Event-Triggered Boundary Control Strategy for a Time Fractional Wave Equation Subject to Boundary Disturbance

In this paper, we investigate the event-triggered boundary feedback control problem for an unstable time fractional wave equation with unknown perturbation at the boundary. To cope with the instability of system when there is no disturbance, the backstepping method is adopted to convert the original unstable system into a stable system. An UDE-based estimator based on low-pass filter is proposed to estimate unknown time-varying input disturbance. With the estimation of disturbance, the event-triggered boundary feedback controller is proposed. It is shown that the event-triggered strategy could asymptotically stabilize system and a positive lower bounded of minimum inter-event time is ensured to exclude the Zeno phenomenon.

Telehealth Therapy for Therapists: Barriers and Benefits

Personal therapy for therapists is described as a means for advancing personal and professional growth. Therapist problems contribute to boundary disturbance, ethical violation, and incompetence. Benefits of therapy include enhanced counselor reflection and therapeutic alliance. Telehealth therapy overcomes barriers and represents an innovation in self-care and career development.

H∞ Iterative Learning Boundary Vibration Control of Uncertain Vibrating String with Iteration-Varying Distributed Disturbance and Boundary Disturbance

By integrating <i>H</i>_∞ control into iterative learning boundary control (ILBC) with the method of lines (MOL), this paper suggests a novel scheme to reduce the vibrations of the uncertain vibrating string system in the presence of iteration-varying distributed/boundary disturbances. The dynamics of the string system are defined by two kinds of differential equations, namely: (a) non-homogenous hyperbolic partial differential equation (PDE) and (b) ordinary differential equations (ODEs). Firstly, MOL is employed to attain the string dynamics in the form of a state-space system instead of a PDE system. Secondly, ILBC is developed in a super-vector framework and integrated with the <i>H</i>_∞ control for decreasing the perturbations of the uncertain string system in the presence of iteration-varying distributed/boundary disturbances. Along the time, position, and iteration coordinates: (a) the boundary deflections of the string system are controlled; (b) the vibrations along the string are attenuated to zero; and (c) the external disturbances are excluded. Based on the <i>H</i>_∞ algebraic approach, performance/stability conditions and global convergence of the closed-loop string system are assured. Conducted simulations illustrate that the suggested scheme is efficient for diminishing the vibrations of certain and uncertain vibrating string system.

Neural-network-based adaptive fault-tolerant vibration control of single-link flexible manipulator

This paper proposes an adaptive fault-tolerant control scheme for a single-link flexible manipulator with actuator failure and uncertain boundary disturbance. The dynamic model of the flexible manipulator as-described by partial differential equations (PDEs) is derived under Hamilton’s principle. The dynamic model is then used to design an adaptive fault-tolerant control (FTC) scheme which tracks the given angle and regulates vibration in the case of actuator failure. The boundary disturbance is compensated by a radial basis function (RBF) neural network. The whole closed-loop system is proven asymptotically stable by Lyapunov direct method and LaSalle’s invariance principle. Simulation results indicate that the proposed controller is superior to the traditional PD controller.