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

Abstract

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. K E Y W O R D S Communication delays, Euler-Lagrange systems, formation-containment, input saturation 1 Int J Robust Nonlinear Control. 2020;30:2999-3022. wileyonlinelibrary.com/journal/rnc• 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. This reduces the communication burden on the network and provides a robust control strategy.Secondly, considering the consensus, a particular case of the main problem investigated in this manuscript, and comparing with those from the literature that primarily study consensus under similar conditions, the following contributions can also be highlighted:• input saturation was previously studied in the context of consensus problem in References 19 and 45, but with some important distinctions from our approach, namely: (a) we now propose a strategy to deal with the input saturation and communication delays simultaneously, (b) different from Reference 45 our dynamic controller does not rely on the knowledge of inertia nor Coriolis matrices and, (c) in contrast with both approaches, as mentioned above, the control strategy proposed here does not depend on relative velocity measurements;• regarding the communication delays among agents, it is noteworthy that the results of Nuño and collaborators 20,21,37,46 seem to contribute with the most notorious conditions on communication delays on the consensus of networked Euler-Lagrange systems. For example, the results in References 33 and 34 hand...

Event-based fixed-time formation-containment control for networked Euler-Lagrange systems

“…For example, the control of leaders is not taken into account, namely, it assumes that the formation of leaders is already formed. In addition, the agreement value that all agents converge to is usually unknown if the desired trajectory of each agent is not available, which may result in the chaos of the entire control system [19][20][21]. Subsequently, it is meaningful to study the event-based FCC issue for NELSs [22].…”

“…It is generally known that actuator saturation is one of the most common problem in many mechanical systems, and actuator saturation nonlinearity can severely restrict system control performance and potentially bring about the instability of control system. Hence the fixed-time control problems of Euler-Lagrange systems subject to input saturations are given much focus [20,21]. The fixed-time tracking control problems for single-agent systems with saturation constraints were solved in [36][37][38].…”

“…(3) The controller update frequency is greatly reduced by the event-triggered mechanism as compared to the results of continuous controller update [19][20][21][22]. Besides, different from existing works [32][33][34][35], a novel fixed-time adaptive control algorithm is first proposed for NELSs with complex input saturation and unknown disturbances.…”

Bipartite containment of descriptor multi‐agent systems via an observer‐based approach

“…Recently, a great deal of attention has been devoted to containment control of MASs, and thus obtained some important results [6][7][8][9][10][11][12]. In [6], containment problem was addressed for leader-follower MASs involving first-order dynamics in the presence of switching communication topologies.Containment of MASs involving second-order dynamics was investigated in [7], where only position information is used and velocity and acceleration information of all agents is unavailable.…”

“…In [11], containment problems of linear MASs were tackled under the situations of zero intermittent control and constant velocity intermittent control, respectively. Under the circumstances of input saturation and communication delays, formation‐containment control issue of MASs with Euler–Lagrange equation was handled in [12].…”