Asymptotical event-based boundary fault-tolerant control for cascaded ODE-belt systems with prescribed-time performance

Abstract

This paper focuses on event-based boundary fault-tolerant control for deferred-constrained cascaded ordinary differential equation (ODE)-belt systems modeled by flexible axially moving belt and nonlinear actuator dynamics subject to unknown parameters, nonlinearities, and actuator failure. To reduce the continuous updating of input signal, a dynamic threshold triggering mechanism is developed. Under these multiple constraints, achieving the asymptotic convergence of cascaded systems presents significant challenges for control design. In control design, radial basis neural networks are used to approximate uncertain nonlinear functions. The prescribed performance funnel and adaptive backstepping technique are applied to skillfully achieve the prescribed performance. Based on the designed adaptive failure compensator, the effect of actuator fault can be compensated for completely. Based on the Barrier Lyapunov function (BLF) approach, a novel boundary event-based fault-tolerant control protocol is successfully designed to achieve asymptotic convergence and vibration suppression. Remarkably, the appealing feature of the designed controller lies in the smooth function norm with a positive integrable function, which makes the controller powerful enough to achieve asymptotic convergence. Furthermore, the Zeno behavior can be excluded. Lastly, some simulation results are presented to validate the constructed results.