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.

This paper proposes a learning-driven passivity-based control (PBC) strategy for sensorless induction motors, combining a nonlinear adaptive observer with recurrent neural networks (RNNs) to improve robustness and estimation accuracy under dynamic conditions. The main novelty is the integration of neural learning into the passivity framework, enabling real-time compensation for un-modeled dynamics and parameter uncertainties with only one gain adjustment across a broad speed range. Lyapunov-based analysis guarantees the global stability of the closed-loop system. Experiments on a 1.1 kW induction motor confirm the approach's effectiveness over conventional observer-based and fuzzy-enhanced methods. Under torque reversal and flux variation, the proposed controller achieves a torque mean absolute error (MAE) of 0.18 Nm and flux MAE of 0.21 Wb, compared to 1.58 Nm and 0.85 Wb with classical PBC. The peak torque deviation drops from 42.52% to 30.85% of nominal, torque symmetric mean absolute percentage error (SMAPE) improves by 7.6%, and settling time is reduced to 985 ms versus 1120 ms. These results validate the controller's precision, adaptability, and robustness in real-world sensorless motor control.