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

• Published in: International journal of robust and nonlinear control Vol. 30; no. 7; pp. 2999 - 3022
• Main Authors: Silva, T. C., Souza, F. O., Pimenta, L. C. A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.05.2020
• Subjects: Algorithms; Communication delays; Containment; Control algorithms; Convergence; Euler-Lagrange equation; Euler‐Lagrange systems; formation‐containment; input saturation; Linear matrix inequalities; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4919

Summary This paper is concerned with the problem of formation‐containment on networked systems, with interconnected systems modeled by the Euler‐Lagrange equation with bounded inputs and time‐varying delays on the communication channels. The main results are the design of control algorithms and sufficient conditions to ensure the convergence of the network. The control algorithms are designed as distributed dynamic controllers, in such a way that the number of neighbors of each agent is decoupled from the bound of the control inputs. That is, in the proposed approach the amplitude of the input signal does not directly increase with the number of neighbors of each agent. The proposed sufficient conditions for the asymptotic convergence follow from the Lyapunov‐Krasovskii theory and are formulated in the linear matrix inequalities framework. The conditions rely only on the upper bound of delays and on a subset of the controller parameters, but they do not depend on the model of each agent, which makes it suitable for networks with agents governed by distinct dynamics. In order to illustrate the effectiveness of the proposed method we present numerical examples and compare with similar approaches existing in the literature.