Local Lyapunov Functions for Consensus in Switching Nonlinear Systems

This note presents two theorems on asymptotic state consensus of continuous time nonlinear multi-agent systems. The agents reside in Rm and have switching interconnection topologies. Both the first theorem, formulated in terms of the states of individual agents, and the second theorem, formulated in terms of the pairwise states for pairs of agents, can be interpreted as variants of Lyapunov’s second method. The two theorems complement each other; the second provides stronger convergence results under weaker topology assumptions, whereas the first often can be applied in a wider context in terms of the structure of the right-hand sides of the systems. The second theorem also sheds some new light on well-known results for consensus of nonlinear systems where the right-hand sides of the agents’ dynamics are convex combinations of directions to neighboring agents. For such systems, instead of proving consensus by using the theory of contracting convex sets, a local quadratic Lyapunov function can be used.The authors gratefully acknowledge the financial support form the Fonds National de la Recherche, Luxembourg (FNR8864515)

Synchronisation of partial multi-matchings via non-negative factorisations

In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equal to the identity. Motivated by clustering and matrix factorisation perspectives of cycle-consistency, we derive an algorithm to tackle the permutation synchronisation problem based on non-negative factorisations. In order to deal with the inherent non-convexity of the permutation synchronisation problem, we use an initialisation procedure based on a novel rotation scheme applied to the solution of the spectral relaxation. Moreover, this rotation scheme facilitates a convenient Euclidean projection to obtain a binary solution after solving our relaxed problem. In contrast to state-of-the-art methods, our approach is guaranteed to produce cycle-consistent results. We experimentally demonstrate the efficacy of our method and show that it achieves better results compared to existing methods

Statistical stability and limit laws for Rovella maps

We consider the family of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used by Rovella to prove that there is a one-parameter family of maps whose derivatives along their critical orbits increase exponentially fast and the critical orbits have slow recurrent to the critical point. Metzger proved that these maps have a unique absolutely continuous ergodic invariant probability measure (SRB measure). Here we use the technique developed by Freitas and show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the continuous variation of the densities of the SRB measures and associated metric entropies with the parameter. Our main result also implies some statistical properties for these maps.Comment: 1 figur

A lifting method for analyzing distributed synchronization on the unit sphere

This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d + 1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence

Coupled economic-ecological models for ecosystem-based fishery management: Exploration of trade-offs between model complexity and management needs

Ecosystem based fishery management has moved beyond rhetorical statements calling for a more holistic approach to resource management, to implementing decisions on resource use that are compatible with goals of maintaining ecosystem health and resilience. Coupled economic-ecological models are a primary tool for informing these decisions. Recognizing the importance of these models, the International Council for the Exploration of the Seas (ICES) formed a Study Group on Integration of Economics, Stock Assessment and Fisheries Management (SGIMM) to explore alternative modelling approaches that bring the multiple disciplines of economics, ecology, and stock assessment into integrated ecosystem models. The theme session was designed to be an extension of a series of workshops and theme sessions organized by the SGIMM, but highlighted the economic component of coupled models. Although economic and ecological systems are inherently complex, models are abstractions of these systems incorporating varying levels of complexity depending on available data and the management issues to be addressed. The objective of this special session was to assess the pros and cons of increasing model complexity to incorporate linkages between ecosystem components and processes. While more complex ecosystem models may provide greater insight into how management decisions and human actions propagate through the ecosystem and impact the value of ecosystem services, the resources and information required to develop and parameterize them is greater and these models tend to require trade-offs such as the inability to quantify uncertainty or model human behaviour as accurately as can be done with models of individual fisheries. The theme session was organized as a moderated panel format representing a progression of economic-ecological models from less to increasingly complex. The panel was selected to represent a range of models from fully integrated, highly detailed and dynamic economic-ecological models such as Atlantis to models that may be less detailed or not fully dynamic or integrated. The special session focused primarily on management issues that are of a longer term strategic nature such as the implications of climate change, fundamental regime change, or the role of forage species in an ecosystem. Each panellist provided an overview of their model including the management questions the model was designed to address, the data and time requirements, as well as any lessons learned. The panellist presentations were followed by an open discussion among the panellists and the audience. The abstracts for each of the panellist presentation are provided below followed by a summary of the issues raised during the moderated discussion sessio

Recreational anglers' valuation of near-shore marine fisheries in Florida

This report describes and summarizes the results from a state-wide survey of Florida resident saltwater anglers. The survey was designed to provide estimates of the economic value anglers place on marginal changes in management of selected near-shore marine species. The Contingent valuation method was used to elicit angler willingness to pay for changes in management for redfish, seatrout , mullet, sheepshead, pompano. and king mackerel. Contingent valuation is a process in which respondents are presented with a detailed scenario that describes an opportunity to express their willingness to pay for a proposed change in current conditions. The process consists of three parts. First. the change in current conditions, or the "good" to be valued is described. Second, the payment method is described. The payment method is usually closely related to typical methods of buying goods similar to the one to be valued. Finally. the respondent is asked how much they would pay for the good described in the scenario. A special saltwater fishing license stamp that would allow the holder to take advantage of the described management change was used as a payment mechanism. (PDF contains 147 pages.