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A qLPV-MPC Control Strategy for Fast Nonlinear Systems with Stability and Feasibility Conditions.

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Title: A qLPV-MPC Control Strategy for Fast Nonlinear Systems with Stability and Feasibility Conditions.
Authors: Daniel, Rodriguez-Guevara1 (AUTHOR) a01280937@tec.mx, Antonio, Favela-Contreras1 (AUTHOR) antonio.favela@tec.mx, Francisco, Beltran-Carbajal2 (AUTHOR) fbeltran.git@gmail.com, Camilo, Lozoya1 (AUTHOR) camilo.lozoya@tec.mx, David, Sotelo1 (AUTHOR) david.sotelo@tec.mx, Carlos, Sotelo1 (AUTHOR) carlos.sotelo@tec.mx
Source: Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ). Jul2025, Vol. 50 Issue 14, p11395-11407. 13p.
Subjects: Stability of nonlinear systems, Linear matrix inequalities, Nonlinear systems, Engineering models, Lyapunov stability, Hypersonic planes
Abstract: Model Predictive Control (MPC) has been a popular control strategy over recent years due to the possibility of ensuring optimal control while dealing with constraints. However, Nonlinear Model Predictive Control (NMPC) suffers from high computational complexity, resulting in long optimization times. This has restricted NMPC to nonlinear systems that have slow dynamics. This approach presents an MPC strategy for nonlinear systems using qLPV representations. In this strategy, the nonlinear dynamics of the nonlinear system are represented by scheduling variables, which are state dependent. Afterward, an LPV state space of the nonlinear system is derived. The future values of the scheduling parameter are determined based on the optimal planned trajectory from the previous MPC iteration. To ensure stability, a stable state feedback controller is designed for a terminal region where asymptotical stability is guaranteed. The stable state feedback controller and the full feasibility of the control strategy are ensured by using Linear Matrix Inequalities based on Lyapunov stability conditions. Finally, the control strategy is tested in two different nonlinear systems with fast dynamics, the van der Pol's oscillator and a quarter vehicle nonlinear suspension system. The performance of the control strategy is compared against a NMPC control strategy and a state feedback controller. The results proved that the proposed qLPV-MPC control strategy performs similar to the NMPC optimal control strategy while requiring significantly less computation time, making it suitable for real-time implementations on fast nonlinear systems. [ABSTRACT FROM AUTHOR]
Copyright of Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A qLPV-MPC Control Strategy for Fast Nonlinear Systems with Stability and Feasibility Conditions.
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  Data: <searchLink fieldCode="DE" term="%22Stability+of+nonlinear+systems%22">Stability of nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+matrix+inequalities%22">Linear matrix inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+models%22">Engineering models</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink><br /><searchLink fieldCode="DE" term="%22Hypersonic+planes%22">Hypersonic planes</searchLink>
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  Data: Model Predictive Control (MPC) has been a popular control strategy over recent years due to the possibility of ensuring optimal control while dealing with constraints. However, Nonlinear Model Predictive Control (NMPC) suffers from high computational complexity, resulting in long optimization times. This has restricted NMPC to nonlinear systems that have slow dynamics. This approach presents an MPC strategy for nonlinear systems using qLPV representations. In this strategy, the nonlinear dynamics of the nonlinear system are represented by scheduling variables, which are state dependent. Afterward, an LPV state space of the nonlinear system is derived. The future values of the scheduling parameter are determined based on the optimal planned trajectory from the previous MPC iteration. To ensure stability, a stable state feedback controller is designed for a terminal region where asymptotical stability is guaranteed. The stable state feedback controller and the full feasibility of the control strategy are ensured by using Linear Matrix Inequalities based on Lyapunov stability conditions. Finally, the control strategy is tested in two different nonlinear systems with fast dynamics, the van der Pol's oscillator and a quarter vehicle nonlinear suspension system. The performance of the control strategy is compared against a NMPC control strategy and a state feedback controller. The results proved that the proposed qLPV-MPC control strategy performs similar to the NMPC optimal control strategy while requiring significantly less computation time, making it suitable for real-time implementations on fast nonlinear systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s13369-024-09931-5
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        Text: English
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        PageCount: 13
        StartPage: 11395
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      – SubjectFull: Stability of nonlinear systems
        Type: general
      – SubjectFull: Linear matrix inequalities
        Type: general
      – SubjectFull: Nonlinear systems
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      – SubjectFull: Engineering models
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      – SubjectFull: Lyapunov stability
        Type: general
      – SubjectFull: Hypersonic planes
        Type: general
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      – TitleFull: A qLPV-MPC Control Strategy for Fast Nonlinear Systems with Stability and Feasibility Conditions.
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              Text: Jul2025
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              Y: 2025
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