Boundary Control of a Vibrating String Subject to Input Saturation and Output Constraint

This paper presents a control framework of a vibrating flexible string system subject to input saturation and output constraint. By integrating the backstepping technique and Lyapunov theory, a smooth function, a Nussbaum function, a barrier function, and an auxiliary system are exploited to establish a constrained boundary control for tacking the output and input constraints as well as stabilizing the system. The derived control can assure the bounded stability in controlled systems depending on Lyapunov criteria. The simulation study and analysis verify the effectiveness of the presented scheme.