Output-Feedback Adaptive Boundary Control of Scalar Hyperbolic ODE–PDE–ODE Cascade Systems

This paper presents an output feedback adaptive boundary control scheme for a hyperbolic ODE–PDE–ODE cascade system with significant uncertainties. The system considers that all parameters, including spatially varying ones, are unknown and that only the ODE subsystem states are measurable. To facilitate the control design, an equivalent system representation is first derived. State observers are then constructed using linear combinations of ODE–PDE cascade filters, while swapping identifiers provide online parameter estimates. By integrating these elements, an adaptive backstepping control law is designed. It is proved that the proposed adaptive control law can stabilize the studied system. Finally, the effectiveness of the derived controller is verified via numerical simulations.