Decentralized Formation Control with A Quadratic Lyapunov Function

In this paper, we investigate a decentralized formation control algorithm for an undirected formation control model. Unlike other formation control problems where only the shape of a configuration counts, we emphasize here also its Euclidean embedding. By following this decentralized formation control law, the agents will converge to certain equilibrium of the control system. In particular, we show that there is a quadratic Lyapunov function associated with the formation control system whose unique local (global) minimum point is the target configuration. In view of the fact that there exist multiple equilibria (in fact, a continuum of equilibria) of the formation control system, and hence there are solutions of the system which converge to some equilibria other than the target configuration, we apply simulated annealing, as a heuristic method, to the formation control law to fix this problem. Simulation results show that sample paths of the modified stochastic system approach the target configuration

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Environmental Governance in Indonesia

Indonesia is one of the countries with the fastest-growing economies in Asia and one of the most biologically diverse countries in the world. With ecosystems ranging from terrestrial to marine and teemed with unique life forms, Indonesia is rich in natural resources. Unfortunately, Indonesia also suffers from overexploitation and environmental threats exacerbated by climate and human pressures. Along with the growing global ambitions for achieving sustainable development and increasing its capacity to adapt to climate change and extreme events, Indonesia is also increasing its commitments to balance development while safeguarding environmental and social sustainability. However, challenges remain, especially on how to effectively govern the responses to environmental issues. Against this background, this book will present state-of-the-art environmental governance research and practices in Indonesia. It offers a wide scope, covering different themes and sectors (e.g., climate change, disaster risk, forestry, mining, etc.), diverse physical and societal landscapes (e.g., urban, rural, deltas, coastal areas, etc.), and multiscalar perspectives (from national to local level). This book has the ambition to incorporate more knowledge to indicate research gaps and future directions for environmental governance research. Our intention is also to reflect a vision to make the national and global environmental governance research agenda to be more diverse, inclusive, interdisciplinary, and transdisciplinary. We hope that this book will be useful for researchers, students, practitioners, and policymakers who are interested in the field of environmental governance, especially in Indonesia as a megadiversity country that encompasses the world’s largest archipelago