sampled data consensus of linear multi agent systems with packet losses in this paper the consensus problem is studied for a class of multi agent systems with sampled data and packet losses where random and deterministic packet losses are considered respectively for random packet losses a bernoulli distributed white sequence is used to describe packet dropouts among agents in a stochastic way for deterministic packet losses a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way the purpose of this paper is to derive consensus criteria such that linear multi agent systems with sampled data and packet losses can reach consensus by means of the lyapunov function approach and the decomposition method the design problem of a distributed controller is solved in terms of convex optimization the interplay among the allowable bound of the sampling interval the probability of random packet losses and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions the obtained criteria are closely related to the maximum eigenvalue of the laplacian matrix versus the second minimum eigenvalue of the laplacian matrix which reveals the intrinsic effect of communication topologies on consensus performance finally simulations are given to show the effectiveness of the proposed results

finite time consensus for controlled dynamical systems in network abstractthe key challenges in networked dynamical systems are the component heterogeneities nonlinearities and the high dimension of the formulated vector of state variables in this paper the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift for each model structure that defines homogeneous and heterogeneous multi system behaviour we derive protocols leading to finite time consensus for each model evolving in networks forming a homogeneous or heterogeneous multi system protocols integrating sufficient conditions are derived leading to finite time consensus likewise for the networking topology we make use of fixed directed and undirected graphs to prove our approaches finite time stability theory and lyapunov methods are considered as illustrative examples the homogeneous multi unicycle kinematics and the homogeneous heterogeneous multi second order dynamics in networks are studied

technical communique forced consensus in networks of double integrator systems with delayed input this communique presents forced second order consensus protocols with communication time delays for the network of agents with double integrator dynamics and gives a measure of the robustness of the protocols to the communication time delays by employing a frequency domain method it is proven that the forced consensus is achieved asymptotically for appropriate time delay if the network is connected particularly the maximum fixed time delay that can be tolerated by the network is found the forced consensus protocols are distributed in the sense that each agent only needs information from its neighboring agents which reduces the complexity of connections between agents significantly numerical simulation results are provided to demonstrate the effectiveness and the sharpness of the theoretical results

pinning dynamic systems of networks with markovian switching couplings and controller node set in this paper we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller node set here the coupling matrices and the controller node sets change with time induced by a continuous time markov chain by constructing lyapunov functions we establish tractable sufficient conditions for exponential stability of the coupled system two scenarios are considered here first we prove that if each subsystem in the switching system i e with the fixed coupling can be stabilized by the fixed pinning controller node set and in addition the markovian switching is sufficiently slow then the time varying dynamical system is stabilized second we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast the time varying system is stabilized two numerical examples are provided to demonstrate the validity of these theoretical results including a switching dynamical system between several stable subsystems and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre designed region

stochastic bounded consensus tracking of second order multi agent systems with measurement noises based on sampled data with general sampling delay this paper is devoted to the stochastic bounded consensus tracking problems of second order multi agent systems where the control input of each agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time varying reference state the measurements are corrupted by random noises and the signal sampling process induces the small sampling delay the augmented matrix method the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking we show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains the network topology the sampled period and the sampling delay and that the static consensus tracking error depends on not only the above mentioned factors but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader the obtained results cover no sampling delay as its one special case simulations are provided to demonstrate the effectiveness of the theoretical results

adaptive finite time consensus in multi agent networks abstract this paper is concerned with the finite time consensus problem of distributed agents having non identical unknown nonlinear dynamics to a leader agent that also has unknown nonlinear control input signal by parameterization of unknown nonlinear dynamics a lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite time consensus control protocol in undirected networks homogeneous lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous theoretical analysis shows that leader following consensus can be achieved in finite time meanwhile finite time parameter convergence can be also guaranteed under the proposed control scheme an example is given to validate the theoretical results

consensus and its ℒ 2 gain performance of multi agent systems with intermittent information transmissions this article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network where each agent can only communicate with its neighbours intermittently a class of control algorithms is first introduced using only intermittent relative local information by combining tools from switching systems and lyapunov stability theory some sufficient conditions are established for consensus of multi agent systems without any external disturbances under a fixed strongly connected topology theoretical analyses are further provided for consensus of multi agent systems in the presence of external disturbances it is shown that a finite 2 gain performance index for the closed loop multi agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology the results are then extended to consensus

adaptive consensus of multi agents in networks with jointly connected topologies in this paper the consensus problem of multi agent following a leader is studied an adaptive design method is presented for multi agent systems with non identical unknown nonlinear dynamics and for a leader to be followed that is also nonlinear and unknown by parameterizations of unknown nonlinear dynamics of all agents a decentralized adaptive consensus algorithm is proposed in networks with jointly connected topologies by incorporating local consensus errors in addition to relative position feedback analysis of stability and parameter convergence of the proposed algorithm are conducted based on algebraic graph theory and lyapunov theory finally examples are provided to validate the theoretical results

an approximation scheme for the minimum time function this paper presents an approximation scheme for the nonlinear minimum time problem with compact target the scheme is derived from a discrete dynamic programming principle and the main convergence result is obtained by applying techniques related to discontinuous viscosity solutions for hamilton jacobi equations the convergence is proved under general controllability assumptions on both the continuous time and the discrete time systems an explicit sufficient condition on the system and the target ensuring the desired controllability is given this condition is shown to be necessary and sufficient for the lipschitz continuity of the minimum time function if the target is smooth an extension to the case of a point shaped target is given

consensus on complete riemannian manifolds in finite time abstract in view of the fact that prototypes of riemannian manifolds range from euclidean surfaces to lie groups operator spaces etc the paper explores common consensus schemes for connected complete riemannian manifolds after studying the restriction exponential map we introduce a local consensus protocol with switching communication topologies for the manifolds via the isometric mapping based on one of the euclidean consensus protocols equipped with the compression decompression functions we extend the local consensus protocol and put forth a global consensus algorithm for any such manifolds these consensus schemes can provide common solutions to the consensus problems arising from various nonlinear spaces or abstract spaces belonging to connected complete riemannian manifolds in particular they are simple and concise and can converge in finite time simulation on the unit sphere is provided to verify our consensus schemes and to demonstrate the usage of our proposed techniques

computation of feedback control for time optimal state transfer using groebner basis abstract computation of time optimal feedback control law for a controllable linear time invariant system with bounded inputs is considered unlike a recent paper by the authors the target final state is not limited to the origin of state space but is allowed to be in the set of constrained controllable states switching surfaces are formulated as semi algebraic sets using groebner basis based elimination theory using these semi algebraic sets a nested switching logic is synthesized to generate the time optimal feedback control however the optimal control law enforces an unavoidable limit cycle in the time optimal trajectory for most non origin target points the time period of this limit cycle is dependent on the target position this dependence is algebraically characterized and a method to compute the time period of the limit cycle is provided as a natural extension the set of constrained controllable states is also computed

distributed average consensus via gossip algorithm with real valued and quantized data for 0 q 1 this paper studies the problem of the gossip consensus algorithm with real valued and quantized data we study the effect of the mixing parameter on the convergence rate of the proposed gossip consensus algorithm and show when the proposed bounds are optimized with respect to the mixing parameter for a gossip consensus algorithm with quantized data we prove that it can achieve the consensus almost surely and the expected value of the final states is equal to the average of the initial states moreover we provide a result characterizing the convergence performance of the distance from consensus and make a comparison with the non quantized gossip consensus algorithm finally simulation results are provided to evaluate the effectiveness of the proposed algorithm

consensus control of a class of lipschitz nonlinear systems this paper deals with consensus control of a class of nonlinear systems with lipschitz nonlinearities certain features of the laplacian matrix are explored in the real jordan form to identify conditions for global consensus control under the identified conditions consensus control and stability of the proposed control are analysed in time domain through lyapunov functions in real domain the proposed control uses relative state information of the system a simulation study is included to demonstrate the proposed control designs with some simulation results shown

mean field lqg control in leader follower stochastic multi agent systems likelihood ratio based adaptation we study large population leader follower stochastic multi agent systems where the agents have linear stochastic dynamics and are coupled via their quadratic cost functions the cost of each leader is based on a trade off between moving toward a certain reference trajectory which is unknown to the followers and staying near their own centroid on the other hand followers react by tracking a convex combination of their own centroid and the centroid of the leaders we approach this large population dynamic game problem by use of so called mean field mf linear quadratic gaussian lqg stochastic control theory in this model followers are adaptive in the sense that they use a likelihood ratio estimator on a sample population of the leaders trajectories to identify the member of a given finite class of models which is generating the reference trajectory of the leaders under appropriate conditions it is shown that the true reference trajectory model is identified by each follower in finite time with probability one as the leaders population goes to infinity furthermore we show that the resulting sets of mean field control laws for both leaders and adaptive followers possess an almost sure en nash equilibrium property for a system with population n where en goes to zero as n goes to infinity numerical experiments are presented illustrating the results

finite time weighted average consensus with respect to a monotonic function and its application abstract the consensus state is an important and fundamental quantity for consensus problems of multi agent systems which indicates where all the dynamical agents reach in this paper weighted average consensus with respect to a monotonic function which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values is studied for a group of kinematic agents with time varying topology by constructing a continuous nonlinear distributed protocol such a consensus problem can be solved in finite time even though the time varying topology involves unconnected graphs then the distributed protocol is employed to compute the maximum likelihood estimation of unknown parameters over sensor networks compared with the existing results the estimate scheme proposed here may reduce the costs of data communication storage memory book keeping and computational overheads

distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks in this paper we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies first when the leaders are stationary and all followers share an inertial coordinate frame we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is fixed we partition the nonsymmetric laplacian matrix and explore its properties to derive the convergence results when the directed network topology is switching the commonly adopted decoupling technique based on the kronecker product in a high dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results the proposed coordinate transformation technique also has potential applications in other high dimensional distributed control scenarios and might be used to simplify the analysis of a high dimensional system to that of a one dimensional system when the decoupling technique based on the kronecker product cannot be applied second when the leaders are dynamic and all followers share an inertial coordinate frame we propose a distributed tracking control algorithm without velocity measurements when the directed network topology is fixed we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension when the directed network topology is switching we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high dimensional space we also show via some counterexamples that it is in general impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high dimensional space simulation results are presented as a proof of concept

finite time consensus using stochastic matrices with positive diagonals we discuss the possibility of reaching consensus in finite time using only linear iterations with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure we show that finite time average consensus can always be achieved for connected undirected graphs for directed graphs we show some necessary conditions for finite time consensus including strong connectivity and the presence of a simple cycle of even length

feedback stabilization and lyapunov functions given a locally defined nondifferentiable but lipschitz lyapunov function we employ it in order to construct a discontinuous feedback law which stabilizes the underlying system to any given tolerance a converse result shows that suitable lyapunov functions of this type exist under mild assumptions we also establish that the feedback in question possesses a robustness property relative to measurement error despite the fact that it may not be continuous

a necessary and sufficient condition for consensus of continuous time agents over undirected time varying networks the average consensus problem of continuous time agents in undirected time varying networks is studied the network is allowed to be disconnected a notion called infinite integral connectivity is proposed based on the notion a necessary and sufficient condition for achieving consensus is given that is when the network topology is described by an undirected time varying graph g t the agents achieve consensus if and only if the infinite integral graph of g t over 0 is connected this criterion does not hold for directed networks

decentralized control of vehicle formations this paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory the vehicles exchange information according to a pre specified communication digraph g a feedback control is designed using relative information between a vehicle and its in neighbors in g we prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that g has a rooted directed spanning tree we show the direct relationship between the rate of convergence to formation and the eigenvalues of the directed laplacian of g various special situations are discussed including symmetric communication graphs and formations with leaders several numerical simulations are used to illustrate the results

deviation bounds in multi agent systems described by undirected graphs the theory of port hamiltonian systems is used to derive upper bounds for the state deviations in multi agent systems described by undirected graphs pinned to a reference signal the upper bounds for the deviations in networks of first or second order agents respectively depend on the minimal eigenvalue of the extended laplacian of the system in networks of first order agents the deviations decay exponentially with a rate depending on the same minimal eigenvalue in case networks of second order systems meet specific design properties it can be shown that the deviations also decay exponentially with half the rate compared to first order systems

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

computation of the target state and feedback controls for time optimal consensus in multi agent systems abstractn identical agents with bounded inputs aim to reach a common target state consensus in the minimum possible time algorithms for computing this time optimal consensus point the control l

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

brief paper collective motions and formations under pursuit strategies on directed acyclic graphs a novel pursuit based approach is presented to investigate collective motions and formations of a large number of agents with both single integrator kinematics and double integrator dynamics on directed acyclic graphs dags each agent pursues its neighbors according to a directed acyclic graph in which the agents without neighbors are leaders based on signal flow graph analysis and mason s rule necessary and sufficient conditions are derived for bibo stability of resulting pursuit systems moreover achievable collective motions and formations are analyzed by adjusting a set of control parameters when leaders keep stationary perform uniform rectilinear motions and perform uniform circular motions finally simulations are provided for achieving a static formation and mimicking several complex collective behaviors observed in nature such as v formation vortex motions and tornado motions

finite time consensus with disturbance rejection by discontinuous local interactions in directed graphs in this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous time first order integrator dynamics affected by bounded disturbances the topology of the network is described by a directed graph the proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time an upper bound to the convergence time is explicitly derived in the technical note simulation results referring to a network of coupled kuramoto like oscillators are illustrated to corroborate the theoretical analysis

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

distributed average tracking for reference signals with bounded accelerations in this technical note the distributed average tracking dat problem for reference signals with bounded accelerations is considered a sliding mode surface is designed such that trajectories on the surface will achieve dat a discontinuous control algorithm is then proposed to guarantee that the surface can be reached in finite time it is shown that if the switching network topology is connected at all time then dat can be solved by properly choosing a gain parameter of the algorithm

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

a decentralized controller observer scheme for multi agent weighted centroid tracking in this technical note a decentralized controller observer scheme for a multi agent system is presented the key idea is to develop for each agent an observer of the collective system s state and a motion controller the observer is updated using only information from the agent itself and from its neighbors the motion controller is designed in order to allow the team s weighted centroid to track an assigned time varying reference convergence of the overall scheme is proven for directed and undirected communication graphs moreover the extensions to the case of switching communication topologies and to the presence of saturation in the control input are discussed finally numerical simulations are illustrated to validate the approach

nonsingular fixed time consensus tracking for second order multi agent networks this paper investigates the fixed time consensus tracking problem for second order multi agent systems in networks with directed topology global well defined nonlinear consensus protocols are constructed with the aid of a newly designed sliding surface for each double integrator agent dynamics in particular the proposed framework eliminates the singularity and the settling time is assignable for any initial conditions this makes it possible for network consensus problems to design and estimate the convergence time off line finally simulation is included to demonstrate the performance of the new protocols

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

the existence of positive solutions with prescribed l2 norm for nonlinear choquard equations in this paper we study the existence of positive solutions with prescribed l2 norm to a class of nonlinear choquard equation u u i f u f u in n where n 3 0 n i n is the riesz potential under some conditions imposed on f by using a minimax procedure and the concentration compactness of p l lions we show that for any c 0 the equation possesses at least a couple uc c h1 n of weak solution such that u l2 rn 2 c

min max time consensus tracking with communication guarantee in this paper a collection of double integrator agents with bounded inputs is considered communication is possible between any two agents only if the inter agent distance is less than a fixed threshold a special node referred to as the leader generates an unknown reference trajectory to which all the other agents are required to converge in the shortest possible time assuming the initial communication graph to be connected a directed spanning tree rooted at the leader is identified using a local algorithm the dynamics of any two agents connected by an edge in the selected tree are modeled as a time optimal pursuit evasion game while maintaining the inter agent communication link using the corresponding feedback saddle point strategies local min max time control laws for each pair of agents are formulated for the selected tree the proposed collection of local min max time control strategies is shown to be the communication preserving global min max time strategy

stability analysis of stochastic delayed systems with an application to multi agent systems this technical note is concerned with the stability problem of stochastic delayed systems by using a more general halanay type inequality with time varying coefficients a new comparison principle of the proposed halanay type inequality is developed to ensure the stability of stochastic delayed systems the p th moment stability p th moment asymptotic stability and p th moment exponential stability are investigated by means of the proposed general halanay type inequality two examples including one of the consensus of multi agent systems with time varying topologies and transmission delays are presented to demonstrate the effectiveness of the proposed results

leader following consensus problem with a varying velocity leader and time varying delays abstract in this paper we study a leader following consensus problem for a multi agent system with a varying velocity leader and time varying delays here the interaction graph among the followers is switching and balanced at first we propose a neighbor based rule for every agent to track a leader whose states may not be measured in addition we consider the convergence analysis of this multi agent system under two different conditions the connection between the followers and the leader is time invariant and time varying for the first case a novel decomposition method is introduced to facilitate the convergence analysis by utilizing a lyapunov krasovskii functional we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors finally two simulations are also presented to illustrate our theoretical results

hilbert integrals singular integrals and radon transforms ii etude des transformations de radon singulieres et des integrales de hilbert appliquees aux problemes aux valeurs limites probleme de neumann

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

brief paper distributed discrete time coordinated tracking with a time varying reference state and limited communication this paper studies a distributed discrete time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete time instants tracks a time varying reference state available to only a subset of the team members we propose a pd like discrete time consensus algorithm to address the problem under a fixed communication graph we then study the condition on the communication graph the sampling period and the control gain to ensure stability and give the quantitative bound of the tracking errors it is shown that the ultimate bound of the tracking errors is proportional to the sampling period the benefit of the proposed pd like discrete time consensus algorithm is also demonstrated through comparison with an existing p like discrete time consensus algorithm simulation results are presented as a proof of concept

global consensus for discrete time multi agent systems with input saturation constraints in this paper we consider the global consensus problem for discrete time multi agent systems with input saturation constraints under fixed undirected topologies we first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents we then focus on two special cases where the agent model is either neutrally stable or a double integrator for the neutrally stable case any linear protocol of a particular form which solves the consensus problem for the case without input saturation constraints also solves the global consensus problem for the case with input saturation constraints for the double integrator case we show that a subset of linear protocols which solve the consensus problem for the case without saturation constraints also solve the global consensus problem for the case with input saturation constraints the results are illustrated by numerical simulations

on the stabilization in finite time of locally controllable systems by means of continuous time varying feedback law it is proven that if for any positive time t there exists an open loop control u a t depending continuously on the initial data a vanishing for a 0 and steering a small neighborhood of 0 into 0 in time t then the control system can be locally stabilized in small time by means of continuous time varying feedback law provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds

computation of time optimal feedback control using groebner basis the synthesis of time optimal feedback control of a single input continuous time linear time invariant lti system is considered if the control input u t is constrained to obey u t 1 then it is known that the optimal input switches between the extreme values 1 according to some switching surfaces in the state space it is shown that for systems with non zero distinct and rational eigenvalues these switching surfaces are semi algebraic sets and a method to compute them using groebner basis is proposed in the process the null controllable region for such systems is characterized and computed numerical simulations illustrate the proposed computational methods

event based model predictive tracking control of nonholonomic systems with coupled input constraint and bounded disturbances this paper studies the event based model predictive control empc for tracking of nonholonomic mobile robot with coupled input constraint and bounded disturbances first an event triggering mechanism is presented by designing a threshold for the error between the actual trajectory and the predicted one aiming at reducing the computational load second a model predictive control strategy is developed based on the event triggering mechanism recursive feasibility is guaranteed by designing a robust terminal region and the proper parameters we show that the tracking system is practically stable and also provides a convergence region for the tracking error the convergence region indicates that the tracking performance is negatively related to the minimal interevent time as well as the bound of the disturbances finally simulation results show that the computation load is significantly reduced and illustrate the efficiency of our proposed strategy

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the 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

distributed observer design for bounded tracking control of leader follower multi agent systems in a sampled data setting this paper studies the observer based bounded tracking control problem of second order multi agent systems in a disturbance environment via sampled data control two sampled data protocols are introduced under the assumption that the dynamic leader is only available to a portion of agents and distributed observers are designed to estimate the velocity of the active leader for the fixed communication topology case necessary and sufficient conditions of bounded consensus tracking are obtained by using the matrix analysis method for the switching communication topology case we prove that system can achieve bounded tracking by applying the common lyapunov function and perturbation theory simulation examples are given to illustrate the effectiveness of our results

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

groundstates of nonlinear choquard equations existence qualitative properties and decay asymptotics we consider a semilinear elliptic problem delta u u i alpha ast abs u p abs u p 2 u quad text in r n where i alpha is a riesz potential and p 1 this family of equations includes the choquard or nonlinear schr odinger newton equation for an optimal range of parameters we prove the existence of a positive groundstate solution of the equation we also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point finally we derive the decay asymptotics at infinity of the groundstates

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

holder estimates for homotopy operators on strictly pseudoconvex domains with c 2 boundary we derive a new homotopy formula for a strictly pseudoconvex domain of c 2 boundary in mathbf c n by using a method of lieb and range and obtain estimates in lipschitz spaces for the homotopy operators for r 1 and q 0 we obtain a lambda r 1 2 solution u to overline partial u f for a overline partial closed 0 q form f of class lambda r in the domain we apply the estimates to obtain boundary regularities of mathcal d solutions for a domain in mathbf c n times mathbf r m

fixed time consensus tracking for multiagent systems with high order integrator dynamics this paper addresses the fixed time leader follower consensus problem for high order integrator multiagent systems subject to matched external disturbances a new cascade control structure based on a fixed time distributed observer is developed to achieve the fixed time consensus tracking control a simulation example is included to show the efficacy and the performance of the proposed control structure with respect to different initial conditions

the bergman projection and weighted c k estimates for the canonical solution to the bar partial problem on non smooth domains we apply integral representations for functions on non smooth strictly pseudoconvex domains the henkin leiterer domains to derive weighted c k estimates for the component of a given function f which is orthogonal to holomorphic functions in terms of c k norms of f the weights are powers of the gradient of the defining function of the domain

existence and instability of standing waves with prescribed norm for a class of schrodinger poisson equations in this paper we study the existence and the instability of standing waves with prescribed l norm for a class of schrodinger poisson slater equations in r 0 1 i t x 1 p 2 0 when p 10 3 6 to obtain such solutions we look to critical points of the energy functional f u 1 2 ou 2l2 r3 1 4

fixed time stable gradient flows applications to continuous time optimization this paper proposes novel gradient flow schemes that yield convergence to the optimal point of a convex optimization problem within a fixed time from any given initial condition for unconstrained optimization constrained optimization and min max problems it is shown that the solution of the modified gradient flow dynamics exists and is unique under certain regularity conditions on the objective function while fixed time convergence to the optimal point is shown via lyapunov based analysis the application of the modified gradient flow to unconstrained optimization problems is studied under the assumption of gradient dominance a relaxation of strong convexity then a modified newton s method is presented that exhibits fixed time convergence under some mild conditions on the objective function building upon this method a novel technique for solving convex optimization problems with linear equality constraints that yields convergence to the optimal point in fixed time is developed finally the general min max problem is considered and a modified scheme to obtain the optimal solution of saddle point dynamics in fixed time is developed

second order consensus for multi agent systems with switching topology and communication delay in this paper two kinds of consensus problems for second order agents under directed and arbitrarily switching topologies are investigated that is the cases without and with communication delay for the former by constructing a new kind of digraph and employing a new graphic method we can specify the least convergence rate for all the agents to reach consensus for the latter in virtue of a matrix inequality method a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus this on the other hand shows that consensus can be reached if the delay is small enough finally two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results

implicit lyapunov krasovski functionals for stability analysis and control design of time delay systems the method of implicit lyapunov krasovski functional ilkf for stability analysis of time delay systems is introduced theorems on lyapunov asymptotic hyper exponential finite time and fixed time stability analysis using ilkf are presented the hyper exponential stabilization algorithm for a time delay system is presented the theoretical result is supported by numerical simulation

non linear protocols for optimal distributed consensus in networks of dynamic agents we consider stationary consensus protocols for networks of dynamic agents with fixed topologies at each time instant each agent knows only its and its neighbors state but must reach consensus on a group decision value that is function of all the agents initial state we show that the agents can reach consensus if the value of such a function is time invariant when computed over the agents state trajectories we use this basic result to introduce a non linear protocol design rule allowing consensus on a quite general set of values such a set includes e g any generalized mean of order p of the agents initial states as a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents this notion suggests a game theoretic interpretation of consensus problems as mechanism design problems under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives we prove that such objectives can be chosen so that rational agents have a unique optimal protocol and asymptotically reach consensus on a desired group decision value we use a lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time invariant undirected network finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles

distributed adaptive asymptotically consensus tracking control of nonlinear multi agent systems with unknown parameters and uncertain disturbances abstract different from traditional centralized control one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems currently most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs in this paper we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high order multi agent systems subjected to mismatched unknown parameters and uncertain external disturbances by introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design a new backstepping based distributed adaptive control protocol is proposed an extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors dynamics which avoids information exchange of local neighborhood consensus errors among connected subsystems it is shown that global uniform boundedness of all the closed loop signals and asymptotically output consensus tracking can be achieved simulation results are provided to verify the effectiveness of our scheme

consensus of multiple nonholonomic chained form systems abstract consensus problems of multiple nonholonomic systems are considered in this paper this problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant the condition on the group reference signal have been further relaxed in this paper simulation results using matlab have illustrated the effectiveness of the results presented in this paper

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed 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

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper