<p>This paper presents model predictive control synthesis which benefits from the Takagi–Sugeno fuzzy model with linear subsystems and dynamical system identification using data. The premise variable and fuzzy rules of the Takagi–Sugeno are determined using from a one-dimensional latent space derived from a vanilla autoencoder. Therefore, online linear model predictive control is computed, with parallel distributed compensation. Thus, actuators’ input commands are determined from linear subsystems’ regulators. The methodology is applied to a control benchmark system named Quadruple Tank Process. The results of the identification task show that the Takagi–Sugeno fuzzy model accurately models the system due to the linear subsystems and the premise variable derived from the autoencoder, achieving a mean square error of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1759_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="98" /> </InlineMediaObject> <EquationSource Format="TEX">\(6.4731 \times 10^{-5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6.4731</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. In control tasks, the results show that the regulator is able to steer the system state to desired references with reduced loss (4 cm in the worst cases and lower for the other cases). Additionally, the added computation time for neural network inference is less than 10 ms.</p>

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Linear model predictive control using Takagi–Sugeno fuzzy model and vanilla autoencoder neural networks

  • Pierre Clément Blaud,
  • Xue Han,
  • Imad Mourtaji

摘要

This paper presents model predictive control synthesis which benefits from the Takagi–Sugeno fuzzy model with linear subsystems and dynamical system identification using data. The premise variable and fuzzy rules of the Takagi–Sugeno are determined using from a one-dimensional latent space derived from a vanilla autoencoder. Therefore, online linear model predictive control is computed, with parallel distributed compensation. Thus, actuators’ input commands are determined from linear subsystems’ regulators. The methodology is applied to a control benchmark system named Quadruple Tank Process. The results of the identification task show that the Takagi–Sugeno fuzzy model accurately models the system due to the linear subsystems and the premise variable derived from the autoencoder, achieving a mean square error of \(6.4731 \times 10^{-5}\) 6.4731 × 10 - 5 . In control tasks, the results show that the regulator is able to steer the system state to desired references with reduced loss (4 cm in the worst cases and lower for the other cases). Additionally, the added computation time for neural network inference is less than 10 ms.