Commande décentralisée et analyse des réseaux partitionnés en groupes

Abstract : Networks appear in several areas of science and engineering such as biology, physics, sociology as well as robotics and communication theory. Studying these networks it is possible to see cluster-like structures, which are disconnected or very weakly connected one to another. The presence of these clusters hampers consensus throughout the overall network. Instead, local agreement is reached within each cluster. To enforce consensus we have to design an appropriate decentralized controller that imposes interactions between clusters. While the interactions inside each cluster are continuous, we propose a quasi-periodic discrete controller to exchange information between clusters. A single agent from each cluster is chosen to be the leader, and at certain moments, the leaders communicate with each other through a new network. This allows consensus in the entire network but generates resets/jumps on the leaders’ state. The first contribution of this manuscript is related to the characterization of the consensus value in the linear impulsive dynamics framework. It is noteworthy that the consensus value depends only on the initial conditions and the topologies of the involved networks. Therefore, the consensus value does not depend on the reset sequence used for the leaders’ states. To study the stability of the consensus value a LMI based condition is proposed. The main advantage of this approach is its flexibility. Indeed with some modifications to the LMI condition it is possible to analyse the convergence speed of the network or to design the leaders’ network. The purpose of leaders’ network design is to reach an a priori specified consensus value with a specified convergence speed. Whatever is the objective, throughout the manuscript we consider that the network topology is fixed and known for each cluster. The set of consensus values that can be reached is restricted to the interval defined by the minimum and maximum initial local agreements. A last contribution is related to the application of the proposed methodology to a practical situation. We consider a fleet of non-holonomic mobile robots separated in clusters. The communication inside each cluster are secured and cheap while between clusters it is expensive and not securely to communicate. Nevertheless the robots have to reach a given formation. In this case our consensus algorithm is in charge of providing reference trajectories to each robot by using only the available local information. The robot follows the reference by using a classical trajectory tracking control.
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Marcos César Bragagnolo. Commande décentralisée et analyse des réseaux partitionnés en groupes. Other. Université de Lorraine, 2015. English. ⟨NNT : 2015LORR0283⟩. ⟨tel-01754576⟩

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