how to get a conservative well posed linear system out of thin air part ii controllability and stability let a0 be a possibly unbounded positive operator on the hilbert space h which is boundedly invertible let c0 be a bounded operator from cal d a 0 1 2 with the norm z 1 2 2 langle

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

uniform controllability of semidiscrete approximations of parabolic control systems controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model in the present paper under the main assumptions that the discretized semigroup is uniformly analytic and that the control operator is mildly unbounded we prove that the semidiscrete approximation models are uniformly controllable moreover we provide a computationally efficient way to compute the approximation controls an example of application is implemented for the one and two dimensional heat equation with neumann boundary control

distributed algorithm for solving convex inequalities in this note a distributed subgradient based algorithm is proposed for continuous time multi agent systems to search a feasible solution to convex inequalities the algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time varying directed communication graph with the validity of a mild connectivity condition associated with the communication graph it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities furthermore the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities simulation examples are presented to demonstrate the effectiveness of the theoretical results

an approximation method for exact controls of vibrating systems we propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator the algorithm combines russell s stabilizability implies controllability principle with the galerkin method the main new feature of this work consists of giving precise error estimates in order to test the efficiency of the method we consider two illustrative examples with the finite element approximations of the wave and the beam equations and describe the corresponding simulations

topology selection for multi agent systems with opposite leaders abstract for the multi agent system with a navigational leader and its opponent the followers cannot converge to the state of the navigational leader in this paper we consider the topology selection problem to minimize the opponent s influence which is measured by the tracking error of the system firstly two combinatorial optimization problems are formulated one is to minimize the tracking error by selecting guided informed agents the followers who can obtain the navigational leader s information the other is to choose minimal number of guided informed agents under an upper bound constraint of the tracking error secondly for the scenario where the guided informed agents are preset we consider the problem of assigning the weights of edges to minimize the tracking error three convex optimization problems are proposed to evaluate the upper and lower bounds of the tracking error finally numerical examples are provided to illustrate the effectiveness of the theoretical results

analysis of the hum control operator and exact controllability for semilinear waves in uniform time we present a regularity result for the hum optimal control associated with the interior control of linear waves we use this analysis together with strichartz inequalities to get results on the exact controllability for subcritical nonlinear waves in a bounded domain of mathbb r 3

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

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

classification and geometrical properties of the xθ valued function spaces abstract this paper is devoted to investigate the x valued function spaces based on the notions of bounded topological lattice banach space net continuous modular net and the dual space net we divide x valued function spaces into two classes norm modular spaces and modular modular spaces for the first class we study the separability of l p i x give a representation of the dual space l p i x find sufficient conditions of the equality l p i x l p i x and prove the reflexivity of l p i x under some reasonable conditions and for the second class we prove the completeness and uniform convexity of l i x in suitable situations to show the naturality and rationality of these results some concrete function spaces such as l p t i l p x t l p t i w 1 p x t and l p t i w 0 1 p x t together with l p p t i l p x t are taken into account

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

distributed control of networked dynamical systems static feedback integral action and consensus this paper analyzes distributed control protocols for first and second order networked dynamical systems we propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain and a sum of nonlinear interaction functions by using integral lyapunov functions we prove the stability of the proposed control protocols and explicitly characterize the equilibrium set we also propose a distributed proportional integral pi controller for networked dynamical systems the pi controllers successfully attenuate constant disturbances in the network we prove that agents with single integrator dynamics are stable for any integral gain and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double integrator dynamics throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites power systems and building temperature control

distributed consensus of heterogeneous multi agent systems with fixed and switching topologies in this article we study distributed consensus of heterogeneous multi agent systems with fixed and switching topologies the analysis is based on graph theory and nonnegative matrix theory we propose two kinds of consensus protocols based on the consensus protocol of first order and second order multi agent systems some necessary and sufficient conditions that the heterogeneous multi agent system solves the consensus problems under different consensus protocols are presented with fixed topology we also give some sufficient conditions for consensus of the heterogeneous multi agent system with switching topology simulation examples are provided to demonstrate the effectiveness of the theoretical results

convergence of type symmetric and cut balanced consensus seeking systems we consider continuous time consensus seeking systems whose time dependent interactions are cut balanced in the following sense if a group of agents influences the remaining ones the former group is also influenced by the remaining ones by at least a proportional amount models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases we prove that such systems always converge we give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same conversely we show that if our condition is not satisfied then these limits are generically different these results allow treating systems where the agent interactions are a priori unknown being for example random or determined endogenously by the agent values

the multi agent rendezvous problem part 2 the asynchronous case this paper is concerned with the collective behavior of a group of n 1 mobile autonomous agents labelled 1 through n which can all move in the plane each agent is able to continuously track the positions of all other agents currently within its sensing region where by an agent s sensing region we mean a closed disk of positive radius r centered at the agent s current position the multi agent rendezvous problem is to devise local control strategies one for each agent which without any active communication between agents cause all members of the group to eventually rendezvous at a single unspecified location this paper describes a family of unsynchronized strategies for solving the problem correctness is established appealing to the concept of analytic synchronization

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

multi agent consensus with relative state dependent measurement noises in this note the distributed consensus corrupted by relative state dependent measurement noises is considered each agent can mea sure or receive its neighbors state information with random noises whose intensity is a vector function of agents relative states by investigating the structure of this interaction and the tools of stochastic differential equa tions we develop several small consensus gain theorems to give sufficient conditions in terms of the control gain the number of agents and the noise intensity function to ensure mean square m s and almost sure a s consensus and quantify the convergence rate and the steady state error especially for the case with homogeneous communication and control channels a necessary and sufficient condition to ensure m s consensus on the control gain is given and it is shown that the control gain is independent of the specific network topology but only depends on the number of nodes and the noise coefficient constant for symmetric measurement models the almost sure convergence rate is estimated by the iterated logarithm law of brownian motions index terms distributed consensus distributed coordination fading channel measurement noises multi agent system

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

exponential stability of fractional order complex multi links networks with aperiodically intermittent control in this article the exponential stability problem for fractional order complex multi links networks with aperiodically intermittent control is considered using the graph theory and lyapunov method two theorems including a lyapunov type theorem and a coefficient type theorem are given to ensure the exponential stability of the underlying networks the theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative to be specific the larger control gain the higher the exponential convergence rate meanwhile when aperiodically intermittent control degenerates into periodically intermittent control a corollary is also provided to ensure the exponential stability of the underlying networks furthermore to show the practicality of theoretical results as an application the exponential stability of fractional order multi links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established finally the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example

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