This article studies a vibration and disturbance rejection problem of a wind turbine tower under exogenous perturbations. The tower dynamics is captured by a nonhomogeneous Euler–Bernoulli beam model. The dissipativity of the system is realized by a boundary feedback control solution with a multivalued symbolic function. A Lyapunov-based stability analysis is established to assess the deflection of the tower is uniformly bounded even subject to exogenous disturbances. The extended Filippov framework and Galerkin approximation scheme are introduced to tackle the existence of the solution to the system with a discontinuous control input. Simulation results demonstrate the performance of the proposed control scheme.

In this article, we propose a redundant fault-tolerant and boundary constraint control in the framework of adaptive method, the neural network approximation, and the barrier Lyapunov function (BLF) with a relaxed initial condition. The actuator failures are compensated by a combination of adaptive methods and redundant actuators when some actuators suffer from partial or even total loss of effectiveness. The radial basis function’s neural network structure is introduced to strengthen the adaptivity in various orientations of the hose and other additionally unmodeled dynamics. To maintain the boundary deflection within a predefined open set after a constraint time, a novel asymmetrical and time-varying BLF is constructed by applying a shifting function to transform the original state into a new state with zero value initially. The performance of the developed adaptive control is demonstrated by numerical simulations. Note to Practitioners—This article is motivated by the limited performances in the existing control designs for flexible unmanned aerial refueling hose systems with failed actuators and boundary constraints. This article considers a redundant actuator case to solve time-varying and partially and totally failed actuator failures that are not settled by adaptive and Nussbaum-based single control. Unlike conventional barrier Lyapunov functions (BLFs), in this article, we resort to a shifting function and propose a novelly asymmetric and time-varying BLF, which is well defined initially and capable to address a deferred constraint control problem. The control design and stability analysis of the actuated system is a Lyapunov-based method rather than relying on semigroup theory or functional analysis, which makes the developed method more engineering orientated. The proposed control strategy is tested to illustrate performances in numerical simulations with the finite difference method.

In this paper, we propose an adaptive fault-tolerant control strategy for flexible string systems and extend the result to Euler-Bernoulli beam systems under deferred and asymmetric boundary partial output constraints. The designed control strategies consist of a boundary control law and two adaptive parameter update laws. A hyperbolic tangent function is applied to realize rejection to disturbance. With the adaptive technique, the unknown actuator faults are compensated. The deferred partial output constraints are addressed by utilizing a shifting function to remove the initial limitation on the boundary output and constructing a novel asymmetric barrier Lyapunov function. Furthermore, it is proven that both the controlled string and Euler-Bernoulli beam systems are well-posed and meet the deferred constraint conditions. Finally, extensive simulation examples are presented to demonstrate the performance of the proposed control methods.

This article proposes an adaptive fuzzy control approach with an event-triggered mechanism and spatial motion constraint for a hybrid spacecraft system. The spacecraft system is composed of a rigid body and a slender flexible panel, with coupled dynamics captured by three ordinary differential equations and two partial differential equations. The overall control objective lies in utilizing an event-triggered control input to regulate the angular velocities of the rigid body and stabilize the vibrations of the flexible panel under unknown input disturbances and prescribed spatial motion performance. We collectively address the posture regulation and disturbance rejection purposes by introducing a barrier Lyapunov function and a fuzzy logic system. The event-triggered solution only updates the control signals at some discrete-time instants, and hence the communication burden is reduced significantly. The potential effectiveness and thrifty efficiency of the developed control strategy are theoretically demonstrated and numerically verified.

Inspired by soft organisms in nature, engineers have been exploring the mechanical design of soft robots manufactured by compliant materials. However, some limitations still exist in the modeling and control of soft robots. This article studies a cable-driven soft robot with shape and bending motion inspired by an octopus tentacle. By the extended Hamilton’s principle, the dynamic equation of the soft robot is derived in a distributed parameter system (DPS), which is governed by a partial differential equation. The boundary control strategy for the soft robot is developed via Lyapunov-based design to achieve distributed bending angle tracking. The stability analysis of the closed-loop system is presented using LaSalle’s invariance principle to show that the total energies in the system, and hence, the distributed states of the system, remain bounded and tend asymptotically to the desired values. Some simulation results are applied to demonstrate the applicability and effectiveness of the employed model and control. This study will promote the application of DPS theory in soft robots.

This paper addresses fuzzy observer design for a nonlinear parabolic equation over an unit square domain in terms of the time delayed spatially averaged measurement, where the observer is composed of m-chain of sub-observers. Due to 2D domain, special emphases are made to the computational complexity. A Lyapunov argument is utilized to give constructive conditions ensuring the exponential stability of the resulting error system. The method used for the continuous-time fuzzy observer is applicable to the sampled-data implementation. Consistent simulation results that support the proposed theoretical statements are presented.