This paper investigates the coordinated behaviour of the multiple Euler–Lagrange systems under diverse interactions with time delays. Specially, in the case of undirected interconnection, the proportional plus damping control strategy is proposed and the sufficient conditions of bipartite consensus are derived via energy function based approach. Subsequently, a velocity‐free controller is further developed by introducing a novel second‐order auxiliary system to each agent. In the case of directed network, by fully investigating the property of the Laplacian matrix associated with the cooperative–competitive interactions, a bipartite consensus controller is devised and the input–output property analysis of the system transfer function in frequency domain is presented. Simulation results are provided to demonstrate the effectiveness of the presented algorithms.

In this study, a backstepping-based fault-tolerant controller for a robotic manipulator system with input and output constraints was developed. First, a barrier Lyapunov function was adopted to ensure that the system output satisfied time-varying constraints. Subsequently, the actuator input saturation and asymmetric dead-zone characteristics were also considered, and the actuator characteristics were described using a continuous function. The impacts of actuator failures and unknown dynamical parameters of the system were eliminated by employing Gaussian radial basis function neural networks. The external disturbances were compensated for, using a disturbance observer. Meanwhile, a finite-time dynamic surface technique was adopted to accelerate the convergence of the system errors. Finally, simulation of a 2-degrees-of-freedom robotic manipulator system showed the effectiveness of the proposed controller.

This study is concerned with the dynamical analysis and vibration attenuation for a three-dimensional (3-D) suspension cable system of a helicopter preceded by output constraints and input backlash. First, the dynamic model of a 3-D suspension cable is constructed in accordance with Hamilton’s principle. Then, a backlash inverse compensator is established to tackle the input backlash nonlinearities. Subsequently, three boundary controllers together with output signal barrier functions are proposed to dampen the oscillations while not violating the cable swing constraints. The uniform boundedness of the closed-loop system is guaranteed with recourse to the direct Lyapunov’s method. Finally, the validity and efficiency of the derived control laws are testified through simulation results.

In this study, we aim to construct the boundary robust adaptive control for weakening the vibration of the flexible Timoshenko manipulator in the presence of unknown disturbances. By Lyapunov’s direct method, the adaptive controllers and disturbance observers are exploited to achieve the angle tracking and handle the external disturbances. With the suggested adaptive laws and disturbance observers, the controlled system with both parametric and disturbance uncertainties is guaranteed to be uniformly bounded. Finally, simulation results are provided to illustrate the applicability and effectiveness of the proposed control.

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to achieve the objective of position tracking under the alignment condition. This extends the existing research on the control of nonlinear teleoperation systems with time delay. The saturation constraint property of the Softsign function ensures that no state of the system exceeds its constraints. The controller learns to simultaneously deal with the uncertainty of system parameters online, reject external disturbances, and eliminate positional errors along the time and iteration axes. All signals in the system for any constant time delay are proved to be bounded. Ultimately, the performance of the proposed controller is further verified through numerical simulations.

This paper concentrates on the control issue of nonlinear teleoperators in the presence of uncertain dynamics and kinematics. An observer-based control framework is introduced to compensate for the unfavorable effects arising from the uncertainties. The employment of the proposed sliding mode observers provide control system with the ability of finite-time estimation errors convergence, upon which, it is demonstrated that the bilateral teleoperators are stable and both of position and velocity tracking can be achieved with uncertain dynamics in joint space. Due to the practical requirement of driving the end-effectors to perform specific tasks, the control law which can ensure position coordination with uncertain dynamics and kinematics in task space is subsequently developed. The Lyapunov method is applied to demonstrate the stability of the closed-loop system. Simulation results are provided to testify the performance of the suggested algorithm.