Adaptive boundary control for a class of inhomogeneous Timoshenko beam equations with constraints

In this study, integral-Barrier Lyapunov function (IBLF)-based boundary controls are proposed for a class of inhomogeneous Timoshenko beam equations with boundary output constraints. An IBLF which depends explicitly on time, is employed to prevent the constraint violation. The adaption laws are designed to compensate for the system uncertainties. By using the proposed adaptive IBLF-based boundary control, the vibration of the Timoshenko beam system is suppressed greatly, without any discretisation or simplification of the dynamics in the time and space. The proposed adaptive IBLF-based boundary controls also guarantee that boundary outputs always remain in the constrained space, subject to significantly relaxed feasibility conditions. In the end, numerical simulations are displayed to illustrate the performance of the proposed control.