Harmonic synchronization under all three types of coupling: position, velocity, and acceleration

Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.Comment: 9 pages, 2 figure

Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.

This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems. In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties

Contraction analysis of switched systems with application to control and observer design

In many control problems, such as tracking and regulation, observer design, coordination and synchronization, it is more natural to describe the stability problem in terms of the asymptotic convergence of trajectories with respect to one another, a property known as incremental stability. Contraction analysis exploits the stability properties of the linearized dynamics to infer incremental stability properties of nonlinear systems. However, results available in the literature do not fully encompass the case of switched dynamical systems. To overcome these limitations, in this thesis we present a novel extension of contraction analysis to such systems based on matrix measures and differential Lyapunov functions. The analysis is conducted first regularizing the system, i.e. approximating it with a smooth dynamical system, and then applying standard contraction results. Based on our new conditions, we present design procedures to synthesize switching control inputs to incrementally stabilize a class of smooth nonlinear systems, and to design state observers for a large class of nonlinear switched systems including those exhibiting sliding motion. In addition, as further work, we present new conditions for the onset of synchronization and consensus patterns in complex networks. Specifically, we show that if network nodes exhibit some symmetry and if the network topology is properly balanced by an appropriate designed communication protocol, then symmetry of the nodes can be exploited to achieve a synchronization/consensus pattern

組合せ最適化問題のための測定フィードバック型コヒーレント・イジングマシンの実現と評価

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 合原 一幸, 東京大学教授 岩田 覚, 東京大学准教授 平田 祥人, 東京大学准教授 大西 立顕, 東京大学准教授 鈴木 大慈University of Tokyo(東京大学

An Initial Framework Assessing the Safety of Complex Systems

Trabajo presentado en la Conference on Complex Systems, celebrada online del 7 al 11 de diciembre de 2020.Atmospheric blocking events, that is large-scale nearly stationary atmospheric pressure patterns, are often associated with extreme weather in the mid-latitudes, such as heat waves and cold spells which have significant consequences on ecosystems, human health and economy. The high impact of blocking events has motivated numerous studies. However, there is not yet a comprehensive theory explaining their onset, maintenance and decay and their numerical prediction remains a challenge. In recent years, a number of studies have successfully employed complex network descriptions of fluid transport to characterize dynamical patterns in geophysical flows. The aim of the current work is to investigate the potential of so called Lagrangian flow networks for the detection and perhaps forecasting of atmospheric blocking events. The network is constructed by associating nodes to regions of the atmosphere and establishing links based on the flux of material between these nodes during a given time interval. One can then use effective tools and metrics developed in the context of graph theory to explore the atmospheric flow properties. In particular, Ser-Giacomi et al. [1] showed how optimal paths in a Lagrangian flow network highlight distinctive circulation patterns associated with atmospheric blocking events. We extend these results by studying the behavior of selected network measures (such as degree, entropy and harmonic closeness centrality)at the onset of and during blocking situations, demonstrating their ability to trace the spatio-temporal characteristics of these events.This research was conducted as part of the CAFE (Climate Advanced Forecasting of sub-seasonal Extremes) Innovative Training Network which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813844

Digital pulse processing

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 71-74).This thesis develops an exact approach for processing pulse signals from an integrate-and-fire system directly in the time-domain. Processing is deterministic and built from simple asynchronous finite-state machines that can perform general piecewise-linear operations. The pulses can then be converted back into an analog or fixed-point digital representation through a filter-based reconstruction. Integrate-and-fire is shown to be equivalent to the first-order sigma-delta modulation used in oversampled noise-shaping converters. The encoder circuits are well known and have simple construction using both current and next-generation technologies. Processing in the pulse-domain provides many benefits including: lower area and power consumption, error tolerance, signal serialization and simple conversion for mixed-signal applications. To study these systems, discrete-event simulation software and an FPGA hardware platform are developed. Many applications of pulse-processing are explored including filtering and signal processing, solving differential equations, optimization, the minsum / Viterbi algorithm, and the decoding of low-density parity-check codes (LDPC). These applications often match the performance of ideal continuous-time analog systems but only require simple digital hardware. Keywords: time-encoding, spike processing, neuromorphic engineering, bit-stream, delta-sigma, sigma-delta converters, binary-valued continuous-time, relaxation-oscillators.by Martin McCormick.S.M

VLSI Design

This book provides some recent advances in design nanometer VLSI chips. The selected topics try to present some open problems and challenges with important topics ranging from design tools, new post-silicon devices, GPU-based parallel computing, emerging 3D integration, and antenna design. The book consists of two parts, with chapters such as: VLSI design for multi-sensor smart systems on a chip, Three-dimensional integrated circuits design for thousand-core processors, Parallel symbolic analysis of large analog circuits on GPU platforms, Algorithms for CAD tools VLSI design, A multilevel memetic algorithm for large SAT-encoded problems, etc

MODELLING AND PROCESSING THE DYNAMICS OF TOPOLOGICAL SIGNALS WITH THE DIRAC OPERATOR

Networks provide a powerful description of the complex systems that surround us. These structures support dynamical processes such as diffusion, synchronisation or percolation. The study of networks has remained limited to the pairwise formalism, where interactions take place between two participants. Simplicial complexes capture interactions between any number of elements. They are naturally equipped with a topological description, and support generalised dynamical variables called topological signals. Such signals can be found in many systems, yet have received little interest so far. Where studied, signals supported by structures of different dimension have been typically treated independently. This thesis explores the use of the Dirac operator as a tool rooted in topology to model the coupled dynamics of topological signals, and capture the interplay between signals of different orders. We apply this framework to describe the synchronisation dynamics of coupled phase os- cillators supported by nodes and edges in networks. We show through analytical and numerical investigations that the system undergoes explosive transitions between syn- chronised and incoherent states, while the synchronised state is characterised by coherent emergent oscillations. In the context of reaction-diffusion systems, we demonstrate how the Dirac operator is key to the formation of spatial heterogeneous patterns in topological signals supported by nodes and edges of a network. As a final illustration, we investi- gate two methods to filter and process real topological signals supported by nodes, edges and triangles in a simplicial complex. With the Dirac operator, we capture the interplay between signals of different orders and successfully jointly filter topological signals from artificial noise. This thesis illustrates how the Dirac operator provides a convenient formalism rooted in topology to consider the coupled dynamics of topological signals. This opens many further research avenues at the intersections of applied topology, dynamical systems, simplicial signal processing and higher-order network science