control strategy is based on introduction of an invariant functional for uncontrolled system and posing the control task as achieving the desired value of the invariant functional by means of control. The design is based on the reduction to the multispecies Lotka–Volterra system and employing the speed-gradient control method. Simulation results demonstrate reasonable control accuracy and the presence of the resonance-like behavior of the controlled system under disturbances.

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All data included in this study are available from the corresponding author on reasonable request.

Notes

  1. Since the LV model is ecology motivated, although the LV model is used in the paper just as a special canonical form of quasi-polynomial systems, we use the term “ species” for denoting its state variables according to the tradition and for convenience.

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Funding

The work was performed in IPME RAS and supported by the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2021-573).

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Authors and Affiliations

  1. Laboratory of Control of Complex Systems, Institute for Problems of Mechanical Engineering, Saint Petersburg, Russia

    Alexander Fradkov & Mikhail Ananyevskiy

  2. Department of Robotics, Kaluga Branch of Bauman Technical University, Kaluga, Russia

    Irina Pchelkina

  3. ITMO University, Saint Petersburg, Russia

    Anatolii Tomchin

  4. Saint Petersburg University, Saint Petersburg, Russia

    Alexander Fradkov

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  1. Alexander Fradkov
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  2. Irina Pchelkina
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  3. Mikhail Ananyevskiy
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  4. Anatolii Tomchin
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Correspondence to Alexander Fradkov.

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The work was performed in IPME RAS and supported by the Ministry of Science and Higher Education of the Russian Federation (Project No. 075-15-2021-573).

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Fradkov, A., Pchelkina, I., Ananyevskiy, M. et al. Control of oscillations by control of invariants in quasi-polynomial nonlinear systems. Nonlinear Dyn 111, 13955–13967 (2023). https://doi.org/10.1007/s11071-023-08566-9

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  • DOI: https://doi.org/10.1007/s11071-023-08566-9

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