Probabilistic fuzzy neural network-based indirect adaptive control framework for dynamic systems

This paper introduces a probabilistic Takagi-Sugeno-Kang fuzzy neural network (PTSK-FNN) within a reliable indirect adaptive control framework that updates the gains of proportional - integral - derivative (PID) controller. The reasons for introducing this study include effective management of chaotic uncertainties by integrating the probabilistic processing with TSK fuzzy neural system, improved system identification needed for calculating control signals, and a novel law for an online learning algorithm based on the Lyapunov theorem to ensure system stability. The proposed controller requires a sensitivity function derived from the system model, which can be obtained through identification techniques utilizing Wiener model based on PTSK-FNN for modeling both linear and nonlinear dynamics of the system. By dynamically modifying both the structure and parameters of the PTSK-FNNs, the PID controller gains are updated, leading to enhance control performance. This control strategy is implemented for nonlinear dynamic systems and compared with other existing controllers, demonstrating its effectiveness in engineering applications. Simulation and experimental results indicate that the proposed controller significantly outperforms its alternatives in mitigating random noise, external disturbances, and system uncertainties. The proposed controller shows minimum performance indices compared to other published controllers, achieving improved performance by reducing the mean absolute error by 34.2 % in simulations and 38.6 % in experimental results, compared to higher-performing published controllers.