Quantum-Inspired Adaptive Neuro-Fuzzy Learning Framework for Real-Time Intelligent Control of Nonlinear Dynamic Systems

Modern industrial processes are increasingly characterized by nonlinear dynamics, parameter uncertainties, external disturbances, and continuously varying operating conditions, posing significant challenges to conventional control strategies. Although adaptive neuro-fuzzy controllers have demonstrated strong nonlinear approximation capability and adaptive learning performance, their online learning mechanisms frequently suffer from slow convergence, premature convergence to local optima, and limited adaptability under rapidly changing process conditions. Furthermore, most existing quantum-inspired approaches have been primarily developed for offline optimization, while their integration into continuous real-time adaptive intelligent control remains largely unexplored. To address this research gap, this paper proposes a Quantum-Inspired Adaptive Neuro-Fuzzy Learning Framework (QIANFL) for the real-time intelligent control of nonlinear dynamic systems. The proposed framework introduces a novel quantum-inspired probabilistic learning mechanism that continuously updates controller parameters through error-driven quantum state evolution, enabling an effective balance between global exploration and local exploitation during online adaptation. Unlike conventional evolutionary optimization algorithms, the proposed method updates only a single adaptive parameter vector at each sampling interval, resulting in linear computational complexity and efficient implementation in embedded real-time control systems. The proposed framework is validated using a nonlinear benchmark dynamic system under reference tracking, parameter uncertainty, and external disturbance conditions. Comparative evaluations against conventional PID and classical adaptive neuro-fuzzy controllers demonstrate improved tracking accuracy, faster transient response, enhanced disturbance rejection, reduced overshoot, and superior robustness while maintaining computational efficiency. The proposed QIANFL establishes a unified intelligent learning architecture that integrates quantum-inspired computation, adaptive neuro-fuzzy reasoning, and online machine learning, providing a scalable and computationally efficient solution for next-generation intelligent process control, industrial automation, cyber-physical production systems, and AI-enabled Industry 4.0 applications.