Observer-Based Fuzzy Quantized Control for a Stochastic Third-Order Parabolic PDE System

The work addresses an observer-based fuzzy quantized control for stochastic third-order parabolic partial differential equations (PDEs) using discrete point measurements. For the first time, we contribute in introducing three types of quantizer—logarithmic quantizer, uniform quantizer, and hysteresis quantizer into the controller designs for the stochastic PDE system. The main advantage of the quantized control law lies in reducing the energy that the system spends. The stability analysis is nontrivial due to the complex stochastic PDE model. Different stability results are presented for each case. Sufficient LMI-based conditions are investigated to ensure the internal mean-square exponential stability and $H_{\infty }$ performance of the perturbed actuated system. Consistent simulation results that support the proposed theoretical statements are provided.