M. di Bernardo

Distributed Adaptive Control of Synchronization in Complex Networks

This technical note studies distributed adaptive control of synchronization in complex networks. An effective distributed adaptive strategy to tune the coupling weights of a network is designed based on local information of node dynamics. The analysis is then extended to the case where only a small fraction of coupling weights can be adjusted. A general criterion is derived and it is found that synchronization can be reached if the subgraph consisting of the edges and nodes corresponding to the updated coupling weights is connected. Finally, simulation examples are given to illustrate the theoretical analysis.

Evolution of Complex Networks via Edge Snapping

In this paper, we present a novel adaptive strategy for consensus and synchronization of complex networks. The strategy is inspired by bistable phenomena that are observed in a variety of mechanical systems. The novelty is that the adaptation involves the topology of the network itself rather than its coupling gains. In particular, we model the evolution of each coupling gain as a second order dynamical system that is subject to the action of a double-well potential. Through a new mechanism, termed as edge snapping, an unweighted network topology emerges at steady state. We assess the stability properties of the proposed scheme through analytical methods and numerical investigations. We conduct an extensive numerical study of the topological properties of the emerging network to elucidate the correlation between the initial conditions of the nodes dynamics and the network structure.

Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks

In this brief, the contraction theory is applied to the synchronization of a network. The association between the contraction principle, the Lyapunov exponents of a system, and the master stability function of the network is pointed out. Novel sufficient criteria for the fulfillment of a synchronous state are derived.

Hybrid Model Reference Adaptive Control of Piecewise Affine Systems

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability.

Synchronization in weighted scale-free networks with degree-degree correlation

Abstract We study synchronization phenomena in scale-free networks of asymmetrically coupled dynamical systems featuring degree–degree correlation in the topology of the connection wiring. We show that when the interaction is dominant from the high-degree to the low-degree (or from the low-degree to the high degree) nodes, synchronization is enhanced for assortative (or disassortative) degree–degree correlations.

Synthesis and Experimental Validation of the Novel LQ-NEMCSI Adaptive Strategy on an Electronic Throttle Valve

This paper is concerned with the design of a novel adaptive controller, namely the linear quadratic new extended minimal control synthesis with integral action (LQ-NEMCSI). We present for the first time the analytical proof of asymptotic stability of the controller and experimental evidence of the algorithm effectiveness for controlling an electronic throttle body: an element of any drive-by-wire system in automotive engineering, affected by many nonlinear perturbations.

EFFECTS OF DEGREE CORRELATION ON THE SYNCHRONIZATION OF NETWORKS OF OSCILLATORS

In this paper, we investigate the effects of degree correlation on the synchronization of networks of coupled identical nonlinear oscillators. Firstly, it is shown both numerically and theoretically that synchronizability is enhanced when the network topology exhibits negative degree correlation. Then, the synchronization dynamics is studied of a network of identical Rossler oscillators under variation of the network degree correlation properties. We observe that negative correlation has a positive effect on the synchronization dynamics of such networks.

Synchronization of Networks of Non-Identical Chua's Circuits: Analysis and Experiments

This paper is concerned with the theoretical and experimental analysis of synchronization and pinning control of networks of non-identical Chuas circuits. The design and implementation is presented of an appropriate setup to carry out experiments on networks of these nonlinear circuits with easily reconfigurable parameter values. Then, the theoretical expectations are validated of the so-called Extended Master Stability Function approach to study the onset of synchronization in the presence of real parameter mismatches between the circuits at the network nodes. The validation is carried out both numerically and experimentally. For the first time, the EMSF is also used to investigate pinning synchronization in a network of non-identical circuits where a master node (or pinner) is used to drive the network dynamics towards some desired synchronous evolution. The numerical and experimental results confirm the viability of the EMSF as an effective analysis and design tool.

Novel switched model reference adaptive control for continuous piecewise affine systems

This paper is concerned with the derivation of a novel model reference adaptive control (MRAC) scheme for piecewise-affine (PWA) continuous systems. A novel version of the minimal control synthesis algorithm, originally developed as a MRAC for smooth systems, is presented. The resulting adaptive algorithm is a switched feedback controller able to cope with uncertain continuous PWA systems. The proof of stability, based on the newly developed passivity theory for hybrid systems, is provided and the effectiveness of the new proposed control strategy is numerically tested.

Two-Parameter Discontinuity-Induced Bifurcation Curves in a ZAD-Strategy-Controlled DC–DC Buck Converter

The dynamics of a zero-average dynamic strategy controlled dc-dc Buck converter, modelled by a set of differential equations with discontinuous right-hand side is studied. Period-doubling and corner-collision bifurcations are found to occur close to each other under small parameter variations. Closer examination of the parameter space leads to the discovery of a novel bifurcation. This type of bifurcation has not been reported so far in the literature and it corresponds to a corner-collision bifurcation of a nonhyperbolic cycle. The bifurcation boundaries are computed analytically in this paper and the system dynamics are unfolded close to the novel bifurcation point.