Robust adaptive boundary control of semilinear PDE systems using a dyadic controller

In this paper, we describe a dyadic adaptive control framework for output tracking in a class of semilinear systems of partial differential equations with boundary actuation and unknown distributed nonlinearities. The dyadic adaptive control framework uses the linear terms in the system to split the plant into 2 virtual subsystems, one of which contains the nonlinearities, whereas the other contains the control input. Full‐plant‐state feedback is used to estimate the unmeasured individual states of the 2 subsystems as well as the nonlinearities. The control signal is designed to ensure that the controlled subsystem tracks a suitably modified reference signal. We prove the well posedness of the closed‐loop system rigorously and derive conditions for closed‐loop stability and robustness using finite‐gain stability theory.