Mohamed Maghenem

Lyapunov Functions for Persistently-Excited Cascaded Time-Varying Systems: Application to Consensus

We present some results on stability of linear time-varying systems with particular structures. Such systems appear in diverse problems, which include the analysis of adaptive systems, persistently-excited observers and consensus of systems interconnected through time-varying links. The originality of our statements rely in the fact that we provide smooth strict Lyapunov functions hence, our proofs are constructive and direct. Moreover, we establish uniform global exponential stability with explicit stability and decay estimates. For illustration, we address a brief but representative case-study of consensus of Lagrangian systems interconnected through unreliable links.

On the estimation of the consensus rate of convergence in graphs with persistent interconnections

ABSTRACT The aim of the current article is to establish myriad convergence rate estimates to consensus for time-varying graphs with persistent interaction. Several novel analysis methodologies for consensus protocols employing the notions of persistence of excitation and Lyapunov functions are provided. The estimates are compared with each other and existing literature. Numerical simulations on test examples are illustrated to support the theoretical findings.

Formation-Tracking Control of Autonomous Vehicles Under Relaxed Persistency of Excitation Conditions

We present a smooth nonlinear time-varying formation-tracking controller for autonomous vehicles modeled as a nonholonomic unicycle. Our first result consists of a leader–follower tracking controller that guarantees uniform global asymptotic stability under the standing assumption that either the rotational or the translational reference velocity is persistently exciting. Then, we extend this result to the case of formation control of a swarm of vehicles. We show that this problem may be solved via decentralized tracking control, under the assumption that each robot communicates with one leader and one follower.

A Cascades Approach to Formation-Tracking Stabilization of Force-Controlled Autonomous Vehicles

We present a cascades-based controller for the problem of formation-tracking control in a group of autonomous vehicles. We consider general models composed of a velocity kinematics equation and a generic force-balance equation. For each vehicle, a local controller ensures tracking of a reference generated by a leader vehicle. One or many vehicles may have access to the reference trajectories; each robot has one leader only, but may have several followers (spanning-tree topology). We establish uniform global asymptotic stability in a closed loop for a wide class of controllers. Our analysis relies on the construction of an original strict Lyapunov function for the position tracking error dynamics and an inductive argument based on the cascades-systems theory.

A robust δ-persistently exciting controller for formation-agreement stabilization of multiple mobile robots

We propose a δ-persistently exciting controller [17] for leader-follower agreement control of a group of non-holonomic mobile robots, under the assumption that the virtual-leader velocities converge to zero. We assume that each of the vehicles in the formation communicates only with one leader and one, or several followers hence, that is, they form a spanning-tree communication topology rooted at the virtual leader. The control is decentralized and guarantees the convergence of the error coordinate of each agent, relatively to its neighbor. More significantly, our proofs are based on Lyapunovs direct method that is, we provide strict Lyapunov functions to guarantee strong integral input-to-state stability with respect to the reference velocities and, hence, uniform global asymptotic stability of the closed-loop system provided that the reference velocities are integrable.

A robust δ -persistently exciting controller for leader-follower tracking-agreement of multiple vehicles

Abstract We solve the leader-follower tracking-agreement control problem for Nonholonomic mobile robots with uncertainties; this consists in controlling a group of robots to take a pre-specified configuration (formation) and to move about following a vanishing reference trajectory. We assume that each robot has one unique leader and it is controlled by a local tracking controller that uses relative position and velocity measurements, but each robot may have one or several followers. We also assume that the reference trajectory is available to only one robot (the swarm leader). The control design is based on a δ-persistently exciting controller (for the kinematics model) that is robust to decaying perturbations and an outer control loop at the force-inputs level. Our proofs are constructive as they are based on Lyapunov’s direct method; moreover, we establish strong integral input-to-state stability. To the best of our knowledge this is the first result of this nature in the literature of nonholonomic mobile robots.

Singular-perturbations-based analysis of synchronization in heterogeneous networks: A case-study

In recent work, we laid the basis of an analysis framework for the study of heterogeneous networks. In essence, it is postulated that in a heterogeneous network a collective non-trivial behaviour arises, which may be modelled as a dynamical system itself. Then, we say that the networked systems synchronize or, more precisely, achieve dynamic consensus if they adopt this emergent behaviour. In this paper we consider the case-study of coupled Andronov-Hopf oscillators. We establish that the emergent dynamics, which is of the same nature as a single oscillator, is orbitally stable. Then, we show that the trajectories of the individual oscillators tend to a neighbourhood of the stable orbit. For the first time in the study of synchronization, the analysis is based on singular-perturbations theory; we show that the emergent dynamics corresponds to a slow system while the synchronization errors form a fast dynamics.