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<p>This work outlines a novel intelligent predictive control method for Multi-Input Multi-Output (MIMO) systems based on solving matrix Diophantine equations. By embedding maximum likelihood identification into an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictive control scheme, this method achieves effective control of a stochastic two-wheeled self-balancing robot, even when system parameters are unknown. The robot’s dynamics were modeled via Newton–Euler equations and linearized around the upright position. The controller regulates tilt angle and rotational speed while adapting to 7% model uncertainty. It efficiently rejects <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44430_2025_11_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:0.1\)</EquationSource> </InlineEquation>-magnitude disturbances under 0.05-noise, achieving a <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44430_2025_11_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:0.92\:\text{s}\)</EquationSource> </InlineEquation> settling time and Integral of Absolute Error (IAE) of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44430_2025_11_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:0.061\)</EquationSource> </InlineEquation>. Compared to existing controllers, simulation results demonstrate superior convergence, disturbance rejection, and robust tracking, validating the robot’s use as a mobile transport platform.</p>

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Intelligent neuro-fuzzy adaptive MIMO control for a self-balancing two wheeled autonomous robot via recursive resolution of the matrix diophantine equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月21日

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  • Belkacem Bekhiti,
  • Raheem Al-Sabur,
  • Mohamed Roudane,
  • Jihad A. Younis,
  • Abdel-Nasser Sharkawy

摘要

This work outlines a novel intelligent predictive control method for Multi-Input Multi-Output (MIMO) systems based on solving matrix Diophantine equations. By embedding maximum likelihood identification into an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictive control scheme, this method achieves effective control of a stochastic two-wheeled self-balancing robot, even when system parameters are unknown. The robot’s dynamics were modeled via Newton–Euler equations and linearized around the upright position. The controller regulates tilt angle and rotational speed while adapting to 7% model uncertainty. It efficiently rejects \(\:0.1\) -magnitude disturbances under 0.05-noise, achieving a \(\:0.92\:\text{s}\) settling time and Integral of Absolute Error (IAE) of \(\:0.061\) . Compared to existing controllers, simulation results demonstrate superior convergence, disturbance rejection, and robust tracking, validating the robot’s use as a mobile transport platform.