Model‐independent consensus control of Euler‐Lagrange agents with interconnecting delays

Abstract

Summary In this paper, we introduce, for the first time, a proportional‐integral‐derivative controller to solve the consensus problem for networked Euler‐Lagrange agents. The proposed control scheme solves both the leaderless and the leader‐follower consensus problems without requiring the exact knowledge of any part of the agent model. Contrary to the previous studies in the literature, we do not require either to cancel any part of the agent model, which renders robust our approach, nor employ discontinuous controllers. It is proven that both consensus problems are solved globally and asymptotically and the presence of bounded time‐varying communicating delays is considered.

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

“…Within this crescent core of literature, there are few works addressing input saturation and communication delays simultaneously and, to the best of authors' knowledge, there is no previously published work on formation‐containment of networks with Euler‐Lagrange systems subject to input saturation and time delays. Similar conditions are found on the study of consensus problem in the works of References and , on the synchronism in Reference , and on the problem of tracking control of multiple systems in Reference . In Reference it is studied the connectivity‐preserving problem for the consensus, and their approach have significant distinctions from ours.…”

“…The problem studied here is more general than the consensus and no initial conditions are imposed other than the connected graph. In Reference the authors are also concerned with the consensus problem and besides that, they propose an integration action on the controllers of the Euler‐Lagrange systems considering communication delays, but input saturation was not analyzed. In Reference the synchronism is studied considering networks with slowly time‐varying communication delays, which are tackled by using estimated values to compensate them.…”

“…Moreover, the approach used in References and to deal with delays among agents is very similar to the one proposed by Reference . Here we handle the communication delays in an alternative way leading to a linear matrix inequality (LMI) test that relates the delays upper bounds with some parameters of the controllers.…”

“…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 and , 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 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 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 and handle the communication delays with the same approach suggested by Nuño and collaborators. On the numerical examples we show that, even though we also consider the input saturation, our proposed conditions are less conservative than the ones found in their work. …”

Consensus in networks of uncertain robot manipulators without using neighbors’ velocity information

“…In Ye et al [29], leaderless consensus problem is solved with a discontinuous control law and semi-global stability is achieved. In Hernández-Guzmán and Orrante-Sakanassi [30], a smooth PID controller is proposed to solve both leaderless and leaderfollower consensus problems and global stability is proved. In Li et al [31], a distributed neural network controller is proposed to deal with the leader-follower problem of nonidentical EL systems and uniform ultimate boundedness of tracking error is achieved.…”