In this paper, the formation control problem is investigated for a team of uncertain underactuated surface vessels (USVs) based on a directed graph. Considering the risk of collision and the limited communication range of USVs, the prescribed performance control (PPC) methodology is employed to ensure collision avoidance and connectivity maintenance. An event-triggered mechanism is designed to reasonably use the limited communication resources. Moreover, neural networks (NNs) and an auxiliary variable are constructed to deal with the problems of uncertain nonlinearities and underactuation, respectively. Then, an event-triggered formation control scheme is proposed to ensure that all signals of the closed-loop system are uniformly ultimately bounded (UUB). Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Distributed Event-Triggered Formation Control of USVs with Prescribed Performance

Human–robot co-transportation allows for a human and a robot to perform an object transportation task cooperatively on a shared environment. This range of applications raises a great number of theoretical and practical challenges arising mainly from the unknown human–robot interaction model as well as from the difficulty of accurately model the robot dynamics. In this article, an adaptive impedance controller for human–robot co-transportation is put forward in task space. Vision and force sensing are employed to obtain the human hand position, and to measure the interaction force between the human and the robot. Using the latest developments in nonlinear control theory, we propose a robot end-effector controller to track the motion of the human partner under actuators’ input constraints, unknown initial conditions, and unknown robot dynamics. The proposed adaptive impedance control algorithm offers a safe interaction between the human and the robot and achieves a smooth control behavior along the different phases of the co-transportation task. Simulations and experiments are conducted to illustrate the performance of the proposed techniques in a co-transportation task. 

Adaptive-Constrained Impedance Control for Human–Robot Co-Transportation

This brief mainly considers trajectory tracking and vibration suppression for a 3-D flexible wing. The dynamical model of the flexible wing is regarded as a distributed parameter system, which is described by partial differential equations and ordinary differential equations. A control strategy regulates the flexible wing to track the desired trajectory by controlling two angles. Meanwhile, two active boundary controllers are proposed to restrain the vibrations both in bending and twisting. By using Lyapunov’s direct method, the stability of the flexible wing system can be ensured. Numerical simulations based on the finite-difference method demonstrate the effectiveness of the proposed control schemes. 

Trajectory Tracking Control for a Three-Dimensional Flexible Wing

This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach. 

Approximation-Based Nussbaum Gain Adaptive Control of Nonlinear Systems With Periodic Disturbances

This article deals with the event-triggered leader-following guaranteed cost consensus control problem for second-order nonlinear multiagent systems, in which the guaranteed cost function is proposed to facilitate to enhance the consensus tracking regulation performance. To reduce the frequency of information transmission, a distributed event-triggered mechanism, which broadcasts the triggered states to its neighbours for each agent, is designed, and the triggering condition is then constructed for leader-following second-order nonlinear multiagent systems. By employing Lyapunov–Krasovskii method and Barbalat’s lemma, some sufficient conditions are derived to ensure the leader-following consensus and guaranteed cost performance for second-order nonlinear multiagent systems. It is also exhibited that the constructed triggering condition can efficaciously exclude the Zeno behavior. To testify the efficacy of the proposed theoretical methodology, a simulation example is offered. 

Event-Triggered Guaranteed Cost Leader-Following Consensus Control of Second-Order Nonlinear Multiagent Systems

An event-triggered control (ETC) system transmits data packages and updates control inputs only when the predefined criterion is satisfied. In this way, network communication and computing resources are scheduled more reasonably in contrast to the traditional periodic sampling strategy. Small-gain approach proposed in recent literatures is a new modeling method to deal with nonlinear ETC systems. Different from traditional ETC models, stability criteria are proposed in the form of input to state stability (ISS) gain to design the triggering mechanisms. This paper introduces additional dynamic variables in this model and proposes a small-gain based dynamic event-triggered strategy. Sufficient conditions to guarantee the stability of the system are derived with the help of cyclic-small-gain theorem and Zeno behaviors are avoided to ensure the feasibility of this method in practical applications. Numerical simulations are given to demonstrate the effectiveness of our approach.

http://sysmath.com/jssc/EN/article/downloadArticleFile.do?attachType=PDF&id=13869

Dynamic Event-Triggered Control for Nonlinear Systems: A Small-Gain Approach

Networked control systems (NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control (ETC) is often used to reduce the amount of communication while still keeping a satisfactory performance of the system, by transmitting the measurements only when an event-triggered condition is satisfied. However, some network-induced problems would happen inevitably, such as communication delay and packet loss, which can degrade the control performance significantly and can even lead to instability. In this paper, a periodic event-triggered NCS considering both time-varying delay and packet loss is studied. The system is discretized into a piecewise linear system with uncertainty. Then the model is handled by a polytopic overapproximation method to be more suitable for stability analysis. Finally, stability conditions are obtained and presented in terms of linear matrix inequalities (LMIs). The result is illustrated by a numerical example.

http://sysmath.com/jssc/EN/article/downloadArticleFile.do?attachType=PDF&id=14042

Yongqiang Bai

Papers

Dynamic Event-Triggered Control for Nonlinear Systems: A Small-Gain Approach

Stability Analysis of Event-Triggered Networked Control Systems with Time-Varying Delay and Packet Loss