A Quantum-Inspired Adaptive Neuro-Fuzzy Controller for Uncertain Nonlinear Processes

Uncertain nonlinear processes are widely encountered in industrial automation, chemical engineering, energy systems, and intelligent manufacturing, where nonlinear dynamics, parameter uncertainties, and external disturbances significantly complicate controller design and degrade closed-loop performance. This study proposes a Quantum-Inspired Adaptive Neuro-Fuzzy Controller (QIANFC) for uncertain nonlinear processes. The proposed controller integrates adaptive neuro-fuzzy inference with a quantum-inspired probabilistic adaptation mechanism implemented entirely on conventional digital computing hardware. Rather than emulating quantum computation, the adaptation strategy is mathematically inspired by the concepts of state superposition and probability-amplitude evolution, representing controller parameters through dynamically updated probability distributions. Recursive probability updates driven by tracking error provide a balanced exploration–exploitation mechanism, improving parameter-search diversity, accelerating convergence, reducing premature convergence, and enhancing robustness while maintaining computational efficiency.The proposed controller was evaluated using a widely adopted benchmark nonlinear process incorporating parameter variations, nonlinear interactions, and external disturbances. This benchmark was selected to provide a controlled and reproducible environment for evaluating the proposed adaptation mechanism. Comparative simulations against conventional PID and adaptive neuro-fuzzy controllers were conducted under reference-tracking, disturbance-rejection, and uncertainty-compensation scenarios. The proposed QIANFC achieved faster convergence, higher tracking accuracy, reduced transient oscillations, and improved disturbance rejection. Furthermore, all closed-loop state trajectories and adaptive parameter estimates remained bounded throughout the investigated operating conditions, providing empirical evidence of practical closed-loop stability and robustness.The proposed adaptation mechanism avoids computationally intensive iterative optimization and relies only on recursive probabilistic parameter updates, supporting efficient software-based online implementation. Although real-time hardware validation, formal Lyapunov-based stability analysis, and comparisons with advanced controllers remain future work, the results establish a rigorous proof-of-concept and provide a foundation for future validation across multiple nonlinear benchmark and industrial processes.