first order aggregation models with alignment abstract we include alignment interactions in a well studied first order attractive repulsive macroscopic model for aggregation the distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density becomes implicit and can have non unique solutions we investigate the well posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second order kinetic equation we work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as essential tools in the analysis a discretization procedure that parallels the analysis is formulated and implemented numerically in one and two dimensions

second order consensus of multi agent systems in the cooperation competition network with switching topologies a time delayed impulsive control approach abstract this paper investigates the consensus problem of second order multi agent systems with switching topologies by designing a time delayed impulsive consensus control scheme all the agents are governed by the same nonlinear intrinsic dynamics in this study agents can cooperate or compete with each other i e the elements in the weight matrix of the coupling graph can be either positive or negative by establishing a comparison system a new comparison principle method is successfully applied to study such consensus problem then several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree meanwhile the exponential consensus rate is also obtained finally simulation results are presented to validate the effectiveness of the theoretical analysis

avoiding collisions in flocks among the many models for flocking systems of interacting particles the one introduced by cucker and smale has attracted attention due to the fact that a convergence to flocking i e to a common velocity could be established depending on conditions on the initial state of the system in this note we extend this model by adding to it a repelling force between particles we show that for this modified model convergence to flocking is established along the same lines while in addition avoidance of collisions i e the respect of a minimal distance between particles is ensured

cucker smale flocking under hierarchical leadership a mathematical theory on flocking serves the foundation for several ubiquitous multiagent phenomena in biology ecology sensor networks and economics as well as social behavior like language emergence and evolution directly inspired by the recent fundamental works of cucker and smale on the construction and analysis of a generic flocking model we study the emergent behavior of cucker smale flocking under hierarchical leadership the rates of convergence towards asymptotically coherent group patterns in different scenarios are established the consistent convergence towards coherent patterns may well reveal the advantages and necessities of having leaders and leadership in a complex biological technological economic or social system with sufficient intelligence

existence of piecewise weak solutions of a discrete cucker smale s flocking model with a singular communication weight abstract we prove existence of global c 1 piecewise weak solutions for the discrete cucker smale s flocking model with a non lipschitz communication weight s s 0 1 we also discuss the possibility of finite in time alignment of the velocities of the particles

flocking of multi agent systems with multiple groups in this paper we consider the flocking problem of multi agent systems with multiple groups first some algorithms using local information are designed to divide the agents into any pre assigned number of groups in fixed and switching heterogeneous networks respectively based on algebraic graph theory and barbalat s lemma convergence criteria are established to ensure velocity alignment and cohesion of each subgroup as well as collision avoidance between any agents in the whole group second an algorithm for homogeneous networks is studied simulation examples are finally presented to verify the effectiveness of our theoretical results

time delay effect on the flocking in an ensemble of thermomechanical cucker smale particles abstract we study the communication time delay effect on the emergent dynamics of thermodynamic cucker smale tcs ensemble with temperature as an internal state in the presence of time delay conservation laws for momentum and energy do not hold so that the analytic tool based on the energy method cannot be applied for the tcs model as it is we show that temperature stays positive in the presence of small time delay as long as temperatures stay positive the tcs model is well posed by direct application of cauchy lipschitz theory when the size of time delay and initial data are sufficiently small we can derive differential inequalities for velocity and temperature diameters using these differential inequalities we show that temperature and velocity diameters tend to zero exponentially fast whereas the position diameter is uniformly bounded we also present several numerical simulations and compare them with analytic results

a global unique solvability of entropic weak solution to the one dimensional pressureless euler system with a flocking dissipation abstract we present a unique global solvability and flocking estimate of an entropic weak solution to the one dimensional pressureless euler system with a flocking dissipation in all to all coupling setting this model appears naturally as a quasi equilibrium model for hydrodynamic description of cucker smale flocking for the unique global solvability we adopt the variation approach from ding and huang s work 19 on the inhomogeneous pressureless gas dynamic model when initial mass and velocity are locally integrable and bounded measurable functions respectively we give explicit representations for the global entropic weak solutions our results do not require any smallness of initial data except that initial mass density is almost everywhere positive

from discrete cucker smale model to continuous cucker smale model in a temperature field we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results we study emergent dynamics of the discrete and continuous cucker smale c s models in a self consistent temperature field and provide refined monocluster flocking estimates more precisely we present a sufficient framework leading to the monocluster flocking toward the constant common temperature and velocity exponentially fast this improves the authors earlier work where existence of common temperature and velocity are not identified our proposed sufficient framework is formulated in terms of the initial data and system parameters using the refined flocking we also provide a uniform in time convergence from the discrete model to the continuous model under some suitable compatibility condition on the asymptotic velocities for the discrete and continuous model as the time step tends to zero we also provide several numerical examples and compare them with analytical results

exact symmetries of unidimensional self similar flow in addition to the symmetries that are known to apply to arbitrary flow the self similar equations may present other symmetries of their own we present here such a symmetry of the self similar unidimensional flow of an adiabatic inviscid fluid with arbitrary polytropic index and arbitrary power law entropy distribution the new symmetry can be extended to the non self similar case if the flow is assumed isentropic a connection with the theory of riemann invariants is also discussed

consensus of multiagent systems with distance dependent communication networks in this paper we study the consensus problem of discrete time and continuous time multiagent systems with distance dependent communication networks respectively the communication weight between any two agents is assumed to be a nonincreasing function of their distance first we consider the networks with fixed connectivity in this case the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough we show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound second we study the networks with distance dependent connectivity it is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range with the validity of some conditions related to the property of the initial communication graph we prove that consensus can be achieved asymptotically third we present some applications of the main results to opinion consensus problems and formation control problems finally several simulation examples are presented to illustrate the effectiveness of the theoretical findings

a general collision avoiding flocking framework we prove a general result of collision avoiding flocking the underlying model allows several forms of coupling forces and the main result ensures flocking provided the initial state of the population does not show simultaneously very different velocities very spread positions or very close agents

equilibria and steering laws for planar formations abstract this paper presents a lie group setting for the problem of control of formations as a natural outcome of the analysis of a planar two vehicle formation control law the vehicle trajectories are described using the planar frenet serret equations of motion which capture the evolution of both the vehicle position and orientation for unit speed motion subject to curvature steering control the set of all possible relative equilibria for arbitrary g invariant curvature controls is described where g se 2 is a symmetry group for the control law and a global convergence result for the two vehicle control law is proved an n vehicle generalization of the two vehicle control law is also presented and the corresponding relative equilibria for the n vehicle problem are characterized work is on going to discover stability and convergence results for the n vehicle problem

rank based selection strategies for the random walk process abstract in many decision situations such as hiring a secretary selling an asset or seeking a job the value of each offer applicant or choice is assumed to be an independent identically distributed random variable in this paper we consider a special case where the observations are auto correlated as in the random walk model for stock prices for a given random walk process of n observations we explicitly compute the probability that the j th observation in the sequence is the maximum or minimum among all n observations based on the probability distribution of the rank we derive several distribution free selection strategies under which the decision maker s expected utility of selecting the best choice is maximized we show that unlike in the classical secretary problem evaluating more choices in the random walk process does not increase the likelihood of successfully selecting the best

styled velocity flocking of autonomous vehicles a systematic design this paper develops a measure theoretic approach for generating the collective behavior of flocking of planar autonomous vehicles under all to all communication scheme to obtain flocking protocol we formulate the notion of state of styled velocity flocking for the target state of a design problem instead of considering solution ansatzes this notion captures a broader class of flocking behaviors of non parallel motions as well as embodies the two important performances of cohesion maintenance and collision avoidance to pose a control design problem a measure valued transition equation is obtained to induce an auxiliary one body continuum model from the exact multi body particle model of the collective system the design problem is then formulated on the auxiliary continuum model and a systematic design procedure is presented the state of styled velocity flocking of the particle model under the obtained flocking protocol is then verified with an important result on the continuous dependence on initial data of solutions of the measured valued transition equation application to elliptical flocking of mobile robots is presented to illustrate the novelty of the presented theory

consensus seeking in multi agent systems with multiplicative measurement noises abstract in this paper the consensus problems of the continuous time integrator systems under noisy measurements are considered the measurement noises which appear when agents measure their neighbors states are modeled to be multiplicative by multiplication of the noises here the noise intensities are proportional to the absolute value of the relative states of an agent and its neighbor by using known distributed protocols for integrator agent systems the closed loop system is described in the vector form by a singular stochastic differential equation for the fixed and switching network topology cases constant consensus gains are properly selected such that mean square consensus and strong consensus can be achieved especially exponential mean square convergence of agents states to the common value is derived for the fixed topology case in addition asymptotic unbiased mean square average consensus and asymptotic unbiased strong average consensus are also studied simulations shed light on the effectiveness of the proposed theoretical results

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

asymptotic behavior and collision avoidance in the cucker smale model for the long range communicated cucker smale c s model asymptotic flocking can be obtained by taking full use of a key equality about the kinetic energy however such behavior does not exist for the short range communicated c s model with general initial data in this note we first establish a new equality about the second order velocity position moments for general c s models then we use this equality to deduce a new type of asymptotic behavior for the short range communicated c s model such behavior not only reflects an essential feature of the short range communication weight but also has some potential applications in the complex multicluster problem besides collision avoidance is also obtained for the c s model with some singular short range communication weights

complete classification of the asymptotical behavior for singular c s model on the real line abstract in this paper we study the singular cucker smale c s model on the real line for long range case i e 1 we prove the uniqueness of the solution in the sense of definition 2 1 and the unconditional flocking emergence moreover the sufficient and necessary condition for collision and sticking phenomenon will be provided for short range case i e 1 we construct the uniform in time lower bound of the relative distance between particles and provide the sufficient and necessary condition for the emergence of multi cluster formation for critical case i e 1 we show the uniform lower bound of the relative distance and unconditional flocking emergence these results provide a complete classification of the collective behavior for c s model on the real line

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only