control of a three coleader formation in the plane this paper considers a formation of three point agents moving in the plane where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour further each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour and the current and desired distance from its neighbour the motion of the formation is studied when distances are initially incorrect a convergence result is established to the effect that provided agents never become collinear the correct distances will be approached exponentially fast and the formation as a whole will rotate by a finite angle and translate by a finite distance

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

the supersingular locus of the shimura variety of gu 1 n 1 ii we complete the study of the supersingular locus mathcal m mathrm ss in the fiber at p of a shimura variety attached to a unitary similitude group gu 1 n 1 over in the case that p is inert this was started by the first author in can j math 62 668 720 2010 where complete results were obtained for n 2 3 the supersingular locus mathcal m mathrm ss is uniformized by a formal scheme mathcal n which is a moduli space of so called unitary p divisible groups it depends on the choice of a unitary isocrystal n we define a stratification of mathcal n indexed by vertices of the bruhat tits building attached to the reductive group of automorphisms of n we show that the combinatorial behavior of this stratification is given by the simplicial structure of the building the closures of the strata and in particular the irreducible components of mathcal n mathrm red are identified with generalized deligne lusztig varieties we show that the bruhat tits stratification is a refinement of the ekedahl oort stratification and also relate the ekedahl oort strata to deligne lusztig varieties we deduce that mathcal m mathrm ss is locally a complete intersection that its irreducible components and each ekedahl oort stratum in every irreducible component is isomorphic to a deligne lusztig variety and give formulas for the number of irreducible components of every ekedahl oort stratum of mathcal m mathrm ss

distributed formation control of multi agent systems using complex laplacian the paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape a new technique based on complex laplacian is introduced to address the problems of which formation shapes specified by inter agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability concerning the first question we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter agent specification of the formation shape is 2 rooted concerning the second question a distributed and linear control law is developed based on the complex laplacian specifying the target formation shape and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed loop system at desired locations are given moreover we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re design and change their control laws

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

comments on global stabilization of rigid formations in the plane automatica 49 2013 14361441 this paper shows that the modified gradient control law proposed in tian and wang 2013 does not globally stabilize rigid formation shapes also further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided

formation tracking of the second order multi agent systems using position only information via impulsive control with input delays in this paper the formation tracking problem for the second order multi agent system with and without input delay are investigated respectively the objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously the impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay by using properties of the laplacian matrix and combining the stability theory of impulsive systems necessary and sufficient conditions are derived to achieve the formation tracking of the second order multi agent system with and without the input delay respectively the numerical examples are given to illustrate the effectiveness of our theoretical results

a graph laplacian approach to coordinate free formation stabilization for directed networks this paper concentrates on coordinate free formation control for directed networks for which the dynamic motion of each agent is assumed to be governed only by a local control we develop a graph laplacian approach to solve the global and exponential formation stablization problem using merely relative position measurements between neighbors first to capture the sensing and control architectures that are needed to maintain the shape of a formation a necessary and sufficient topological condition is proposed second a laplacian based control law is developed for the stablization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures simulation results are provided to demonstrate that our laplacian based formation control strategy is inherently fault tolerant and robust to node failures

time varying formation control for general linear multi agent systems with switching directed topologies time varying formation analysis and design problems for multi agent systems with general linear dynamics and switching directed interaction topologies are investigated different from the previous results the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed firstly necessary and sufficient conditions for general linear multi agent systems with switching directed topologies to achieve time varying formations are proposed where a description of the feasible time varying formation set and approaches to expand the feasible formation set are given then an explicit expression of the time varying formation reference function is derived to describe the macroscopic movement of the whole formation an approach to assign the motion modes of the formation reference is provided moreover an algorithm consisting of four steps to design the formation protocol is presented in the case where the given time varying formation belongs to the feasible formation set it is proven that by designing the formation protocol using the proposed algorithm time varying formation can be achieved by multi agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold finally numerical simulations are presented to demonstrate the effectiveness of the theoretical results

vanishing cycles for formal schemes let k be a non archimedean field and let x be a formal scheme locally finitely presented over the ring of integers k see 1 in this work we construct and study the vanishing cycles functor from the category of etale sheaves on the generic fibre x of x which is a k analytic space to the category of etale sheaves on the closed fibre xs of x which is a scheme over the residue field of k we prove that if x is the formal completion x of a scheme x finitely presented over k along the closed fibre then the vanishing cycles sheaves of x are canonically isomorphic to those of x as defined in sga7 exp xiii in particular the vanishing cycles sheaves of x depend only on x and any morphism x induces a homomorphism from the pullback of the vanishing cycles sheaves of x under s ys xs to those of y furthermore we prove that for each x one can find a nontrivial ideal of k such that if two morphisms x coincide modulo this ideal then the homomorphisms between the vanishing cycles sheaves induced by and coincide these facts were conjectured by p deligne in 1 we associate with a formal scheme x locally finitely presented over k a k analytic space x in the sense of ber1 and ber2 in 2 we find that the morphism y x which is induced by an etale morphism of formal schemes y x possesses a certain property morphisms of k analytic spaces with this property are called quasi etale and they give rise to a quasi etale site xqet of a k analytic space x there is a canonical morphism of sites xqet xet where xet is the etale site introduced in ber2 we show that the inverse image functor identifies the category of etale sheaves x et with a full subcategory of

target point formation control in this paper a new distributed feedback strategy is proposed for controlling a rigid acyclic formation of kinematic point modeled mobile autonomous agents in the plane the strategy makes use of a new concept called a target point and is applicable to any two dimensional acyclic formation whose underlying directed graph can be generated by a sequence of henneberg vertex additions it is shown that the method can cause a group of agents starting in any given initial positions in the plane to move into a prescribed formation exponentially fast provided the formation s designated leader and first follower start in different positions

cell decomposition of some unitary group rapoport zink spaces in this paper we study the p adic analytic geometry of the basic unitary group rapoport zink spaces mathcal m k with signature 1 n 1 using the theory of harder narasimhan filtration of finite flat groups developed in fargues journal fur die reine und angewandte mathematik 645 1 39 2010 fargues theorie de la reduction pour les groupes p divisibles prepublications http www math jussieu fr fargues prepublications html 2010 and the bruhat tits stratification of the reduced special fiber mathcal m red defined in vollaard and wedhorn invent math 184 591 627 2011 we find some relatively compact fundamental domain mathcal d k in mathcal m k for the action of g mathbb q p times j b mathbb q p the product of the associated p adic reductive groups and prove that mathcal m k admits a locally finite cell decomposition by considering the action of regular elliptic elements on these cells we establish a lefschetz trace formula for these spaces by applying mieda s main theorem in mieda lefschetz trace formula for open adic spaces preprint arxiv 1011 1720 2013

generalized ensemble and tempering simulations a unified view from the underlying master equations we derive one dimensional stochastic processes that describe generalized ensemble simulations as well as tempering simulated and parallel simulations the representations obtained are either in the form of a one dimensional fokker planck equation or a hopping process on a one dimensional chain in particular we discuss the conditions under which these representations are valid approximate markovian descriptions of the random walk in order parameter or control parameter space they allow a unified discussion of the stationary distribution on as well as of the stationary flow across each space we demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space and discuss the consequences of our results for optimizing simulations finally we point out the limitations of these representations under conditions of broken ergodicity

finite time stabilisation of cyclic formations using bearing only measurements this paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing only sensors since the inter vehicle distance cannot be measured the target formation involves no distance constraints more specifically the target formation considered in this paper is an angle constrained cyclic formation where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre specified to stabilise the target formation we propose a discontinuous control law that only requires the sign information of the angle errors due to the discontinuity of the proposed control law the stability of the closed loop system is analysed by employing a locally lipschitz lyapunov function and nonsmooth analysis tools we prove that the target formation is locally finite time stable with collision avoidance guaranteed

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

exponential stability for formation control systems with generalized controllers a unified approach this paper discusses generalized controllers for distance based rigid formation shape stabilization and aims to provide a unified approach for the convergence analysis we consider two types of formation control systems according to different characterizations of target formations minimally rigid target formation and non minimally rigid target formation for the former case we firstly prove the local exponential stability for rigid formation systems when using a general form of shape controllers with certain properties from this viewpoint different formation controllers proposed in previous literature can be included in a unified framework we then extend the result to the case that the target formation is non minimally rigid and show that exponential stability of the formation system is still guaranteed with generalized controllers

rigid formation control of double integrator systems in this chapter we move our focus from formation control systems modelled by single integrators e g those considered in previous chapters to formation systems modelled by double integrators two kinds of double integrator formation systems are considered namely formation stabilization systems and flocking control systems novel observations on the measurement requirement the null space and eigenvalues of the system jacobian matrix will be provided which reveal important properties of system dynamics and the associated convergence results we also establish some new links between single integrator formation systems and double integrator formation systems via a parameterized hamiltonian system which in addition provide novel stability criteria for different equilibria in double integrator formation systems by using available results from single integrator formation systems

on the cohomology of certain pel type shimura varieties in this article we study the local geometry at a prime p of pel type shimura varieties for which there is a hyperspecial level subgroup we consider the newton polygon stratification of the special fiber at p of shimura varieties and show that each newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding pel type rapoport zink spaces with certain smooth varieties which we call igusa varieties and of the action on them of a p adic group that depends on the stratum we then extend our construction to characteristic zero and in the case of bad reduction at p use it to compare the vanishing cycle sheaves of the shimura varieties to those of the rapoport zink spaces as a result of this analysis in the case of proper shimura varieties we obtain a description of the l adic cohomology of the shimura varieties in terms of the l adic cohomology with compact supports of the igusa varieties and of the rapoport zink spaces for any prime l p

global stabilization of rigid formations in the plane this paper considers the problem of distributed control of rigid formation shapes in the plane for multi agent systems a constructive perturbation method is proposed and combined with the conventional gradient control law the proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location it also avoids collisions between any two communicating agents during the motion simulation results are provided to illustrate the effectiveness of the control algorithm

simultaneous velocity consensus and shape control for a finite number of point agents on the unit circle in this paper we study a second order distributed control system for a finite number of point agents on the unit circle that achieves simultaneously velocity consensus and distance based formation shape control based on tools from riemannian geometry we propose a system of second order differential equations on the n dimensional torus that achieves these two goals we prove convergence of the trajectories to single closed geodesics on a torus and investigate the stability properties of the distributed algorithm

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

the supercuspidal representations of p adic classical groups let g be a unitary symplectic or special orthogonal group over a locally compact non archimedean local field of odd residual characteristic we construct many new supercuspidal representations of g and bushnell kutzko types for these representations moreover we prove that every irreducible supercuspidal representation of g arises from our constructions

distributed formation stabilization using relative position measurements in local coordinates in this paper we present a novel distributed method to stabilize a set of agents moving in a two dimensional environment to a desired rigid formation in our approach each agent computes its control input using the relative positions of a set of formation neighbors but contrary to most existing works this information is expressed in the agent s own independent local coordinate frame without requiring any common reference the controller is based on the minimization of a lyapunov function that includes locally computed rotation matrices which are required due to the absence of a common orientation our contribution is that the proposed distributed coordinate free method achieves global stabilization to a rigid formation with the agents using only partial information of the team does not require any leader units and is applicable to both single integrator or unicycle agents to guarantee global stability we require that the network induced by the agent interactions belongs to a certain class of undirected rigid graphs in two dimensions which we explicitly characterize the performance of the proposed method is illustrated with numerical simulations

stabilisation of infinitesimally rigid formations of multi robot networks this article considers the design of a formation control for multivehicle systems that uses only local information the control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation a potential function is obtained from the graph from which a gradient control is derived under this controller the target formation becomes a manifold of equilibria for the multivehicle system it is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold a complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well finally the controller is validated experimentally

on a conjecture of rapoport and zink in their book rapoport and zink constructed rigid analytic period spaces mathcal f wa for fontaine s filtered isocrystals and period morphisms from pel moduli spaces of p divisible groups to some of these period spaces they conjectured the existence of an etale bijective morphism mathcal f a to mathcal f wa of rigid analytic spaces and of a universal local system of p vector spaces on mathcal f a such a local system would give rise to a tower of etale covering spaces breve mathcal e widetilde k of mathcal f a equipped with a hecke action and an action of the automorphism group j p of the isocrystal with extra structure

ratio of distance rigidity theory with application to similar formation control this paper develops a ratio of distance rod rigidity theory to study when a framework can be uniquely determined by a set of rod constraints up to similar transformations translation rotation scaling and reflection in particular a framework is specified by a set of rod constraints the rod of a pair of edges joining a common vertex instead of distance bearing and angle constraints assumed in existing literature its relations to three existing rigidity theories distance bearing and angle rigidity theories are established the proposed rod rigidity theory is further applied to the rod based similar formation stabilization problem where the desired formation shape is expressed as a set of rod constraints finally numerical simulations are presented to illustrate the effectiveness of the theoretical results

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

on the cohomology of rapoport zink spaces of el type in this article we are interested in determining the l adic cohomology of rapoport zink spaces associated to rm gl n over an unramified extension of bbb q p called unramified el type in connection with the local langlands correspondence for rm gl n in fact we compute the alternating sum of certain representation theoretic functors defined in terms of their cohomology on the level of grothendieck groups in case rapoport zink spaces parametrize p divisible groups of dimension one the above alternating sum is determined by harris and taylor without the unramifiedness assumption for p divisible groups of rm dim 1 fargues has obtained an answer for the supercuspidal part when the p divisible groups are basic i e their associated newton polygons are straight lines our main result is an identity among the cohomology of rapoport zink spaces that appear in the newton stratification of the same unitary shimura variety our result implies a theorem of fargues providing a second proof and reveals new information about the cohomology of rapoport zink spaces for non basic p divisible groups we propose an inductive procedure to completely determine the above alternating sum assuming a strengthening of our main result along with a conjecture of harris

temperature random walk sampling of protein configurations abstract we study generalizations of parallel tempering also known as replica exchange method that aim at maximizing the sampling of independent low energy configurations through enforcing random walks in temperature or other control variables the advantage of these techniques is the easily tunable high acceptance rate for replica exchange simulating the villin headpiece hp 36 we evaluate the efficiency of our techniques and present criteria for its tuning