Formation-containment control of networked Euler–Lagrange systems: An event-triggered framework

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...

Section: Introductionmentioning

confidence: 91%

𝒱_{L} = {1, \dots, 6}

, and four followers

𝒱_{F} = {7, \dots, 10}

.…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Silva

Souza

Pimenta

2020

“…In the case of tracking one stationary leader, two model‐independent controllers are proposed in Reference , where the variable‐gain control law is suitable for undirected networks and the constant‐gain control algorithm is applied to directed networks. More recently, an event‐triggered formation‐containment control framework is developed in Reference to improve the simultaneous performance of leaders' formation and followers' containment. As is known to all, a dynamic leader has more application values than a stationary one in practical scenarios.…”

Section: Introductionmentioning

confidence: 99%

Distributed event‐triggered tracking control with a dynamic leader for multiple Euler‐Lagrange systems under directed networks

Duan

Sun

et al. 2020

The distributed tracking control for multiple Euler-Lagrange systems with a dynamic leader is investigated in this article via the event-triggered approach.Only a portion of followers have access to the leader, and the communication topology among all agents is directed that contains a directed spanning tree rooted at the leader. The case that the leader's generalized velocity is constant is first considered, and a distributed event-based control law is developed by using a velocity estimator. When the leader's generalized velocity is time-varying, novel distributed continuous estimators are proposed to avoid the undesirable chattering effect while guaranteeing that the estimate errors converge to zeros.With the designed distributed estimators, another distributed event-based control protocol is provided. Controller update frequency and resource consumption in our work can be reduced by applying the aforementioned two distributed control laws, and the tracking errors can converge to zeros. In addition, it is rigorously proved that no agent exhibits Zeno behavior. Finally, the effectiveness of the proposed distributed event-based control laws is elucidated by a number of simulation examples. K E Y W O R D Sdirected graph, distributed tracking control, dynamic leader, event-triggered control, Euler-Lagrange system INTRODUCTIONCoordination control of multiagent systems, including cooperative tracking, 1 formation, 2 flocking, 3 distributed filtering, 4 distributed optimization, 5 and so forth, has attracted enormous attention due to a wide range of applications. Cooperative systems provide several advantages in implementing synergic tasks, such as high robustness, strong adaptivity, great flexibility, and low operational costs. 6 A large class of mechanical systems, such as air vehicles, robot manipulators, and spacecraft, can be modeled by the Euler-Lagrange system. Various fundamental results on distributed tracking for multiple Euler-Lagrange systems have been established. In the following, we just name a few examples. In the case of tracking one or multiple stationary leaders, a distributed tracking law is addressed in Reference 7 over undirected networks, where the requirement on velocity measurements is relaxed. In Reference 8, a distributed adaptive control law is designed to solve the containment control problem under directed graphs. If one or multiple dynamic leaders are considered, a sliding mode control algorithm is Int J Robust Nonlinear Control. 2020;30:3073-3093.wileyonlinelibrary.com/journal/rnc

“…One of the potential applications of formation-containment control (FCC) is "search and rescue problem" of mobile robots in hazardous and extreme environments, where the leader robots with detection devices are able to achieve a predefined formation depending on the surrounding environment and the follower robots then move into a safe region formed by the leaders. The articles [25][26][27] have laid major contribution in the area of FCC of Euler-Lagrange systems: in Reference 25, a cooperative and adaptive FCC framework has been introduced for networked Euler-Lagrange systems without using relative velocity information; in Reference 26, the development of Reference 25 has been extended to consider the effect of input saturation; while in Reference 27, the FCC problem of Euler-Lagrange systems is solved in an event-triggered framework. FCC of first-order and second-order multiagent systems are investigated in References 28 and 29, respectively.…”

Section: Introductionmentioning

confidence: 99%

Two‐layer distributed formation‐containment control strategy for linear swarm systems: Algorithm and experiments

Bhowmick

Lanzon

2020

This article addresses the problem of designing a two-layer distributed formation-containment control scheme for linear time-invariant swarm systems with directed communication topology, where the states of the leaders attain a prespecified time-varying/stationary formation and the states of the followers converge into the convex hull spanned by the states of the leaders. To achieve formation-containment, a set of distributed control protocols is developed utilizing the neighboring state information, which enables the proposed scheme operate without using global information about the entire interaction topology. The conditions to achieve formation-containment are suggested and a theoretical proof of the proposed scheme is also derived exploiting the Lyapunov stability approach. An algorithm is written to provide systematic guidelines on how to implement the control protocols in practice. It is argued that the consensus problem, formation tracking problem, and containment control problem can all be viewed as special cases of formation-containment. A simulation case study has been presented to demonstrate the usefulness and effectiveness of the proposed scheme and moreover, lab-based hardware experiments involving networked mobile robots were performed to test the feasibility of the scheme in real-time implementation.