Adaptive fuzzy control for uncertain beam PDE-ODE cascade system with output constraint

This paper studies the adaptive stabilization problem of a class of uncertain beam PDE-ODE (partial differential equation – ordinary differential equation) cascade system under time-varying distributed and boundary disturbances. To eliminate the influence of distributed and boundary disturbances on the system and achieve stabilization, an adaptive fuzzy boundary control scheme based on the inversion method is proposed. This scheme integrates the uncertainty of system parameters and environmental interference, and dynamically approximates the uncertain nonlinear terms by constructing an adaptive fuzzy logic system, thereby improving the adaptability and robustness of the system. On this basis, a barrier Lyapunov function is constructed to constrain the output state of the system and a virtual control law is designed to ensure that the system state does not exceed the limited range. Finally, without simplifying or discretizing the infinite-dimensional dynamics, the stability of the closed-loop system is analyzed and proved. Numerical examples demonstrate the effectiveness of the proposed control.