Neural operator for observer gains and output-feedback control of coupled PDE-ODE systems

Controlling coupled dynamical systems with spatially varying coefficients present a major challenge in control theory, particularly when some of state variables can not be directly measured. To address this issue, this paper proposes an innovative approach that leverages deep neural networks, specifically DeepONet, as a neural operator to approximate both the observer gain and the controller gain. An advantage of this method is that it eliminates the need to pre-solve differential equations. By leveraging the ability of DeepONet to approximate nonlinear operators, a backstepping control strategy is developed to guarantee the system’s exponential stability. Effectiveness of the proposed approach in stabilizing complex coupled systems is demonstrated through simulation results.