Distributed Fixed-time Formation-containment Control for Multiple Euler-Lagrange Systems with Directed Graphs
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Distributed Fixed-time Formation-containment Control for Multiple Euler-Lagrange Systems with Directed Graphs Menghu Hua, Huafeng Ding*, Xiang-Yu Yao, and Xinxin Zhang Abstract: In this paper, the distributed fixed-time formation-containment (DFTFC) problem of multiple EulerLagrange systems with parametric uncertainties and input disturbances is studied under directed graphs. First, a distributed fixed-time sliding-mode estimator is constructed to estimate the desired states of each robot with that only parts of followers can access the information of leaders. Next, based on the estimator, a distributed fixed-time formation control algorithm is developed to drive leaders to achieve a specified formation. Then, the distributed fixed-time containment control algorithm is proposed for followers with its estimated states being tracked in a fixed time. Note that an explicit upper bound of the convergence time of DFTFC control algorithm is obtained independent of initial conditions. Finally, numerical simulations are performed to show the effectiveness of the obtained theoretical results. Keywords: Directed graphs, fixed-time control, formation-containment control, multiple Euler-Lagrange systems.
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INTRODUCTION
Recently, distributed coordinated control of multi-agent systems has been a popular research topic due to its wide applications in a variety of fields, such as spacecraft, underwater robots and autonomous vehicles [1–3]. Meanwhile, distributed coordinated control has been studied by numerous meaningful works to achieve various collective behaviors, including consensus, formation, containment and so on [4–9]. For detailed instance, references [4, 7] addressed the consensus problem of linear multi-agent systems in the presence of actuator faults under switching communication network. The authors in [8] investigated the task-space formation tracking problem of nonlinear heterogeneous robotic systems with external disturbances, kinematic and dynamic uncertainties. Without relying on velocity and acceleration measurements, the distributed finite-time containment problem of a group of mobile agents modeled by double-integrator dynamics was discussed in [9], where all followers were eventually contained in a convex hull formed by leaders. It is worthy to notice that the above-mentioned works mainly focus on single-task control problems, while the systems in real applications are usually demanded to solve multi-task control problem via the cooperation of agents. As a typical topic, the formation-containment control is
recently investigated where some agents in first layer are driven to achieve a convex formation and the others in second layer are forced into the structured convex hull, and it is of great significance in practical application and theory research. Different task controllers can be respectively designed on two layers to obtain tasks successively such that it is more flexible for practical applications. For theory research, the two-layer syst
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