Noncollocated Output Feedback Control for the Semilinear Parabolic PDEs Under Input and Output Quantization

In the context of increasingly networked control systems, this article concentrates on the noncollocated control issue of input and output quantization for industrial processes governed by semilinear parabolic partial differential equation (PDE) systems. Both the control and measurement signals are quantized and transmitted through the network, which causes signal errors and reduces the stability and robustness of the system. A Luenberger-type PDE observer is developed to overcome the control difficulty of quantized measurement feedback signals and noncollocated pointwise sensors. Based on the observed value, a feedback controller is proposed, which undergoes quantization and operates on the distributed actuators within the domain. By employing the Lyapunov direct method, it is demonstrated that the observer can accurately track the system state with exponential precision, and the closed-loop system is exponentially converged. The well-posedness analysis of the closed-loop system is discussed via the $C_{0}$-semigroup method. The performance of the developed control strategy is validated through simulation examples.