Adaptive boundary vibration control for flexible manipulators under intermittent actuator failures

Investigating the suppression of intermittent elastic vibrations caused by actuator failures in flexible manipulators is both challenging and important, yet only limited studies have been reported. This paper proposes an adaptive boundary vibration control scheme to address this issue. First, intermittent jumps in failure parameters may lead to unbounded estimated parameters in the controller. To prevent this, a projection operator is employed to update the estimates, ensuring their boundedness as well as that of the parameter estimation errors. Second, since the derivatives of the estimation errors are undefined at failure times, a piecewise Lyapunov function incorporating the estimation errors is developed. This function demonstrates that all closed-loop signals are uniformly ultimately bounded (UUB) under the proposed control scheme. Furthermore, when the jump amplitudes of the Lyapunov function are sufficiently small and the time intervals between successive failures are sufficiently long, the steady-state performance in terms of angle tracking error and elastic deflection is enhanced. Third, based on the piecewise Lyapunov function, two explicit bounds for the angle tracking error and the elastic deflection are derived, showing that transient performance can be improved through appropriate selection of design constants. Finally, numerical simulations confirm the effectiveness and superiority of the proposed approach.