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<p>This paper presents a novel monitoring signal for the decision logic unit of the supervisory strategies, utilizing the probability-weighted robust multiple model adaptive control (P-W RMMAC) methodology design tools in linear time-invariant systems. The implementation of the online Baram Proximity Index (BPI) measures, defined in a stochastic metric space, as monitoring signals, is introduced. Since the true plant parameter values are unknown, the online relative BPI values between the true plant model and the predefined nominal models not to be accessible, consequently, an online computation of relative BPI values utilizing the recursive expectation–maximization (R-EM) algorithm has been proposed. Subsequently, the switching logic/mechanism for the supervisory architecture of the closed-loop control system, which employs these BPI metrics as monitoring signals, is presented. In summary, in this study, the R-EM algorithm employs instant values of each residual (estimation error) signals to generate the online relative BPI values as monitoring signals to select one of the proper local mixed-<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1711_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> robust controllers in the bank of candidate controllers. Finally, the offered outline is applied to the synthesized controllers for a two-cart mass–spring–dashpot system, and the simulation results of the provided decision logic mechanism are presented and compared with those of the P-W RMMAC. Simulation shows that in most cases, the correct controller is inserted (switched) into the closed-loop system by the presented decision logic mechanism based on the BPI value monitoring signals in a finite time so that the correct controller's identification time duration is shorter than that of the P-W RMMAC, and the control signal magnitude is lower.</p>

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A novel monitoring signal for the decision logic unit of the estimator-based supervisory robust multiple model adaptive control implementing the expectation–maximization algorithm

  • 期刊论文

  • 发表日期：

    2025年6月3日

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  • Mohammad Mahdi Amini,
  • Naser Eskandarian,
  • Abbas Dideban,
  • Mohammad Hossein Kazemi

摘要

This paper presents a novel monitoring signal for the decision logic unit of the supervisory strategies, utilizing the probability-weighted robust multiple model adaptive control (P-W RMMAC) methodology design tools in linear time-invariant systems. The implementation of the online Baram Proximity Index (BPI) measures, defined in a stochastic metric space, as monitoring signals, is introduced. Since the true plant parameter values are unknown, the online relative BPI values between the true plant model and the predefined nominal models not to be accessible, consequently, an online computation of relative BPI values utilizing the recursive expectation–maximization (R-EM) algorithm has been proposed. Subsequently, the switching logic/mechanism for the supervisory architecture of the closed-loop control system, which employs these BPI metrics as monitoring signals, is presented. In summary, in this study, the R-EM algorithm employs instant values of each residual (estimation error) signals to generate the online relative BPI values as monitoring signals to select one of the proper local mixed- \(\mu \) μ robust controllers in the bank of candidate controllers. Finally, the offered outline is applied to the synthesized controllers for a two-cart mass–spring–dashpot system, and the simulation results of the provided decision logic mechanism are presented and compared with those of the P-W RMMAC. Simulation shows that in most cases, the correct controller is inserted (switched) into the closed-loop system by the presented decision logic mechanism based on the BPI value monitoring signals in a finite time so that the correct controller's identification time duration is shorter than that of the P-W RMMAC, and the control signal magnitude is lower.