Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

Abstract

Summary In this paper, distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding‐mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite‐time convergence for the error variables. Then, a distributed finite‐time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite‐time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite‐time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.

Distributed formation‐containment control with Euler‐Lagrange systems subject to input saturation and communication delays

“…Then, we derive sufficient convergence conditions for the formation‐containment. More specifically, the contributions of this work come in twofold: first, regarding the problem of formation‐containment it extends the existing works found in the literature in the following aspects: the agents dynamics of the multi‐agent system are nonlinear and modeled by the Euler‐Lagrange equation, which can be used to represent numerous mechanical and electrical systems, while most part of the literature on formation‐containment control is focused on linear dynamics, with some recent exceptions; the actuators limits are considered along with the nonlinear dynamics. This consideration is pertinent because it eases the implementation of the control strategy on real systems.…”

“…In Reference it is studied the robust containment of uncertain Euler‐Lagrange systems subject to disturbances, without taking into account input‐saturation nor delays. The finite‐time containment is addressed in Reference with agents subject to constant communication delay and using neural networks to estimate model uncertainties and disturbances, in Reference the finite‐time containment is also addressed using neural networks to compensate the effects of uncertainties and disturbances, and they additionally utilize the error constraint strategy and sliding mode control. It is interesting to point out that the error constraint technique employed in References and might improve the network convergence performance.…”

“…On the formation‐control with linear agents, stochastic communication topologies were recently considered in References , and time delays in Reference . With interconnected Euler‐Lagrange agents, communication delays were recently studied in Reference and in Reference . In Reference , to handle time delays, it is used an estimative of their values assuming sufficiently slow change in their variations, our methodology is based on the delays upper bounds and we only require the existence of the first delays derivative.…”

“…In Reference , to handle time delays, it is used an estimative of their values assuming sufficiently slow change in their variations, our methodology is based on the delays upper bounds and we only require the existence of the first delays derivative. In Reference time delays among agents are considered constant and uniform, unlike in the present paper, in which time delays are assumed time‐varying and nonuniform over the network; the formation‐containment is approached taking into account communication delays among agents and input saturation simultaneously, which to the best of authors' knowledge it is a scenario that has not yet been addressed on the literature. Additionally, the proposed distributed control strategy does not depend on the knowledge of the agents inertia matrix nor the Coriolis forces, it also does not rely on the neighbors velocity information.…”

Decentralized active sensor fault tolerance in attitude control of satellite formation flying

“…Satellite formation flying (SFF) missions have been increasingly attracted in the last two decades as a promising technology in aerospace fields 1 . Its advantages include maintenance enhancement and redundancy capability.…”