a hybrid method for hydrodynamic kinetic flow part ii coupling of hydrodynamic and kinetic models in this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic kinetic problems in which the knudsen number may span from equilibrium to highly rarefied regimes our approach is characterized by using the full boltzmann equation for the kinetic regime the compressible euler equations for equilibrium with a buffer zone in which the bgk es equation is used to represent the transition between fully kinetic to equilibrium flows in this fashion the boltzmann solver is used only when the collision integral is non stiff and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities thus in principle the same mesh size and time steps can be used in the whole computation moreover the time step is limited only by convective terms since the boltzmann solver is applied only in wholly kinetic regimes we use the reduced noise dsmc scheme we have proposed in part i of the present work this ensures a smooth exchange of information across the different domains with a natural way to construct interface numerical fluxes several tests comparing our hybrid scheme with full boltzmann dsmc computations show the good agreement between the two solutions on a wide range of knudsen numbers

spectral lagrangian methods for collisional models of non equilibrium statistical states we propose a new spectral lagrangian based deterministic solver for the non linear boltzmann transport equation bte in d dimensions for variable hard sphere vhs collision kernels with conservative or non conservative binary interactions the method is based on symmetries of the fourier transform of the collision integral where the complexity in its computation is reduced to a separate integral over the unit sphere s d 1 the conservation of moments is enforced by lagrangian constraints the resulting scheme implemented in free space is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro reversibility inelastic interactions or elastic models of slowing down process our simulations are benchmarked with available exact self similar solutions exact moment equations and analytical estimates for the homogeneous boltzmann equation both for elastic and inelastic vhs interactions benchmarking of the simulations involves the selection of a time self similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for maxwell molecules as studied first in bobylev et al a v bobylev c cercignani g toscani proof of an asymptotic property of self similar solutions of the boltzmann equation for granular materials journal of statistical physics 111 2003 403 417 and generalized to a wide range of related models in bobylev et al a v bobylev c cercignani i m gamba on the self similar asymptotics for generalized non linear kinetic maxwell models communication in mathematical physics in press url the method also produces accurate results in the case of inelastic diffusive boltzmann equations for hard spheres inelastic collisions under thermal bath where overpopulated non gaussian exponential tails have been conjectured in computations by stochastic methods t v noije m ernst velocity distributions in homogeneously cooling and heated granular fluids granular matter 1 57 1998 m h ernst r brito scaling solutions of inelastic boltzmann equations with over populated high energy tails journal of statistical physics 109 2002 407 432 s j moon m d shattuck j swift velocity distributions and correlations in homogeneously heated granular media physical review e 64 2001 031303 i m gamba s rjasanow w wagner direct simulation of the uniformly heated granular boltzmann equation mathematical and computer modelling 42 2005 683 700 and rigorously proven in gamba et al i m gamba v panferov c villani on the boltzmann equation for diffusively excited granular media communications in mathematical physics 246 2004 503 541 39 and a v bobylev i m gamba v panferov moment inequalities and high energy tails for boltzmann equations with inelastic interactions journal of statistical physics 116 2004 1651 1682

towards an ultra efficient kinetic scheme part i basics on the bgk equation in this paper we present a new ultra efficient numerical method for solving kinetic equations in this preliminary work we present the scheme in the case of the bgk relaxation operator the scheme being based on a splitting technique between transport and collision can be easily extended to other collisional operators as the boltzmann collision integral or to other kinetic equations such as the vlasov equation the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport linear part by following the characteristics backward in time the main difference between the method proposed and semi lagrangian methods is that here we do not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost of the method and it permits for the first time to the author s knowledge to compute solutions of full six dimensional kinetic equations on a single processor laptop machine numerical examples up to the full three dimensional case are presented which validate the method and assess its efficiency in 1d 2d and 3d

a multiscale fast semi lagrangian method for rarefied gas dynamics in this paper we consider the extension of the method developed in dimarco and loubere 2013 22 23 with the aim of facing the numerical resolution of multi scale problems arising in rarefied gas dynamics the scope of this work is to consider situations in which the whole domain does not demand the use of a kinetic model everywhere this is the case of many realistic applications some regions of the computational domain require a microscopic description given by a kinetic model while the rest of the domain can be described by a coarser model of fluid type our aim is to show how the kinetic scheme developed in the pre cited articles is perfectly suited for building domain decomposition strategies which make the method more attractive with respect to classical numerical techniques for kinetic equations and multi scale realistic problems several numerical evidences are provided in this work in the two dimensional and three dimensional settings to assess the efficiency of the domain decomposition scheme

consensus problems in discrete time multiagent systems with fixed topology abstract in this paper we study the consensus problems in discrete time multiagent systems with fixed topology a necessary and sufficient condition for a system that solves a consensus problem is established and the structure of consensus functions is characterized based on them we introduce the standard topologies graphs of information flow with which the systems can be viewed as single leader multi follower systems moreover the convex combination of these topologies can create a system that solves any predeterminate consensus problem additionally we characterize the structural decomposition the leaders followers decomposition of a multiagent system and establish a necessary and sufficient condition for an agent to be a leader

dissipativity based resilient filtering of periodic markovian jump neural networks with quantized measurements the problem of dissipativity based resilient filtering for discrete time periodic markov jump neural networks in the presence of quantized measurements is investigated in this paper due to the limited capacities of network medium a logarithmic quantizer is applied to the underlying systems considering the fact that the filter is realized through a network randomly occurring parameter uncertainties of the filter are modeled by two mode dependent bernoulli processes by establishing the mode dependent periodic lyapunov function sufficient conditions are given to ensure the stability and dissipativity of the filtering error system the filter parameters are derived via solving a set of linear matrix inequalities the merits and validity of the proposed design techniques are verified by a simulation example

on stabilization and set stabilization of multivalued logical systems the stabilization and set stabilization of a multivalued logical system are investigated in this paper by using pinning control first new algorithms are presented to redesign the transition matrix of the multivalued logical system such that the system is stable or set stable then by using reconstruction theory of a k valued logical system the pinning nodes are selected in addition the transition matrix of the pinning control is given by solving some logical matrix equations then a pinning control design algorithm is provided finally an example is employed to illustrate the proposed control design procedure

dynamic behaviors in directed networks motivated by the abundance of directed synaptic couplings in a real biological neuronal network we investigate the synchronization behavior of the hodgkin huxley model in a directed network we start from the standard model of the watts strogatz undirected network and then change undirected edges to directed arcs with a given probability still preserving the connectivity of the network a generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks we observe that the directedness of complex networks plays an important role in emerging dynamical behaviors which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

adaptive nn controller design for a class of nonlinear mimo discrete time systems an adaptive neural network tracking control is studied for a class of multiple input multiple output mimo nonlinear systems the studied systems are in discrete time form and the discretized dead zone inputs are considered in addition the studied mimo systems are composed of n subsystems and each subsystem contains unknown functions and external disturbance due to the complicated framework of the discrete time systems the existence of the dead zone and the noncausal problem in discrete time it brings about difficulties for controlling such a class of systems to overcome the noncausal problem by defining the coordinate transformations the studied systems are transformed into a special form which is suitable for the backstepping design the radial basis functions nns are utilized to approximate the unknown functions of the systems the adaptation laws and the controllers are designed based on the transformed systems by using the lyapunov method it is proved that the closed loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set the simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm

consensus for networks with unknown but bounded disturbances we consider stationary consensus protocols for networks of dynamic agents the measure of the neighbors states is affected by unknown but bounded disturbances here the main contribution is the formulation and solution of what we call the epsilon consensus problem where the states are required to converge in a target set of radius epsilon asymptotically or in finite time we introduce as a solution a dead zone policy that we denote as the lazy rule

adaptive consensus control for a class of nonlinear multiagent time delay systems using neural networks because of the complicity of consensus control of nonlinear multiagent systems in state time delay most of previous works focused only on linear systems with input time delay an adaptive neural network nn consensus control method for a class of nonlinear multiagent systems with state time delay is proposed in this paper the approximation property of radial basis function neural networks rbfnns is used to neutralize the uncertain nonlinear dynamics in agents an appropriate lyapunov krasovskii functional which is obtained from the derivative of an appropriate lyapunov function is used to compensate the uncertainties of unknown time delays it is proved that our proposed approach guarantees the convergence on the basis of lyapunov stability theory the simulation results of a nonlinear multiagent time delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm

adaptive dynamic programming for finite horizon optimal control of discrete time nonlinear systems with varepsilon error bound in this paper we study the finite horizon optimal control problem for discrete time nonlinear systems using the adaptive dynamic programming adp approach the idea is to use an iterative adp algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an error bound the optimal number of control steps can also be obtained by the proposed adp algorithms a convergence analysis of the proposed adp algorithms in terms of performance index function and control policy is made in order to facilitate the implementation of the iterative adp algorithms neural networks are used for approximating the performance index function computing the optimal control policy and modeling the nonlinear system finally two simulation examples are employed to illustrate the applicability of the proposed method

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

flocking with connectivity preservation for disturbed nonlinear multi agent systems by output feedback abstractthis paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi agent systems in order to deal with the nonlinearities in the dynamic of all agents some auxiliary variables are introduced into the state observer for stability analysis by proposing a bounded potential function and using adaptive theory a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

distributional solutions of the beltrami equation abstract we study the distributional solutions to the generalized beltrami equation under sobolev assumptions on the beltrami coefficients in this setting we prove that these distributional solutions are true quasiregular maps and they are smoother than expected that is they have second order derivatives in l l o c 1 e for some e 0

an asymptotic preserving automatic domain decomposition method for the vlasov poisson bgk system with applications to plasmas in this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present the method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones in this paper we extend domain decomposition techniques obtained through dynamic coupling and buffer zones to the study of plasmas and moreover we combine them with asymptotic preserving and asymptotically accurate strategies for the time integration we use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods in order to guarantee high efficiency and accuracy in all regimes the numerical scheme is validated and its performances are analyzed by numerical simulations

a multiscale kinetic fluid solver with dynamic localization of kinetic effects this paper collects the efforts done in our previous works 7 9 10 to build a robust multiscale kinetic fluid solver our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move merge appear or disappear in time the main ingredients of the present work are the followings ones a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary this multiscale description of the flow is obtained by using a micro macro decomposition of the distribution function 9 the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself several numerical examples are presented to validate the method and measure its computational efficiency

coupling boltzmann and navier stokes equations by friction the aim of this paper is to introduce and validate a coupled navier stokes boltzman approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles the proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global navier stokes solver dif ferent numerical experiments illustrate the potentialities of the method

virtual strain gauge based on a fuzzy discrete angular domain observer application to engine and clutch torque estimation issues abstract in many real time applications information of transmitted torque is a mandatory input of the embedded control strategies in the most of cases the use of a physical torque sensor strain gauge is compromised by cost and bulk reasons and the torque is not measured unfortunately the need of an embedded torque measurement is a general real time application problem and can only be solved through an accurate embeddable estimation method this issue is especially common in automotive industry concerning the powertrain management for example a virtual strain gauge based on an unknown input takagi sugeno discrete observer designed in the angular domain and a shaft angular deformation estimation method is proposed as a universal torque estimator the static torque estimation is ensured rebuilding the shaft torsion angle by a virtual tooth adding method into the encoder sensors disposed at each edge of the shaft the observer performs the dynamic part of the transmitted torque through a mass spring model structure of the shaft the virtual strain gauge has been applied on real torque estimation issues in automotive application such as the engine and the clutch torque estimation simulation and real time results have permitted to validate the feasibility the versatility and the accuracy of the virtual strain gauge

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

a consistency result for a discrete velocity model of the boltzmann equation in this paper we study the link between a certain class of discrete velocity models dvms and the boltzmann equation those models possess an infinite number of velocities laying on a regular grid of step h in r3 our aim is to prove that it is possible to construct models consistent with the boltzmann equation i e such that the discrete collision term can be seen as an approximation of the collision integral of the boltzmann equation

fuzzy observed based adaptive consensus tracking control for second order multiagent systems with heterogeneous nonlinear dynamics in this paper the consensus tracking control problem of second order multiagent systems with unknown nonlinear dynamics immeasurable states and disturbances is investigated the nonlinear dynamics in multiagent systems do not satisfy the matched condition in this paper fuzzy logic system is introduced to approximate the unknown nonlinear dynamics and adaptive high gain observer is designed to estimate the unmeasured states based on backstepping approach and lyapunov theory a new adaptive fuzzy distributed controller is proposed for each agent only using the information of itself and its neighbors then the consensus tracking is achieved under the designed distributed controller moreover it is proved that all the signals in the multiagent systems are semiglobally uniformly ultimately bounded and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible finally the simulation result illustrates the effectiveness of the designed controller

fuzzy tracking control for nonlinear multi agent systems with actuator faults and unknown control directions abstract this paper studies the fuzzy tracking control problem of nonlinear multi agent systems with time varying actuator faults and unknown control directions the term of time varying actuator faults is estimated via designing adaptive parameter for the problem of the unknown control directions the nussbaum function is introduced to ensure the controller is unaffected on unknown direction moreover based on algebraic graph theory and lyapunov stability theory a new distributed controller is designed to guarantee that the tracking error converges to a small neighborhood near the origin finally simulation examples are given to verify the theoretical results

decentralized adaptive fuzzy control for nonlinear large scale systems with random packet dropouts sensor delays and nonlinearities abstract this paper investigates the adaptive fuzzy decentralized control problem for a class of uncertain nonlinear large scale systems different from the conventional backstepping based adaptive output feedback control technique the output measurements are imperfect and considered to suffer random packet dropouts rpds random sensor delays rsds and random sensor nonlinearities rsns which result typically from a network environment such as sensor networks a novel sensor model is established for describing the random phenomena within a unified representation by introducing a multi markovian variable based on this sensor model two main difficulties arise first is that the system output cannot be used directly for controller design due to the randomly occurring phenomena second is how to deal with the complex nonlinear stochastic terms with unknown interconnections unknown time varying delays and unknown sensor nonlinearities entangled together with the help of new coordinate transformations and mean value theorem by using appropriate lyapunov krasovskii functionals a new adaptive decentralized memoryless output feedback controller is designed it is proved that the constructed controller ensures the boundedness in probability of all the closed loop signals in presence of rpds rsds and rsns the simulation results are presented to show the effectiveness of the proposed scheme

a particle particle hybrid method for kinetic and continuum equations we present a coupling procedure for two different types of particle methods for the boltzmann and the navier stokes equations a variant of the dsmc method is applied to simulate the boltzmann equation whereas a meshfree lagrangian particle method similar to the sph method is used for simulations of the navier stokes equations an automatic domain decomposition approach is used with the help of a continuum breakdown criterion we apply adaptive spatial and time meshes the classical sod s 1d shock tube problem is solved for a large range of knudsen numbers results from boltzmann navier stokes and hybrid solvers are compared the cpu time for the hybrid solver is 3 4 times faster than for the boltzmann solver

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

robust adaptive fuzzy fault tolerant control for a class of non lower triangular nonlinear systems with actuator failures in this paper the problem of adaptive fuzzy fault tolerant tracking control is studied for a class of non lower triangular nonlinear systems with actuator failures according to the same structure of virtual control inputs and the monotonously increasing property of the bounding functions a variable separation approach is proposed by applying the backstepping technique an adaptive fuzzy control approach is presented which can guarantee the semi global boundedness of all signals within the closed loop system the tracking error using the proposed control scheme eventually converges to a small neighborhood of the origin

stability of nonlinear differential systems with state dependent delayed impulses we consider nonlinear differential systems with state dependent delayed impulses impulses which involve the delayed state of the system for which the delay is state dependent such systems arise naturally from a number of applications and the stability issue is complex due to the state dependence of the delay we establish general and applicable results for uniform stability uniform asymptotic stability and exponential stability of the systems by using the impulsive control theory and some comparison arguments we show how restrictions on the change rates of states and impulses should be imposed to achieve system s stability in comparison with general impulsive delay differential systems with state dependent delay in the nonlinearity or the differential systems with constant delays in our approach the boundedness of the state dependent delay is not required but derives from the stability result obtained examples are given to demonstrate the sharpness and applicability of our general results and the proposed approach

some results on the forced pendulum equation abstract this paper is devoted to the study of the forced pendulum equation in the presence of friction namely u a u sin u f t with a r and f l 2 0 t using a shooting type argument we prove the existence of at least two essentially different t periodic solutions under appropriate conditions on t and f we also prove the existence of solutions decaying with a fixed rate 0 1 by the leray schauder theorem finally we prove the existence of a bounded solution on 0 using a diagonal argument

reinforcement learning design based adaptive tracking control with less learning parameters for nonlinear discrete time mimo systems based on the neural network nn approximator an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output mimo nonlinear discrete time systems with unknown functions and disturbances in the design procedure two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function an optimal control signal and adaptation laws can be generated based on two nns in the previous approaches the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design consequently compared with the existing results the main contributions of this paper are 1 only two parameters are needed to be adjusted and thus the number of the adaptation laws is smaller than the previous results and 2 the updating parameters do not depend on the number of the subsystems for mimo systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks it is proven that the tracking errors the adaptation laws and the control inputs are uniformly bounded using lyapunov analysis method the simulation examples are employed to illustrate the effectiveness of the proposed algorithm

robust h_ infty control for t s fuzzy systems with state and input time varying delays via delay product type functional method this paper investigates the problem of robust h infty control for a class of nonlinear systems with state and input time varying delays the nonlinearity is presented by a continuous time takagi sugeno t s fuzzy model with parameter uncertainties a sufficient asymptotic stability condition is first proposed by constructing a delay product type augmented lyapunov krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a wirtinger based integral inequality then a state feedback controller is derived that guarantees the closed loop fuzzy system being asymptotically stable with an h infty performance index finally four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques

avoiding congestion in cluster consensus of the second order nonlinear multiagent systems in order to avoid congestion in the second order nonlinear leader following multiagent systems over capacity limited paths an approach called cluster lag consensus is proposed which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus it is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold the cluster lag consensus can be achieved furthermore the cluster lag consensus with a time varying communication topology is investigated finally an illustrative example is presented to demonstrate the effectiveness of the theoretical results in particular when the physical sizes of the agents are taken into consideration it is shown that with a rearrangement and a position transformation the multiagent system will reach cluster lag consensus in the new coordinate system this means that all agents in the same cluster will reach consensus on the velocity but their positions may be different and yet their relative positions converge to a constant asymptotically

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

a modular particle continuum numerical method for hypersonic non equilibrium gas flows a modular particle continuum mpc numerical method for steady state flows is presented which solves the navier stokes equations in regions of near equilibrium and uses the direct simulation monte carlo dsmc method to simulate regions of non equilibrium gas flow existing state of the art dsmc and navier stokes solvers are coupled together using a novel modular implementation which requires only a limited number of additional hybrid functions hybrid functions are used to adaptively position particle continuum interfaces and update boundary conditions in each module at appropriate times the mpc method is validated for 2d flow over a cylinder at various hypersonic mach numbers where the global knudsen number is 0 01 for the cases considered the mpc method is verified to accurately reproduce dsmc flow field results as well as local particle velocity distributions up to 2 2 times faster than full dsmc simulations

formation potential field for trajectory tracking control of multi agents in constrained space abstractin this paper a novel formation potential field method is proposed for the multi agent formation control the objective is to control a group of agents to automatically generate and maintain a specific formation while avoiding internal collisions and collisions with spatial constraints a formation potential field is designed combining multiple local attractive potential fields with multiple local repulsive potential fields to further relax requirements of agents initial positions and enhance the robustness a global attractive potential field is added outside the influence range of the local formation potential field the optimality of the proposed scheme in formation time is analysed as well as illustrated by contrast simulation results following the design of the formation potential field two controllers are proposed accordingly to achieve a stable dynamic formation during the process of trajectory tracking while the saturation effect of input is taken into account furthermore a collisi

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

a sliding mode approach to stabilization of nonlinear markovian jump singularly perturbed systems this paper presents a sliding mode control smc method for a class of nonlinear markovian jump singularly perturbed systems mjspss the system is subject to parameter uncertainties and partly unknown transition probabilities to fully employ the model characteristics of such a hybrid system a novel integral type switching function is firstly designed by adopting the e dependent stochastic lyapunov function method sufficient conditions are presented to ensure the mean square asymptotic stability of the sliding mode dynamics a mode dependent fuzzy smc law is then synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties finally the developed method is applied to stabilize a modified series dc motor system

smooth neuroadaptive pi tracking control of nonlinear systems with unknown and nonsmooth actuation characteristics this paper considers the tracking control problem for a class of multi input multi output nonlinear systems subject to unknown actuation characteristics and external disturbances neuroadaptive proportional integral pi control with self tuning gains is proposed which is structurally simple and computationally inexpensive different from traditional pi control the proposed one is able to online adjust its pi gains using stability guaranteed analytic algorithms without involving manual tuning or trial and error process it is shown that the proposed neuroadaptive pi control is continuous and smooth everywhere and ensures the uniformly ultimately boundedness of all the signals of the closed loop system furthermore the crucial compact set precondition for a neural network nn to function properly is guaranteed with the barrier lyapunov function allowing the nn unit to play its learning approximating role during the entire system operation the salient feature also lies in its low complexity in computation and effectiveness in dealing with modeling uncertainties and nonlinearities both square and nonsquare nonlinear systems are addressed the benefits and the feasibility of the developed control are also confirmed by simulations

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

non quadratic local stabilization for continuous time takagi sugeno models this paper is concerned with non quadratic stabilization of continuous time takagi sugeno ts models the well known problem of handling time derivatives of membership functions mfs as to obtain conditions in the form of linear matrix inequalities lmis is overcome by reducing global goals to the estimation of a region of attraction instead of parallel distributed compensation pdc a non pdc control law is proposed according to the non quadratic nature of the lyapunov function examples are provided to show the advantages over the quadratic and some non quadratic approaches

fast algorithms for computing the boltzmann collision operator the development of accurate and fast numerical schemes for the five fold boltzmann collision integral represents a challenging problem in scientific computing for a particular class of interactions including the so called hard spheres model in dimension three we are able to derive spectral methods that can be evaluated through fast algorithms these algorithms are based on a suitable representation and approximation of the collision operator explicit expressions for the errors in the schemes are given and spectral accuracy is proved parallelization properties and adaptivity of the algorithms are also discussed

consensus of second order multi agent systems with delayed nonlinear dynamics and intermittent communications this article investigates the second order consensus problem of multi agent systems with inherent delayed nonlinear dynamics and intermittent communications each agent is assumed to obtain the measurements of relative states between its own and the neighbours only at a sequence of disconnected time intervals a new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second order consensus under a fixed strongly connected and balanced topology by constructing a common lyapunov function it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values respectively finally simulation examples are provided to verify the effectiveness of the theoretical analysis

observer and adaptive fuzzy control design for nonlinear strict feedback systems with unknown virtual control coefficients this paper considers the problems of designing a robust observer and developing a backstepping based adaptive fuzzy control scheme for a class of strict feedback systems in which the virtual control coefficients are unknown by using convex combination method a robust fuzzy observer has been constructed to estimate the unmeasurable system state variables further an observer based adaptive fuzzy control scheme has been proposed during the controller design procedure fuzzy logic systems are used to model the unknown nonlinear functions adaptive technique and backstepping are combined to construct the ideal virtual and the real laws the proposed adaptive fuzzy output feedback controller guarantees that the tracking error converges to a small neighborhood of the origin and all the signals in the adaptive closed loop system are bounded simulation results are provided to demonstrate the effectiveness of the presented approach

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

towards an ultra efficient kinetic scheme part ii in a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the boltzmann type dimarco and loubere 2013 17 the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport part by following the characteristics backward in time on the contrary to classical semi lagrangian methods one does not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost and to perform efficient numerical simulations of kinetic equations up to the six dimensional case without parallelization however the main drawback of the method developed was the loss of spatial accuracy close to the fluid limit in the present work we modify the scheme in such a way that it is able to preserve the high order spatial accuracy for extremely rarefied and fluid regimes in particular in the fluid limit the method automatically degenerates into a high order method for the compressible euler equations numerical examples are presented which validate the method show the higher accuracy with respect to the previous approach and measure its efficiency with respect to well known schemes direct simulation monte carlo finite volume muscl weno

adaptive neural asymptotic control for uncertain nonlinear multiagent systems with a fuzzy dead zone constraint abstract a consensus control scheme is developed for a class of leader follower multiagent systems with a fuzzy dead zone constraint differently from previous work the method developed implements a predefined convergence of tracking errors for multiagent systems especially the dynamic model for each follower has a fuzzy dead zone input to solve the problem not only a set of smooth functions are used within the control design to increase the stability of the systems but also the unfuzziness and center of gravity method are used to analyze and process the actuator constraint model where each slope of the dead zone is uncertain and fuzzy it is verified that the method developed effectively guarantees that the tracking errors of multiagent systems can converge to a predefined interval that is the problem of better asymptotic consensus performance for nonlinear multiagent systems is solved simulation illustrates the results obtained

distributed consensus tracking for multiple uncertain nonlinear strict feedback systems under a directed graph in this brief we study the distributed consensus tracking control problem for multiple strict feedback systems with unknown nonlinearities under a directed graph topology it is assumed that the leader s output is time varying and has been accessed by only a small fraction of followers in a group the distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader the function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure from the lyapunov stability theorem it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin

coupling of the boltzmann and euler equations with automatic domain decomposition a criterion for automatic domain decomposition has been introduced for the coupling of the boltzmann and euler equations this criterion is obtained by using the grad s 13 moments expansion method the boltzmann and euler equations have been solved by the particle method this criterion has been further tested for the spatial homogeneous relaxation case and the coupling of the boltzmann and euler equations in two dimensional physical space some numerical results obtained from the particle code of the full boltzmann equation are compared with those of coupling of the boltzmann and euler equations

high order numerical methods for the space non homogeneous boltzmann equation in this paper we present accurate methods for the numerical solution of the boltzmann equation of rarefied gas the methods are based on a time splitting technique the transport is solved by a third order accurate in space positive and flux conservative pfc method the collision step is treated by a fourier approximation of the collision integral which guarantees spectral accuracy in velocity coupled with several high order integrators in time strang splitting is used to achieve second order accuracy in space and time several numerical tests illustrate the properties of the methods

area distortion of quasiconformal mappings in recent years quasiconformal mappings have been an efficient tool in the study of dynamical systems of the complex plane we show here that in turn methods or ideas from dynamical systems can be used to solve a number of open questions in the theory of planar quasiconformal mappings it has been known since the work of ahlfors a and mori mo that k quasiconformal mappings are locally h51der continuous with exponent 1 k the function

adaptive finite time control of stochastic nonlinear systems with actuator failures abstract this paper investigates a finite time tracking control of stochastic nonlinear systems with actuator failures as the nonlinearities and actuator failures are completely unknown the existing control methods are unavailable by applying an approximation property of fuzzy logic systems an adaptive finite time control strategy is presented since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error lemma 5 is first established under the proposed scheme the actuator failures are compensated successfully and the finite time tracking performance and stability of stochastic nonlinear system are assured based on lemma 5 and jessen s inequality the finite time stability of stochastic nonlinear systems is proved

an adaptive domain decomposition procedure for boltzmann and euler equations in this paper we present a domain decomposition approach for the coupling of boltzmann and euler equations particle methods are used for both equations this leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains adaptive time and space discretizations and a direct coupling procedure lead to considerable gains in cpu time compared to a solution of the full boltzmann equation several test cases involving a large range of knudsen numbers are numerically investigated

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

prescribed performance distributed consensus control for nonlinear multi agent systems with unknown dead zone input in this paper the problem of prescribed performance distributed output consensus for higher order non affine nonlinear multi agent systems with unknown dead zone input is investigated fuzzy logic

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

a moving interface method for dynamic kinetic fluid coupling this paper is a continuation of earlier work p degond s jin l mieussens a smooth transition between kinetic and hydrodynamic equations journal of computational physics 209 2005 665 694 in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale the basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations are solved discontinuities or sharp gradients of the solution are responsible for locally strong departures to local equilibrium which require the resolution of the kinetic model the buffer zone is drawn around the kinetic region by introducing a cut off function which takes values between zero and one and which is identically zero in the fluid zone and one in the kinetic zone in the present paper we specifically consider the possibility of moving the kinetic region or creating new kinetic regions by evolving the cut off function with respect to time we present algorithms which perform this task by taking into account indicators which characterize the non equilibrium state of the gas the method is shown to be highly flexible as it relies on the time evolution of the buffer cut off function rather than on the geometric definition of a moving interface which requires remeshing by contrast to many previous methods numerical examples are presented which validate the method and demonstrate its performances

beltrami operators in the plane we determine optimal lp properties for the solutions of the general nonlinear elliptic system in the plane of the form fz h z fz h l c where h is a measurable function satisfying h z w1 h z w2 k w1 w2 and k is a constant k 1 we will also establish the precise invertibility and spectral properties in lp c for the operators i t i t and t where t is the beurling transform these operators are basic in the theory of quasiconformal mappings and in linear and nonlinear elliptic partial differential equations in two dimensions in particular we prove invertibility in lp c whenever 1 p 1 1 we also prove related results with applications to the regularity of weakly quasiconformal mappings

unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement this paper describes a unified flow solver ufs for rarefied and continuum gas flows the ufs separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models the direct numerical solution of the boltzmann transport equation is used in rarefied regions while kinetic schemes of continuum fluid dynamics are used elsewhere using similar computational techniques for the kinetic and continuum solvers and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the ufs solutions of test problems are presented to illustrate the capabilities of the ufs for high and low speed flows it is shown that the ufs can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

conditions of output stabilization for nonlinear models in the takagi sugeno s form this paper deals with the control law design with an observer for models in the takagi sugeno s ts form in the general case where the nonlinearities and the variables involved are not measurable the results presented in this paper give sufficient conditions of stabilization for the global loop i e ts model stabilized with a state feedback and a fuzzy observer conditions are given in the form of linear matrix inequalities lmi problem

locally refined discrete velocity grids for stationary rarefied flow simulations most of deterministic solvers for rarefied gas dynamics use discrete velocity or discrete ordinate approximations of the distribution function on a cartesian grid this grid must be sufficiently large and fine to describe the distribution functions at every space position in the computational domain for 3 dimensional hypersonic flows like in re entry problems this induces much too dense velocity grids that cannot be practically used for memory storage requirements in this article we present an approach to generate automatically a locally refined velocity grid adapted to a given simulation this grid contains much less points than a standard cartesian grid and allows us to make realistic 3 dimensional simulations at a reduced cost with a comparable accuracy

consensus of a class of second order multi agent systems with time delay and jointly connected topologies this technical note investigates consensus problems of a class of second order continuous time multi agent systems with time delay and jointly connected topologies we first introduce a neighbor based linear protocol with time delay then we derive a sufficient condition in terms of linear matrix inequalities lmis for average consensus of the system furthermore we discuss the case where the time delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time delay finally simulation results are provided to demonstrate the effectiveness of our theoretical results

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

analysis of pinning controlled networks a renormalization approach in this paper a renormalization approach is introduced for analyzing pinning controlled networks the renormalization process consists of two operations edge weighting and node reduction and is built on a new concept of passivity comparison in the sense of lyapunov v stability furthermore a cascaded model resulted from the renormalization process in a layer structure is presented for estimating the v stability of a network finally simulation studies are presented for illustration and verification of the theoretical results

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

adaptive neural control for a class of nonlinear systems with uncertain hysteresis inputs and time varying state delays in this paper adaptive variable structure neural control is investigated for a class of nonlinear systems under the effects of time varying state delays and uncertain hysteresis inputs the unknown time varying delay uncertainties are compensated for using appropriate lyapunov krasovskii functionals in the design and the effect of the uncertain hysteresis with the prandtl ishlinskii pi model representation is also mitigated using the proposed control by utilizing the integral type lyapunov function the closed loop control system is proved to be semi globally uniformly ultimately bounded sguub extensive simulation results demonstrate the effectiveness of the proposed approach

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

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

consensus problems in networks of agents with double integrator dynamics and time varying delays in this article we consider consensus problems in networks of agents with double integrator dynamics and non uniform time varying delays the agent dynamics is adopted as a typical point mass model based on newton s law without assuming that the weighting factors in the information update schemes are non negative we propose two protocols such that both the state and the velocity of agents achieve consensus an equivalent reduced order system is introduced to analyse the convergence of the protocols some necessary and or sufficient conditions for consensus are established in terms of linear matrix inequalities simulation results are provided that demonstrate the effectiveness of our theoretical results

robust consensus control for a class of multi agent systems via distributed pid algorithm and weighted edge dynamics abstract this paper studies the robust proportional integral derivative pid consensus control for a class of linear multi agent systems mass with external disturbances different from the existing results both the consensus analysis and the transient performance characteristics for high order linear mass are considered based on a factorization of laplacian matrix the initial mas is firstly transformed into the so called weighted edge dynamics and then a design equivalence between the proposed pid consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results furthermore by combining lyapunov theory and barbalat s lemma it is proved that both the stabilization of weighted edge dynamics and the consensus of mas can be guaranteed even in the presence of external disturbances in particular some relationships between the transient time performance of weighted edge dynamics and the pid design parameters are given finally some numerical examples on lc oscillator network are provided to illustrate the validity of theoretical results