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\: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.
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Bekhiti et al. (2025) studied this question.