Event-triggered adaptive safe-oriented barrier Lyapunov function-based boundary control of flexible beam systems characterized by uncertain Euler–Bernoulli PDEs

The territory of safe boundary control for PDE characterized flexible beam systems in an event-triggering context is both intriguing and under-explored. The underlying problem becomes even more complicated if such systems are subject to potentially conflicting time-varying hard and soft constraints, as well as uncertainties and disturbances. In this study, we present a solution to this technically significant and challenging problem. Firstly, we introduce a dynamic constraint region with an adjustable planning scheme, facilitating the establishment of time-varying constraints and prescribed soft constraint recovery. Within this strategy, higher priority is given to hard constraints, ensuring that safety requirements are consistently met, while soft constraints are accommodated only when they align with the hard constraints. Secondly, we develop an event-triggered adaptive safe boundary controller, where the actuator signal and parameter estimators are executed intermittently on an event-driven basis, ensuring that both the control input and parameter estimates employ piecewise-constant values. Consequently, the unknown damping coefficients (i.e., viscous, structural, and Kelvin–Voigt damping), the bending stiffness, and boundary disturbances are handled simultaneously, while effectively suppressing undesired vibrations or even resonances in the control input posed by the transient of adaptive learning. Through co-design, we guarantee the safety and stability of the closed-loop system, ensuring a minimal dwell-time between triggering instants, as rigorously verified by Lyapunov analysis. Finally, we validate the benefits and efficiency of the proposed algorithm through comprehensive numerical simulations.