Adaptive stabilization for uncertain hyperbolic PDE-ODE cascade systems

This paper is devoted to the adaptive stabilization for uncertain hyperbolic PDE-ODE cascade systems. Remarkably, unknown spatially varying and unknown constant parameters exist in the PDE and ODE subsystems, respectively. This brings essential difficulties in the design of compensator and boundary controller, and in the involved performance analysis. To solve the control problem, an infinite-dimensional backstepping transformation (simplified as IDBT) and its inverse are first introduced to change the original system into a new system (called target system). Then, a state-feedback boundary controller is constructed for the target system by incorporating the adaptive technique based on projection operator, which can guarantee the desirable stability of the resulting closed-loop system. Finally, a simulation example is provided to illustrate the effectiveness of the proposed adaptive controller.

Automated summary

This paper focuses on adaptive stabilization for uncertain hyperbolic PDE-ODE cascade systems, addressing challenges posed by unknown spatially varying and constant parameters. By introducing an infinite-dimensional backstepping transformation and state-feedback boundary controller with adaptive techniques, the study ensures stability of the resulting closed-loop system, as demonstrated through a simulation example.