optimal tracking control of nonlinear partially unknown constrained input systems using integral reinforcement learning in this paper a new formulation for the optimal tracking control problem otcp of continuous time nonlinear systems is presented this formulation extends the integral reinforcement learning irl technique a method for solving optimal regulation problems to learn the solution to the otcp unlike existing solutions to the otcp the proposed method does not need to have or to identify knowledge of the system drift dynamics and it also takes into account the input constraints a priori an augmented system composed of the error system dynamics and the command generator dynamics is used to introduce a new nonquadratic discounted performance function for the otcp this encodes the input constrains into the optimization problem a tracking hamilton jacobi bellman hjb equation associated with this nonquadratic performance function is derived which gives the optimal control solution an online irl algorithm is presented to learn the solution to the tracking hjb equation without knowing the system drift dynamics convergence to a near optimal control solution and stability of the whole system are shown under a persistence of excitation condition simulation examples are provided to show the effectiveness of the proposed method

a general mass conservative numerical solution for the unsaturated flow equation numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems numerical solution based on the standard h based form of richards equation generally yields poor results characterized by large mass balance errors and erroneous estimates of infiltration depth conversely numerical solutions based on the mixed form of richards equation can be shown to possess the conservative property so that mass is perfectly conserved this leads to significant improvement in numerical solution performance while requiring no additional computational effort however use of the mass conservative method does not guarantee good solutions accurate solution of the unsaturated flow equation also requires use of a diagonal time or mass matrix only when diagonal time matrices are used can the solution be shown to obey a maximum principle which guarantees smooth nonoscillatory infiltration profiles this highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

a linear domain decomposition method for partially saturated flow in porous media abstract the richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated unsaturated flow in porous media we assume that the medium occupies a bounded lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface this leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at after an euler implicit discretisation of the resulting nonlinear subproblems a linear iterative l type domain decomposition scheme is proposed the convergence of the scheme is proved rigorously in the last part we present numerical results that are in line with the theoretical finding in particular the convergence of the scheme under mild restrictions on the time step size we further compare the scheme to other approaches not making use of a domain decomposition namely we compare to a newton and a picard scheme we show that the proposed scheme is more stable than the newton scheme while remaining comparable in computational time even if no parallelisation is being adopted after presenting a parametric study that can be used to optimise the proposed scheme we briefly discuss the effect of parallelisation and give an example of a four domain implementation

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

synchronization via pinning control on general complex networks this paper studies synchronization via pinning control on general complex dynamical networks such as strongly connected networks networks with a directed spanning tree weakly connected networks and directed forests a criterion for ensuring network synchronization on strongly connected networks is given it is found that the vertices with very small in degrees should be pinned first in addition it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers which implies that the vertices with very large out degrees may be pinned then a criterion for achieving synchronization on networks with a directed spanning tree which can be composed of many strongly connected components is derived it is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls

distributed tracking control for linear multiagent systems with a leader of bounded unknown input this technical note considers the distributed tracking control problem of multiagent systems with general linear dynamics and a leader whose control input is nonzero and not available to any follower based on the relative states of neighboring agents two distributed discontinuous controllers with respectively static and adaptive coupling gains are designed for each follower to ensure that the states of the followers converge to the state of the leader if the interaction graph among the followers is undirected the leader has directed paths to all followers and the leader s control input is bounded a sufficient condition for the existence of the distributed controllers is that each agent is stabilizable simulation examples are given to illustrate the theoretical results

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

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

noniterative time stepping schemes with adaptive truncation error control for the solution of richards equation 1 noniterative implicit time stepping schemes with adaptive temporal truncation error control are developed for the solution of the pressure form of richards equation first and second order linearizations of an adaptive backward euler thomas gladwell formulation are introduced and are shown to constrain the temporal truncation errors near a user prescribed tolerance and maintain adequate mass balance numerical experiments demonstrate that accurate noniterative linearizations achieve cost effective solutions of problems where soils are described by highly nonlinear and nonsmooth constitutive functions for these problems many conventional iterative solvers fail to converge the noniterative formulations are considerably more efficient than analogous time stepping schemes with iterative solvers the second order noniterative scheme is found to be more efficient than the first order noniterative scheme the proposed adaptive noniterative algorithms can be easily incorporated into existing backward euler software which is widely used for richards equation and other nonlinear pdes

a triangle based mixed finite element finite volume technique for modeling two phase flow through porous media triangle based discretization techniques offer great advantages relative to standard finite difference methods for the modeling of flow through geometrically complex geological features the purpose of this paper is to develop and apply a triangle based method for the modeling of two phase flow through porous formations the formulation includes the effects of gravity compressibility and capillary pressure the technique entails a triangle based mixed finite element method for solution of the variable coefficient parabolic pressure equation and a second order tvd type total variation diminishing finite volume scheme for solution of the essentially hyperbolic saturation equation the method is applied to a variety of example problems and is shown to perform very well on problems involving geometric complexity coupled with heterogeneous generally anisotropic permeability descriptions

adaptive backward euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow an automatic time stepping scheme with embedded error control is developed and applied to the moisture based richards equation the algorithm is based on the first order backward euler scheme and uses a numerical estimate of the local truncation error and an efficient time step selector to control the temporal accuracy of the integration local extrapolation equivalent to the use of an unconditionally stable thomas gladwell algorithm achieves second order temporal accuracy at minimal additional costs the time stepping algorithm also provides accurate initial estimates for the iterative non linear solver numerical tests confirm the ability of the scheme to automatically optimize the time step size to match a user prescribed temporal error tolerance an important merit of the proposed method is its conceptual and computational simplicity it can be directly incorporated into existing or new software based on the backward euler scheme currently prevalent in subsurface hydrologic modelling and markedly improves their performance compared with simple fixed or heuristic time step selection the generality of the approach also makes possible its use for solving pdes in other engineering applications where strong non linearity stability or implementation considerations favour a simple and robust low order method or where there is a legacy of backward euler codes in current use copyright 2001 john wiley sons ltd

consensus tracking of linear multi agent systems under networked observability conditions this paper addresses the consensus tracking problem for both continuous and discrete time linear multi agent systems with a dynamic leader under networked observability conditions among followers the communication topology is assumed to be undirected and connected two networked observability conditions are introduced and discussed the first one extends the traditional detectability condition for a single system while the second one is a full rank condition which is stronger than the first one in the continuous time case two distributed observer based protocols are designed under corresponding networked observability conditions respectively specifically the second protocol is an adaptive one which has a better robustness performance than the first one in the discrete time case a distributed observer based protocol is presented under the full rank networked observability condition it is found that under the networked observability conditions consensus tracking can still be achieved even if

distributed consensus for sampled data control multi agent systems with missing control inputs abstract this paper is concerned about the distributed consensus problem for general sampled data control multi agent systems without or with a leader under control inputs missing over some sampling intervals for these two cases a distributed adaptive dynamical consensus algorithm is proposed based only on the relative information of network structure under the assumption that the dynamical network contains a directed spanning tree some sufficient consensus conditions are induced under a switched model these obtained consensus criteria are independent of dynamical network topology namely they are valid for both undirected and directed topology besides they do not rely on the spectra and the eigenvalue of laplacian matrix furthermore some quantitative relations included in dynamical systems such as sampling period admissible control inputs missing rate and exponential reaching rate of the consensus performance are established finally simulation examples are given to show the effectiveness of the proposed results

persistency of excitation results for structured nonminimal models it is frequently convenient to use specially structured nonminimal models for parameter estimation such as in the case of direct adaptive control where the model is parameterized in terms of the desired control law parameters this is done for example in direct model reference adaptive control and in direct pole assignment adaptive control algorithms it is shown that the parameters appearing in these nonminimal models can be uniquely estimated if and only if a certain design identity has a unique solution the result is used to develop persistency of excitation results for these models

parameter convergence and uniqueness in nonminimal parameterizations for multivariable adaptive control the issue of parameter convergence in multivariable adaptive control is addressed in a general framework parameter convergence is guaranteed if a certain design identity has a unique solution and if the inputs satisfy persistency of excitation conditions the uniqueness of the solution of the design identity can be obtained in general by using parameterizations that although nonminimal are structured so as to guarantee uniqueness this concept is illustrated with a direct adaptive pole placement algorithm which is modified to guarantee uniqueness and it is shown how the results can be used to establish stability and convergence properties of the algorithm

finite element approximation of the diffusion operator on tetrahedra linear galerkin finite element discretizations of the laplace operator produce nonpositive stiffness coefficients for internal element edges of two dimensional delaunay triangulations this property also called the positive transmissibility pt condition is a prerequisite for the existence of an m matrix and ensures that nonphysical local extrema are not present in the solution for tetrahedral elements it has already been shown that the linear galerkin approach does not in general satisfy the pt condition we propose a modification of the three dimensional galerkin scheme that if a delaunay triangulation is used satisfies the pt condition for internal edges and if further conditions on the boundary are specified yields an m matrix the proposed approach can also be extended to the general diffusion operator with nonconstant or anisotropic coefficients

frequency domain conditions for parameter convergence in multivariable recursive identification abstract a multivariable adaptive identifier is designed on the basis of a canonical form leading to a unique set of parameters to identify frequency domain conditions for parameter convergence are derived the sufficient condition to guarantee convergence in all cases is that n v distinct frequency components be present in each input of the plant where v is the maximum of the observability indices and n the order of the plant on the other hand the necessary condition requires n mv distinct frequency components distributed over the inputs where m is the number of inputs and at least v frequency components are in each separate input through examples it is shown that convergence may or may not occur for intermediate numbers of frequency components depending on their location and on the plant parameters

analysis of a linearization scheme for an interior penalty discontinuous galerkin method for two phase flow in porous media with dynamic capillarity effects shellnwo fom cser project 14cser016 nwo visitors grant 040 11 499 researchfoundation flanders fwo odysseus project g0g1316n statoil akademia grant

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

on minimum spanning blocks in discrete linear systems the question of spanning blocks in linear discrete systems arises in many adaptive identification and control problems and is related to the convergence of these algorithms specifically in block invariant adaptive control it is of importance to know the minimum length of these spanning blocks establishing this minimum length is the topic of the present note it is found to be equal to the sum of the dimensions of the system s state space and its controllable subspace

techniques for making finite elements competitve in modeling flow in variably saturated porous media a galerkin finite element formulation is developed for the numerical simulation of water flow in variably saturated soil systems included in this formulation is a solution strategy based on picard and newton raphson algorithms both algorithms are designed especially to cope with severely nonlinear field problems the two algorithms are formulated for both rectangular and triangular elements the element matrices are evaluated in a simple and efficient manner using a technique referred to as the influence coefficient technique this technique avoids numerical integration and leads to a substantial saving of computational cost four examples are presented to demonstrate the effectiveness of the present finite element approach these examples show that the nonlinear solution schemes are capable of accomodating cases involving large variations in the saturated hydraulic conductivity as well as highly nonlinear soil moisture characteristics a comparative study of the picard and the newton raphson algorithms is also provided the study indicates that despite the higher cost per iteration of the newton raphson scheme it usually requires a substantially smaller number of iterations than the picard scheme in some instances where convergence difficulties are experienced with the latter scheme it is desirable to use the newton raphson scheme in order to obtain a cost effective solution to the problem

continuous groundwater velocity fields and path lines in linear bilinear and trilinear finite elements darcy velocity fields obtained from finite element solutions of heads in groundwater flow exhibit discontinuities at element boundaries thus giving rise to inaccuracies in path line construction several methods have been developed to resolve those inaccuracies including global postprocessing of velocity fields mixed hybrid finite element formulations and stream function formulations all of these techniques either lead to a considerable increase in the computational effort or are not general enough for all purposes the point of view taken here is that standard finite element flow models yield exact water balances which in the usual approach to path line computation are not fully used by starting out from patches with flux conserving boundaries a new postprocessing procedure is derived that allows construction of a continuous flux distribution over the whole model domain in this procedure only the head gradients of adjacent elements are used thus avoiding the solution of another global system of equations furthermore application of a stream function interpolation inside each patch allows the fast computation of path lines without any time stepping the path lines computed with the proposed procedure are compared to path lines computed by usual particle tracking and examples are presented showing that the new method is vastly superior to traditional particle tracking

a modified l scheme to solve nonlinear diffusion problems abstract in this work we propose a linearization technique for solving nonlinear elliptic partial differential equations that are obtained from the time discretization of a wide variety of nonlinear parabolic problems the scheme is inspired by the l scheme which gives unconditional convergence of the linear iterations here we take advantage of the fact that at a particular time step the initial guess for the iterations can be taken as the solution of the previous time step first it is shown for quasilinear equations that have linear diffusivity that the scheme always converges irrespective of the time step size the spatial discretization and the degeneracy of the associated functions moreover it is shown that the convergence is linear with convergence rate proportional to the time step size next for the general case it is shown that the scheme converges linearly if the time step size is smaller than a certain threshold which does not depend on the mesh size and the convergence rate is proportional to the square root of the time step size finally numerical results are presented that show that the scheme is at least as fast as the modified picard scheme faster than the l scheme and is more stable than the newton or the picard scheme

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

a robust linearization scheme for finite volume based discretizations for simulation of two phase flow in porous media in this work we consider a mathematical model for two phase flow in porous media the fluids are assumed immiscible and incompressible and the solid matrix non deformable the mathematical model for the two phase flow is written in terms of the global pressure and a complementary pressure obtained by using the kirchhoff transformation as primary unknowns for the spatial discretization finite volumes have been used more precisely the multi point flux approximation method and in time the backward euler method has been employed we present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization we show that the scheme is linearly convergent numerical experiments are presented that sustain the theoretical results

a globally convergent adaptive pole placement algorithm without a persistency of excitation requirement this paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase global convergence is established for the scheme in the sense that the closed loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time a key feature of the scheme is that no persistency of excitation condition is required the algorithm uses recursive least squares with variable forgetting factor normalized regression vectors and a matrix gain with constant trace

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

consensus tracking for higher order multi agent systems with switching directed topologies and occasionally missing control inputs abstract this paper studies the distributed consensus tracking problem of linear higher order multi agent systems with switching directed topologies and occasionally missing control inputs in this framework the underlying topology of dynamic agents may switch among several directed graphs each having a directed spanning tree rooted at the leader furthermore the control inputs to the followers may be temporally missed due to actuator failures and network induced packet loss to guarantee asymptotic consensus tracking in such a multi agent system several distributed controllers are constructed based only on the relative state information of neighboring agents by appropriately constructing a switching lyapunov function and using tools from the m matrix theory some sufficient conditions for achieving distributed consensus tracking are provided finally some numerical simulations are given to illustrate the theoretical analysis

stabilization of sampled data control systems with control inputs missing this note is concerned with the stabilization problem for sampled data control systems with control inputs missing a sufficient condition is derived for the existence of exponentially stabilizing state feedback controllers via the switched system approach the obtained condition establishes several quantitative relations among some system parameters such as the sampling period and the exponential decay rate the actual data missing rate and the admissible data missing rate bound two illustrative examples are given to show the effectiveness of the proposed results

auxiliary space preconditioning for mixed finite element discretizations of richards equation abstract we propose an auxiliary space method for the solution of the indefinite problem arising from mixed method finite element discretizations of scalar elliptic problems the proposed technique uses conforming elements as an auxiliary space and utilizes special interpolation operators for the transfer of residuals and corrections between the spaces we show that the corresponding method provides optimal solver for the indefinite problem by only solving symmetric and positive definite auxiliary problems we apply this preconditioner to the mixed form discretization of richards equation linearized with the l scheme we provide numerical tests validating the theoretical estimates

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

mixed finite elements and newton type linearizations for the solution of richards equation we present the development of a two dimensional mixed hybrid finite element mhfe model for the solution of the non linear equation of variably saturated flow in groundwater on unstructured triangular meshes by this approach the darcy velocity is approximated using lowest order raviart thomas rt0 elements and is exactly mass conserving hybridization is used to overcome the ill conditioning of the mixed system the scheme is globally first order in space nevertheless numerical results employing non uniform meshes show second order accuracy of the pressure head and normal fluxes on specific grid points the non linear systems of algebraic equations resulting from the mhfe discretization are solved using picard or newton iterations realistic sample tests show that the mhfe newton approach achieves fast convergence in many situations in particular when a good initial guess is provided by either the picard scheme or relaxation techniques copyright 1999 john wiley sons ltd

nonlinear second order multi agent systems subject to antagonistic interactions without velocity constraints abstract this paper studies the nonlinear second order multi agent systems without velocity information while subject to antagonistic interactions among the reciprocal agents when being free of nonlinear disturbances a necessary and sufficient condition for the consensus resp stability problem is presented which essentially shows that the coupling weights and topology structure suffice to assure the consensus resp stability of the agents whereas nonzero eigenvalues of the laplacian matrix also act a crucial role provided that merely the absolute information of the auxiliary variable is demanded the derived results implicitly manifest that structurally balanced graph resp isolated structurally balanced graph or containing the in isolated structurally balanced subgraph is merely the necessary condition for the consensus resp stability of the agents within the second order dynamical setting in the presence of nonlinear dynamics we explicitly extend the derived results with the help of the lyapunov based technique under quite mild assumptions furthermore some comparisons are presented in contrast to some of the existing literature finally numerical examples are given to validate the efficiency of the obtained results

high order godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media two dimensional godunov mixed methods have been shown to be effective for the numerical solution of density dependent flow and transport problems in groundwater even when concentration gradients are high and the process is dominated by density effects this class of discretization approaches solves the flow equation by means of the mixed finite element method thus guaranteeing mass conserving velocity fields and discretizes the transport equation by mixed finite element and finite volumes techniques combined together via appropriate time splitting in this paper we extend this approach to three dimensions employing tetrahedral meshes and introduce a spatially variable time stepping procedure that improves computational efficiency while preserving accuracy by adapting the time step size according to the local courant friedrichs lewy cfl constraint careful attention is devoted to the choice of a truly three dimensional limiter for the advection equation in the time splitting technique so that to preserve second order accuracy in space in the sense that linear functions are exactly interpolated the three dimensional elder problem and the saltpool problem recently introduced as a new benchmark for testing three dimensional density models provide assessments with respect to accuracy and reliability of this numerical approach

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

locally conservative stabilized finite element methods for variably saturated flow standard galerkin finite element methods for variably saturated groundwater flow have several deficiencies for instance local oscillations can appear around sharp infiltration fronts without the use of mass lumping and velocity fields obtained from differentiation of pressure fields are discontinuous at element boundaries here we consider conforming finite element discretizations based on a multiscale formulation along with recently developed local postprocessing schemes the resulting approach maintains the basic flexibility and appeal of traditional finite element methods while controlling nonphysical oscillations and producing element wise mass conservative velocity fields accuracy and efficiency of the proposed schemes are evaluated through a series of steady state and transient variably saturated groundwater flow problems in homogeneous as well as heterogeneous domains the schemes are formulated for a generic nonlinear advection diffusion equation and are thus applicable to many other flow models

an analysis of monotonicity conditions in the mixed hybrid finite element method on unstructured triangulations in this paper we consider the mixed hybrid finite element method on unstructured triangular grids and evaluate its monotonicity properties by using a non standard set of basis functions for the velocity approximation space the mixed hybrid discretization of the steady state diffusion equation produces a system matrix that depends only on the inner product of the outward normals to the edges of the triangulation and not on the choice of the velocity space basis this property is used to study the characteristics of the system matrix it is well known that this matrix is of type m if the angles of the triangulation are not bigger than 2 an m matrix has a nonnegative inverse i e all the elements are nonnegative this implies the existence of a discrete maximum principle and thus monotonicity of the discretization we show that when the triangulation is of delaunay type and satisfies the property that no circumcenters of boundary elements with dirichlet conditions lie outside the domain the inverse of the final matrix is always positive even in the presence of obtuse angles

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

a comparison of picard and newton iteration in the numerical solution of multidimensional variably saturated flow problems picard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media the method is simple to code and computationally cheap but has been known to fail or converge slowly the newton method is more complex and expensive on a per iteration basis than picard and as such has not received very much attention its robustness and higher rate of convergence however make it an attractive alternative to the picard method particularly for strongly nonlinear problems in this paper the picard and newton schemes are implemented and compared in one two and three dimensional finite element simulations involving both steady state and transient flow the eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency including problem size spatial and temporal discretization initial solution estimates convergence error norm mass lumping time weighting conductivity and moisture content characteristics boundary conditions seepage faces and the extent of fully saturated zones in the soil previous strategies for enhancing the performance of the picard and newton schemes are revisited and new ones are suggested the strategies include chord slope approximations for the derivatives of the characteristic equations relaxing convergence requirements along seepage faces dynamic time step control nonlinear relaxation and a mixed picard newton approach the tests show that the picard or relaxed picard schemes are often adequate for solving richards equation but that in cases where these fail to converge or converge slowly the newton method should be used the mixed picard newton approach can effectively overcome the newton scheme s sensitivity to initial solution estimates while comparatively poor performance is reported for the various chord slope approximations finally given the reliability and efficiency of current conjugate gradient like methods for solving linear nonsymmetric systems the only real drawback of using newton rather than picard iteration is the algebraic complexity and computational cost of assembling the derivative terms of the jacobian matrix and it is suggested that both methods can be effectively implemented and used in numerical models of richards equation

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

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

some new procedures for numerical solution of variably saturated flow problems persistent difficulties that arise in forming numerical solutions of variably saturated flow problems include controlling the stability of the nonlinear equation solvers and devising a reliable yet efficient method for determining the positions of seepage surfaces new techniques for addressing these problems are applied to a subdomain finite element discretization of the governing flow equations a series of test problems demonstrates that the techniques are reliable and efficient for a wide variety of problems

convergence of adaptive control schemes using least squares parameter estimates the stability convergence asymptotic optimality and self tuning properties of stochastic adaptive control schemes based on least squares estimates of the unknown parameters are examined it is assumed that the additive noise is i i d and gaussian and that the true system is of minimum phase the bayesian embedding technique is used to show that the recursive least squares parameter estimates converge in general the normal equations of least squares are used to establish that all stable control law designs used in a certainty equivalent i e indirect procedure generally yield a stable adaptive control system four results are given to characterize the limiting behavior precisely a certainty equivalent self tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one even without any excitation in the reference trajectory

superconvergence and postprocessing of fluxes from lowest order mixed methods on triangles and tetrahedra certain finite difference methods on rectangular grids for second order elliptic equations are known to yield superconvergent flux approximations a class of related finite difference methods recently have been defined for triangular meshes by applying special quadrature rules to an extended version of a mixed finite element method by arbogast dawson and keenan mixed finite element methods as finite difference methods for solving elliptic equations on triangular elements tech report 93 53 dept of computational and applied mathematics rice university houston tx 1993 in computational methods in water resources kluwer academic publishers norwell ma 1994 the usual hybrid mixed method can also be applied to meshes of triangular and tetrahedral elements unfortunately the flux vectors from these methods are only first order accurate empirical evidence indicates that a local postprocessing technique described by keenan in an efficient postprocessor for velocities from mixed methods on triangular elements dept of computational and applied mathematics tech report 94 22 rice university houston tx 1994 recovers second order accurate velocities at special points in this paper a class of local postprocessing techniques generalizing the one in an efficient postprocessor for velocities from mixed methods on triangular elements tech report 94 22 rice university houston tx 1994 are presented and analyzed these postprocessors are shown to recover second order accurate velocity fields on three lines meshes numerical experiments illustrate these results and investigate more general situations including meshes of tetrahedral elements

computational experience with sequential and parallel preconditioned jacobi davidson for large sparse symmetric matrices the jacobi davidson jd algorithm was recently proposed for evaluating a number of the eigenvalues of a matrix jd goes beyond pure krylov space techniques it cleverly expands its search space by solving the so called correction equation thus in principle providing a more powerful method preconditioning the jacobi davidson correction equation is mandatory when large sparse matrices are analyzed we considered several preconditioners classical block jacobi and ic 0 together with approximate inverse ainv or fsai preconditioners the rationale for using approximate inverse preconditioners is their high parallelization potential combined with their efficiency in accelerating the iterative solution of the correction equation analysis was carried on the sequential performance of preconditioned jd for the spectral decomposition of large sparse matrices which originate in the numerical integration of partial differential equations arising in physical and engineering problems it was found that jd is highly sensitive to preconditioning and it can display an irregular convergence behavior we parallelized jd by data splitting techniques combining them with techniques to reduce the amount of communication data our own parallel preconditioned code was executed on a dedicated parallel machine and we present the results of our experiments our jd code provides an appreciable parallel degree of computation its performance was also compared with those of parpack and parallel dacg

necessary and sufficient conditions for parameter convergence in adaptive control a complete description of parameter convergence in model reference adaptive control may be given in terms of the spectrum of the exogenous reference input signal abstract using generalized harmonic analysis a complete description of parameter convergence in model reference adaptive control mrac is given in terms of the spectrum of the exogenous reference input signal roughly speaking if the reference signal contains enough frequencies then the parameter vector converges to its correct value if not it converges to an easily characterizable subspace in parameter space

the mast edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media a novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium the computational domain is descretized using triangular meshes and the governing pdes are discretized using a lumped in the edge centres numerical technique the dependent unknown variable of the problem is the piezometric head a fractional time step methodology is applied for the solution of the original system solving consecutively a prediction and a correction problem a scalar potential of the flow field exists and in the prediction step a marching in space and time mast formulation is applied for the sequential solution of the ordinary differential equation of the cells ordered according to their potential value computed at the beginning of the time step in the correction step the solution of a large linear system with order equal to the number of edges is required a semi analytical procedure is also proposed for the solution of the prediction step the computational performance the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models

implementation of an exact finite reduction scheme for steady state reaction diffusion equations in this paper we propose the numerical solution of a steady state reaction diffusion problem by means of application of a non local lyapunov schmidt type reduction originally devised for field theory a numerical algorithm is developed on the basis of the discretization of the differential operator by means of simple finite differences the eigendecomposition of the resulting matrix is used to implement a discrete version of the reduction process by the new algorithm the problem is decomposed into two coupled subproblems of different dimensions a large subproblem is solved by means of a fixed point iteration completely controlled by the features of the original equation and a second problem with dimensions that can be made much smaller than the former which inherits most of the non linear difficulties of the original system the advantage of this approach is that sophisticated linearization strategies can be used to solve this small non linear system at the expense of a partial eigendecomposition of the discretized linear differential operator the proposed scheme is used for the solution of a simple non linear one dimensional problem the applicability of the procedure is tested and experimental convergence estimates are consolidated numerical results are used to show the performance of the new algorithm copyright 2006 john wiley sons ltd

brief paper novel decentralized adaptive strategies for the synchronization of complex networks this paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach in particular time varying feedback coupling gains are considered whose gradient is a function of the local synchronization error over each edge in the network it is shown that under appropriate conditions the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network the theoretical derivation is complemented by its validation on a set of representative examples

remarks on the adaptive control of linear plants with unknown high frequency gain abstract adaptive control of first order linear systems of the form x ax bu with the sign of b unknown is considered it is shown that stabilizing adaptive controllers exist that have globally bounded gain and prespecified terminal dynamics