Observer-oriented quantized tracking control design for parabolic non-linear uncertain PDE systems with dissipative constraints

This study accentuates the intricacies of designing a quantized observer-oriented model reference tracking controller for parabolic non-linear uncertain partial differential equation (PDE) systems with dissipative constraints. To be precise, a PDE-type Luenberger state estimator is incorporated for accessing the states of examined PDE system with high precision. This strategic incorporation empowers the model reference tracking controller with essential state estimations contributing to the realization of targetted state tracking objectives. Furthermore, as a measure to lighten the load on the communication medium, the input signals are quantized through the utilization of logarithmic quantizers before being transmitted to the actuator and a quantized observer-oriented tracking controller is then implemented to counteract and alleviate the consequential effects arising from quantization. Additionally, to attenuate the repercussions made by disturbances in the proposed system design, a dissipative based performance is incorporated. In the interim by applying the theory of Lyapunov’s stability, the adequate constraints for the undertaken system are frameworked in the context of linear matrix inequalities terms. Further, under the lights of established criteria, the gain matrices are reckoned. At the end, two numerical examples along with simulation outcomes are offered with the intent of showcase the applicability and usefulness of devised control. •PDE-type Luenberger observer is constructed to estimate states of addressed system.•Observer-based reference tracking control is developed for state tracking results.•Logarithmic quantizer is incorporated to reduce the network burden.•(Q,S,R)-γ dissipativity is implemented to reduce the disturbance effects.