Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs

We analyse the solutions of networked heterogeneous nonlinear systems. We assume that the closed-loop interconnected systems form a network with an underlying connected directed graph that contains a directed spanning tree. For these systems, we establish global uniform ultimate boundedness of the solutions, under the assumption that each agent's dynamics defines a semi-passive. As a corollary, we also establish global uniform global boundedness of the solutions

Dynamic Consensus under Weak Coupling: a case study of nonlinear oscillators

International audienceDynamic consensus is a term coined in 1 [1] to denote the state of synchronization of complex networked systems. It covers the common paradigm of consensus in which case all the systems stabilize at a common equilibrium point. It is known that for certain networks (e.g., of homogeneous systems) dynamic consensus is achievable provided the interconnection gain is elevated. In this case, all the systems behave as one average dynamical system. In this paper we analyze the collective behavior of heterogeneous Stuart-Landau oscillators under weak coupling. We show that their behavior cannot be characterized by a single average system, but by a reducedorder network. We give a detailed characterization of the latter and establish a relation with the eigenvalues of the underlying Laplacian matrix, hence, with the network's topology

Robust leader-follower formation control of autonomous vehicles with unknown leader velocities

Submitted for presentation at the European Control ConferenceWe address the problem of formation-tracking control of velocity-controlled unicycles in a leader-follower configuration, both with known and unknown leader velocities. The controller design is based on relative measurements: distances and line-of-sight angles. This type of measurements are provided by onboard sensors rather than global positioning systems. We assume that a virtual leader generates a desired reference trajectory for the whole swarm, that is once continuously differentiable, bounded and with bounded derivative. We propose two controllers, one for which it is assumed that the leader velocities are known and one in which they are unknown

On the robustness of networks of heterogeneous semi-passive systems interconnected over directed graphs

In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are semi-passive [1] and the graph contains a spanning tree

On Global Asymptotic Stability of Heterogeneous Modular Networks with Three Time-Scales

International audienceWe analyse the collective bahaviour of relatively large networks with the characteristic that nodes may be compartmentalised in modules. These are groups of systems that may be regarded as subnetworks in which each group of nodes achieves consensus with a certain rapidity. The dynamics of such networks exhibits, at least, two time-scales, for which singular perturbations methods may be used to assess the overall behaviour. In this paper, we demonstrate that there are actually three natural time-scales and, accordingly, three interconnected dynamical systems with distinct speeds of convergence coexist. Our main statement establishes conditions for global asymptotic stability of the origin in such networked systems. In particular, we focus on bilinear heterogeneous systems and provide an illustrative example concerning chaotic oscillators

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

We examine the collective behavior of largescale networks of heterogeneous nonlinear systems with directed weighted interconnections, and containing a spanning tree. We consider networks that are composed of groups of densely interconnected nodes, called modules, that are in turn sparsely interconnected. Such networks are called modular. The modules represent sub-networks wherein consensus may be rapidly achieved, while synchronization among modules occurs at a lower pace. Furthermore, relying on the framework of [1], we identify an underlying dynamics that corresponds to a weighted average of the nodes' respective states. This average dynamics evolves on a yet slower timescale. Such triple timescale make modular networks are amenable to be analyzed via singular-perturbations theory. We show that if the nodes' dynamics are semi-passive and the average dynamics is globally asymptotically stable, so is the entire network. In the case that the average dynamics is not globally asymptotically stable we show how our main analysis statement can be used for network control, via the addition of control nodes, in order to globally asymptotically stabilize the network