We analyze the collective behavior of relatively large networks with the characteristic that nodes may be compartmentalized 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 exhibit, at least, two time-scales, for which singular perturbation methods may be used to assess the overall behavior. 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.

We address a classical identification problem that consists in estimating a vector of constant unknown parameters from a given linear input/output relationship. The proposed method relies on a network of gradient-descent-based estimators, each of which exploits only a portion of the input-output data. A key feature of the method is that the input-output signals are hybrid, so they may evolve in continuous time (i.e., they may flow), or they may change at isolated time instances (i.e., they may jump). The estimators are interconnected over a weakly-connected directed graph, so the alternation of flows and jumps combined with the distributed character of the algorithm introduce a rich behavior that is impossible to obtain using continuous- or discrete-time estimators. A condition of persistence of excitation in hybrid form ensures exponential convergence of the estimation errors. The proposed approach generalizes the existing centralized gradient-descent algorithms and yields relaxed sufficient conditions for (uniform-exponential) parameter estimation. In addition, we address the observation/identification problem for a class of hybrid systems with unknown parameters using a distributed network of adaptive observers/identifiers.

In this paper we solve the full-consensus problem for multiple nonholonomic vehicles interacting over a directed leader-follower topology and subject to sensing constraints in the form of limited range and limited field-of-view. Remarkably, based on a polar-coordinates model transformation, the designed controller is time-invariant and smooth (in the domain of definition). Moreover, the control laws rely only on local measurements, making it well suited for implementation. The asymptotic convergence to the consensus manifold as well as the respect of the constraints is established using Lyapunov’s first method and cascaded systems theory. Realistic simulations in the Gazebo-ROS environment, which illustrate the effectiveness of our theoretical contributions, are shown in an accompanying video.

It is known in the practice of closed-loop identification of mechanical systems that, since the Langrangian dynamic model is linear in the constant physical parameters, a sufficient condition for parameter convergence is that the robot be made to follow reference trajectories which render the regressor matrix, persistently exciting. Slotine and Li established this many years ago for a particular adaptive controller. This result is based on adaptive linear systems theory and relies on the condition that the applied control law makes the robot asymptotically track the imposed rich reference trajectories. This paper revisits this problem and establishes a proof that this condition is not only sufficient but also necessary to establish the stronger property of uniform global asymptotic stability of the overall closed-loop system.

In this paper we characterize a class of passivity-based regulators for robot manipulators which, without assuming velocity measurement, aims at modifying the total energy of the closed loop and adding the required dissipation. The class is parametrized in terms of the desired closed loop total energy function, specified by the designer. We show that several apparently unrelated stabilizing output feedback regulators recently reported in the literature, are in fact particular cases of this class. Our results aim at providing a unified framework to compare different stabilizing schemes via analysis of their energy dissipation properties.>