on reliable stabilization via rectangular dilated lmis and dissipativity based certifications in this short note we consider the problem of reliable stabilization for multi channel systems where our main objective is to maintain the robust stability of the perturbed closed loop system when there is a single controller failure in any of the control channels specifically we present a less conservative result than results in the literature in terms of a set of dilated lmis for the reliable state feedback stabilization of the nominal system while a dissipativity based certification is used to extend the stability condition when there is an additive model perturbation in the system finally a numerical example is presented to illustrate the applicability of the proposed technique

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

reliable h_ infty control of linear systems with adaptive mechanism this technical note studies the problem of designing reliable h controllers with adaptive mechanism for linear systems a new method for designing indirect adaptive reliable controller via state feedback is presented for actuator fault compensations based on the on line estimation of eventual faults the proposed reliable controller parameters are updated automatically to compensate the fault effects on systems a notion of adaptive h performance index is proposed to describe the disturbance attenuation performances of closed loop systems the design conditions are given in terms of solutions to a set of linear matrix inequalities lmis the resultant designs can guarantee the asymptotic stability and adaptive h performances of closed loop systems even in the cases of actuator failures the effectiveness of the proposed design method is illustrated via a numerical example

a mortar spectral finite element method for complex 2d and 3d elastodynamic problems abstract we present a hybrid spectral element finite element domain decomposition method for solving elastic wave propagation problems aim of the method is to exploit both the enhanced accuracy of spectral elements allowing significant reductions of the computational load and the flexibility of finite elements in treating irregular geometries and non linear media interfaces between finite and spectral elements are managed by the mortar method which enjoys optimal accuracy and allows to discretize the different regions independently several test cases illustrate the robustness of this method and its tolerance to a significant range of geometrical models characterized by different grid refinements

isogeometric numerical dispersion analysis for two dimensional elastic wave propagation abstract in this paper we carry out a numerical dispersion analysis for the linear two dimensional elastodynamics equations approximated by means of nurbs based isogeometric analysis in the framework of the galerkin method specifically we consider the analysis of harmonic plane waves in an isotropic and homogeneous elastic medium we compare and discuss the errors associated with the compressional and shear wave velocities and we provide the anisotropic curves for numerical approximations obtained by considering b spline and nurbs basis functions of different regularity namely globally c 0 and c p 1 continuous p being the polynomial degree we conclude our analysis by numerically simulating the seismic wave propagation in a sinusoidal shaped valley with discontinuous elastic parameters across an internal interface

approximation of acoustic waves by explicit newmark s schemes and spectral element methods a numerical approximation of the acoustic wave equation is presented the spatial discretization is based on conforming spectral elements whereas we use finite difference newmark s explicit integration schemes for the temporal discretization a rigorous stability analysis is developed for the discretized problem providing an upper bound for the time step dt we present several numerical results concerning stability and convergence properties of the proposed numerical methods

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

dynamic journeying under uncertainty abstract we introduce a journey planning problem in multi modal transportation networks under uncertainty the goal is to find a journey possibly involving transfers between different transport services from a given origin to a given destination within a specified time horizon due to uncertainty in travel times the arrival times of transport services at public transport stops are modeled as random variables if a transfer between two services is rendered unsuccessful the commuter has to reconsider the remaining path to the destination the problem is modeled as a markov decision process in which states are defined as paths in the transport network the main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time by assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination the proposed approximations may be useful for practical purposes due to their computational simplicity in addition to on time arrival probability we show how travel and overdue costs can be taken into account making the model applicable to freight transportation problems

note an improved conditional monte carlo technique for the stochastic shortest path problem this paper describes a simulation procedure for estimating the distribution function of the shortest path length in a network with random arc lengths the method extends the concept of conditional monte carlo utilizing special properties of the uniformly directed cutsets and the unique arcs the objective here is to reduce the sampling effort and utilize known probability information to derive multivariate integrals of lower dimension the experimental results show that the proposed method is substantially cost effective and performs better than traditional monte carlo and conditional methods

brief paper reliable stabilization with integral action in decentralized control systems reliable stabilization with integral action is studied in a linear time invariant multi input multi output two channel decentralized control system where the plant is stable the objective is to achieve closed loop stability when both controllers act together and when each controller acts alone necessary and sufficient conditions are obtained for existence of block diagonal decentralized controllers that ensure reliable stabilization and integral action and all such decentralized controllers are parametrized explicit controller design approaches are discussed for the case of square channels

reliable control of nonlinear systems via variable structure scheme this study proposes a class of variable structure stabilizing laws which make the closed loop system be capable of tolerating the abnormal operation of actuators within a pre specified subset of actuators the ranges of acceptable change in control gain magnitude that preserves system s stability are estimated for the whole set of actuators these ranges are shown to be able to be made larger than those obtained by linear quadratic regulator lqr reliable design veillette 1995 and liang 2000 by the choice of control parameters besides this approach does not need the solution of hamilton jacobi hj equation or inequality which is essential for optimal approaches such as lqr and h infin reliable designs as a matter of fact this approach can also relax the computational burden for solving the hj equation or inequality

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

stochastic shortest path problems with piecewise linear concave utility functions this paper considers a stochastic shortest path problem where the arc lengths are independent random variables following a normal distribution in this problem the optimal path is one that maximizes the expected utility with the utility function being piecewise linear and concave such a utility function can be used to approximate nonlinear utility functions that capture risk averse behaviour for a wide class of problems the principal contribution of this paper is the development of exact algorithms to solve large problem instances two algorithms are developed and incorporated in labelling procedures computational testing is done to evaluate the performance of the algorithms overall both algorithms are very effective in solving large problems quickly the relative performance of the two algorithms is found to depend on the curvature of the piecewise linear utility function

non conforming high order approximations of the elastodynamics equation in this paper we formulate and analyze two non conforming high order strategies for the approximation of elastic wave problems in heterogeneous media namely the mortar spectral element method and the discontinuous galerkin spectral element method starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy convergence grid dispersion and stability

technical note a note on the stochastic shortest route problem an optimality index for choosing the shortest route in an acyclic stochastic network has recently been proposed the present note identifies certain anomalies in using that index and proposes another optimality index the results of using these indices are compared in a simple example

arc reduction and path preference in stochastic acyclic networks the paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network the focus is on shortest route problems where a general nonlinear utility function is used to measure outcomes for such problems enumerating all feasible paths is the only way to guarantee that the global optimum has been found alternatively we develop a reduction algorithm based on stochastic dominance to speed up the computations monte carlo simulation is used to evaluate the approach in all 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed the results indicate that the heuristic produces significant computational saving as the size of the network grows and that the quality of the reduced network solutions are better than those obtained from the original formulation

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

a theoretical analysis of a new second order finite volume approximation based on a low order scheme using general admissible spatial meshes for the one dimensional wave equation abstract this paper details our note 6 and it is an extension of our previous works 4 5 which dealt with first order both in time and space and second order time accurate second order in time and first order in space implicit finite volume schemes for second order hyperbolic equations with dirichlet boundary conditions on general nonconforming multidimensional spatial meshes introduced recently in 14 we aim in this work and some forthcoming studies to get higher order both in time and space finite volume approximations for the exact solution of hyperbolic equations using the class of spatial generic meshes introduced recently in 14 on low order schemes from which the matrices used to compute the discrete solutions are sparse we focus in the present contribution on the one dimensional wave equation and on one of its implicit finite volume schemes described in 4 the implicit finite volume scheme approximating the one dimensional wave equation we consider hereafter referred to as the basic finite volume scheme yields linear systems to be solved successively the matrices involved in these linear systems are tridiagonal symmetric and definite positive the finite volume approximate solution of the basic finite volume scheme is of order h k where h resp k is the mesh size of the spatial resp time discretization we construct a new finite volume approximation of order h k 2 in several discrete norms which allow us to get approximations of order two for the exact solution and its first derivatives this new high order approximation can be computed using linear systems whose matrices are the same ones used to compute the discrete solution of the basic finite volume scheme while the right hand sides are corrected the construction of these right hand sides includes the approximation of some high order spatial derivatives of the exact solution the computation of the approximation of these high order spatial derivatives can be performed using the same matrices stated above with another two tridiagonal matrices the manner by which this new high order approximation is constructed can be repeated to compute successively finite volume approximations of arbitrary order using the same matrices stated above these high order approximations can be obtained on any one dimensional admissible finite volume mesh in the sense of 13 without any condition to reach the above results a theoretical framework is developed and some numerical examples supporting the theory are presented some of the tools of this framework are new and interesting and they are stated in the one space dimension but they can be extended to several space dimensions in particular a new and useful a prior estimate for a suitable discrete problem is developed and proved the proof of this a prior estimate result is based essentially on the decomposition of the solution of the discrete problem into the solutions of two suitable discrete problems a new technique is used in order to get a convenient finite volume approximation whose discrete time derivatives of order up to order two are also converging towards the solution of the wave equation and their corresponding time derivatives

dft modal analysis of spectral element methods for the 2d elastic wave equation the dft modal analysis is a dispersion analysis technique that transforms the equations of a numerical scheme to the discrete fourier transform domain sampled in the mesh nodes this technique provides a natural matching of exact and approximate modes of propagation we extend this technique to spectral element methods for the 2d isotropic elastic wave equation by using a rayleigh quotient approximation of the eigenvalue problem that characterizes the dispersion relation taking full advantage of the tensor product representation of the spectral element matrices numerical experiments illustrate the dependence of dispersion errors on the grid resolution polynomial degree and discretization in time we consider spectral element methods with chebyshev and legendre collocation points

dispersive and dissipative behavior of the spectral element method if the nodes for the spectral element method are chosen to be the gauss legendre lobatto points and a lagrange basis is used then the resulting mass matrix is diagonal and the method is sometimes then described as the gauss point mass lumped finite element scheme we study the dispersive behavior of the scheme in detail and provide both a qualitative description of the nature of the dispersive and dissipative behavior of the scheme along with precise quantitative statements of the accuracy in terms of the mesh size and the order of the scheme we prove that a the gauss point mass lumped scheme i e spectral element method tends to exhibit phase lag whereas the consistent finite element scheme tends to exhibit phase lead b the absolute accuracy of the spectral element scheme is 1 p times better than that of the finite element scheme despite the use of numerical integration c when the order p the mesh size h and the frequency of the wave omega satisfy 2p 1 approx omega h the true wave is essentially fully resolved as a consequence one obtains a proof of the general rule of thumb sometimes quoted in the context of spectral element methods pi modes per wavelength are needed to resolve a wave

risk taking in stochastic pert networks abstract this paper studies a pert problem which incorporates project managers risk taking behavior in stochastic environments in this stochastic pert network which we refer to as riskpert activity durations are nonnegative random variables and a project manager uses a disutility function to evaluate each path and chooses that path which maximizes his expected disutility as an optimal or critical path this path as opposed to the classical critical path is used as a basis to analyze the pert network and to estimate the probability of completion time the general riskpert is difficult to solve however special cases when activity durations are statistically independent and disutility functions are linear exponential quadratic or linear exponential are solvable exactly the illustrative examples demonstrate that riskpert captures managers risk taking behavior and provides results that are more realistic than those of the classical pert models furthermore this paper extends some of the riskpert models to include multi dimensional pert networks

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

a homotopy approach for stabilizing single input systems with control structure constraints a linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized some examples of feedback realizations which impose constraints on the gain vector are static output feedback constant gain feedback for several operating points of a system and two controller feedback we consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them each of these problems is cast into a problem of solving a system of equalities and inequalities in this formulation the coefficients of the quadratic and linear factors of the closed loop characteristic polynomial are the variables to solve the system of equalities and inequalities a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework our method is illustrated with an example for each class of control structure constraint

stochastic stability analysis for continuous time fault tolerant control systems active fault tolerant control systems are feedback control systems that reconfigure the control law in real time based on the response from an automatic failure detection and identification fdi scheme the dynamic behaviour of such systems is characterized by stochastic differential equations because of the random nature of the failure events and the fdi decisions the stability analysis of these systems is addressed in this paper using stochastic lyapunov functions and supermartingale theorems both exponential stability in the mean square and almost sure asymptotic stability in probability are addressed in particular for linear systems where the coefficients of the closed loop system dynamics are functions of two random processes with markovian transition characteristics one representing the random failures and the other representing the fdi decision behaviour necessary and sufficient conditions for exponential stability in the mean square are developed

bounding the project completion time distribution in pert networks we consider the pert model of a project composed of activities whose durations are random variables with known distributions for the situations in which the activity durations are completely independent we present a new method for obtaining a probability distribution function that bounds the exact probability distribution of the project completion time from below the bounding distribution can be used to obtain an upper bound on the mean completion time of the project we also prove and illustrate that this bounding distribution is better tighter than any of the existing lower bounds implying that the corresponding upper bound on the mean completion time is tighter than any of the existing upper bounds

generalized galerkin approximations of elastic waves with absorbing boundary conditions abstract for the propagation of elastic waves in unbounded domains absorbing boundary conditions abcs at the fictitious numerical boundaries have been proposed in this paper we focus on both first and second order abcs in the framework of variational weak approximations like those stemming from galerkin method or its variants for finite element or spectral approximations 1 in particular we recover first order conditions as natural or neumann conditions whereas we propose a penalty residual method for the treatment of second order abcs the time discretization is based on implicit backward finite differences whereas we use spectral legendre collocation methods set in a variational form for the spatial discretization treatment of finite element or spectral element approximations is completely similar numerical experiments exhibit that the present formulation of second order abcs improves the one based on first order abcs with regard to both the reduction of the total energy in the computational domain and the fourier spectrum of the displacement field at selected points of the elastic medium a stability analysis is developed for the variational problem in the continuous case both for first and second order abcs a suitable treatment of abcs at corners is also proposed

risk criteria in a stochastic knapsack problem we consider an investor who wants to allocate funds among several projects each project is expected to yield a certain reward and the objective is that a total reward will achieve a certain given amount called the target this problem is relatively easy to solve when rewards are deterministic but may be hard in a more realistic setting when the rewards are stochastic and the investor wants to maximize the probability of attaining the target we show that by combining dynamic programming with a search procedure the stochastic version of the problem can be solved relatively fast when rewards are normally distributed the procedure is also useful for other risk criteria which involve both the mean and the variance of the total reward

a domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change a domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces inside each subdomain the method presented coincides with the second order finite difference schemes traditionally used in geophysical modeling however the possibility of assigning to each subdomain its own space step makes numerical simulations much less expensive another interest of the method lies in the fact that its hybrid variational formulation naturally leads to exact equations for gridpoints on the interfaces transposing babuska brezzi s formalism on mixed and hybrid finite elements provides a suitable functional framework for this domain decomposition formulation and shows that the inf sup condition remains the basic requirement for convergence to occur

numerical approximation of elastic waves equations by implicit spectral methods a numerical treatment of the linear elasto dynamic problem is presented the spatial discretization is based on legendre collocation methods also called pseudo spectral methods set in weak form whereas we use implicit integration schemes based on finite differences for the temporal discretization absorbing boundary conditions are introduced in order to face wave propagation problems in unbounded domains we present several numerical results concerning stability convergence absorption properties for waves leaving the boundaries and comparison between explicit and implicit time advancing schemes the main result of the paper is as follows the implicit advancing time scheme allows us to adopt an integration step time about ten times larger than the one obtained by assuming an explicit advancing time scheme

coupling finite element and spectral methods first results a poisson equation on a rectangular domain is solved by coupling two methods the domain is divided in two squares a finite element approximation is used on the first square and a spectral discretization is used on the second one two kinds of matching conditions on the interface are presented and compared in both cases error estimates are proved

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

explicit second order isogeometric discretizations for acoustic wave problems abstract this paper presents a stability analysis of isogeometric iga and explicit newmark discretizations for acoustic wave problems with absorbing boundary conditions in spite of the very ill conditioned iga mass and stiffness matrices especially with respect to the polynomial degree p of the b splines and non uniform rational b splines nurbs basis functions employed the stability bounds of the proposed newmark iga method depend linearly on the meshsize h of the iga mesh and inversely on the iga polynomial degree p several numerical tests in the plane confirm these stability bounds and additionally explore the newmark iga order of convergence with respect to h p t domain deformation and the absorbing boundary conditions performance in the presence of a ricker wavelet in a nurbs domain

an algorithm for permanent fluid structure interaction in explicit transient dynamics abstract this paper presents the strategies and models adopted in the plexis 3c computer code for the description of interactions of the permanent type between fluids and structures in fast transient dynamic problems a careful analysis of geometrical issues and the use of a method based on lagrange multipliers for the treatment of essential boundary conditions lead to a scheme which appears to be both general and robust while remaining reasonably simple the method is implemented via an algorithm able to deal automatically with situations of large geometrical complexity such as those encountered with box like structures multiple interactions structural bifurcations or even arbitrary structural intersections submerged structural edges etc in the presence of large structural displacements rotations and deformations the algorithm turns out to be efficient and dramatically reduces the amount of information that has to be supplied in order to describe a given interaction compared with the algorithms used in previous plexis 3c implementations as a consequence the time and effort needed for input preparation in large and complex realistic simulations is substantially reduced and the possibility for human errors in this phase is almost eliminated several examples show the application of the method to problems of practical interest

geophysical astrophysical spectral element adaptive refinement gaspar object oriented h adaptive fluid dynamics simulation an object oriented geophysical and astrophysical spectral element adaptive refinement gaspar code is introduced like most spectral element codes gaspar combines finite element efficiency with spectral method accuracy it is also designed to be flexible enough for a range of geophysics and astrophysics applications where turbulence or other complex multiscale problems arise the formalism accommodates both conforming and non conforming elements several aspects of this code derive from existing methods but here are synthesized into a new formulation of dynamic adaptive refinement dare of non conforming h type as a demonstration of the code several new 2d test cases are introduced that have time dependent analytic solutions and exhibit localized flow features including the 2d burgers equation with straight curved radial and oblique colliding fronts these are proposed as standard test problems for comparable dare codes quantitative errors are reported for 2d spatial and temporal convergence of dare

fuzzy model based reliable static output feedback mathscr h _ infty control of nonlinear hyperbolic pde systems this paper investigates the problem of output feedback robust mathscr h infty control for a class of nonlinear spatially distributed systems described by first order hyperbolic partial differential equations pdes with markovian jumping actuator faults the nonlinear hyperbolic pde systems are first expressed by takagi sugeno fuzzy models with parameter uncertainties and then the objective is to design a reliable distributed fuzzy static output feedback controller guaranteeing the stochastic exponential stability of the resulting closed loop system with certain mathscr h infty disturbance attenuation performance based on a markovian lyapunov functional combined with some matrix inequality convexification techniques two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy pde systems it is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite difference method in space finally two examples are presented to demonstrate the effectiveness of the proposed methods

the h p and h p versions of the finite element method in 1 dimension this paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting the main emphasis is placed on the analysis when the exact solution has singularity of x type the first part analyzes thep version the second theh version and generalh p version and the final third part addresses the problems of the adaptiveh p version

implicit spectral element methods and neumann neumann preconditioners for acoustic waves abstract a numerical approximation of the acoustic wave equation with first order absorbing boundary conditions is considered the discretization is based on conforming spectral elements in space and implicit finite differences in time a stability analysis based on the energy method is developed for the fully discrete scheme the linear system arising at each step is solved by the conjugate gradient method with balancing neumann neumann preconditioning several numerical results illustrate the stability and convergence properties of the approximation schemes that result spectrally accurate in space and up to second order in time while the neumann neumann solver at each time step is scalable and quasi optimal

reliable control using redundant controllers this paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant the resulting closed loop control system is reliable in the sense that it provides guaranteed internal stability and h sub spl infin performance in terms of disturbance attenuation not only when all controllers are operational but also when some controller outages sensor and or actuator occur a numerical example is given to illustrate the proposed design procedures

the h p and h p versions of the finite element method in 1 dimension part ii the error analysis of the h and h p versions the paper is the second in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimensional setting the first part 1 analyzed thep version the present one concentrates on theh andh p versions

brief paper reliable control of uncertain nonlinear systems this paper is concerned with the reliable controller design problem for a class of uncertain nonlinear systems for the primary contingency problem a procedure of designing reliable nonlinear controllers is presented in terms of solutions of hamilton jacobi inequalities the resulting closed loop nonlinear system is reliable in the sense that the performance i e internal stability and h attenuation of the closed loop system is guaranteed not only when all sensors and actuators are operational but also when some sensor and actuator outages occur

dynamic shortest paths in acyclic networks with markovian arc costs we examine shortest path problems in acyclic networks in which arc costs are known functions of certain environment variables at network nodes each of these variables evolves according to an independent markov process the vehicle can wait at a node at a cost in anticipation of more favorable arc costs we first develop two recursive procedures for the individual arc case one based on successive approximations and the other on policy iteration we also solve the same problem via parametric linear programming we show that the optimal policy essentially classifies the state of the environment variable at a node into two categories green states for which the optimal action is to immediately traverse the arc and red states for which the optimal action is to wait we then extend these concepts for the entire network by developing a dynamic programming procedure that solves the corresponding problem the complexity of this method is shown to be o n2k nk3 where n is the number of network nodes and k

estimating network characteristics in stochastic activity networks this paper describes a monte carlo method based on the theory of quasirandom points for estimating the distribution functions and means of network completion time and shortest path time in a stochastic activity network in particular the method leads to estimators whose absolute errors converge as log kn k where k denotes the number of replications collected in the experiment and n is the number of dimensions for sampling this rate compares favorably with the standard error of estimate o1 k1 2 which obtains for experiments that use random sampling moreover since quasirandom points are nonrandom the upper bound log kn k is deterministic in contrast to the random sampling rate o1 k1 2 which is probabilistic the paper demonstrates how the use of a cutset of the network reduces n in the bound when estimating the distribution functions two examples illustrate the benefits and costs of using quasirandom points

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

reliable control of nonlinear systems in this paper we extend veillette s results 1995 to the study of reliable linear quadratic regulator problem for nonlinear systems this is achieved by employing the hamilton jacobi inequality in the nonlinear case instead of algebraic riccati equation in the linear one the proposed state feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators both the gain margins of guaranteeing system stability and retaining a performance bound are estimated

infinite gain margin problem in multivariable feedback systems this paper deals with the problem of designing feedback compensators that achieve infinite gain margin for stability in the face of the uncertainty in the gain factor of the plant a necessary and sufficient condition is given for the existence of compensators in terms of the closed right half plane zeros of the plant

reliable h sub spl infin control for affine nonlinear systems this paper addresses the reliable h sub spl infin control problems for affine nonlinear systems based on the hamilton jacobi inequality approach developed in the h spl infin control problems for affine nonlinear systems a method for the design of reliable nonlinear control systems is presented the resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and h sub spl infin performance not only when all control components are operational but also in the case of some component outages within a prespecified subset of control components a numerical example is also given

exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function in this paper the stochastic shortest path problem of determining a path that maximizes the expected utility is considered the nature of the utility function used to evaluate paths is of a decreasing deadline type the principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures one type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations specifically two algorithms are developed each containing the same preference relation but two different relaxations our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly more importantly even for large problems both the algorithms solved them by enumerating a very small percentage of all paths

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

a multiple controller structure and design strategy with stability analysis this paper proposes a multi controller structure for a plant and develops associated stability results the main theoretical result of the paper is a quite simple necessary and sufficient condition for the closed loop stability of the scheme the result also specializes as a multi controller generalization of the single controller youla kucera theory for the class of all stabilizing controllers for a plant and to known results concerning simultaneous stabilization the plants considered are recursively expressed in terms of a set of approximations of frequency shaped plant model errors the controllers in successive loops can be designed based on increasing refinement in model approximation perhaps via on line identification an advantage of the proposed multi controller strategy is that a number of various controller design techniques can be employed to achieve performance objectives which are not conveniently achievable by any one technique a design example is included with first an lqg design applied for stabilization of a crude nominal model and then an h optimal design and finally an h2 optimal design the latter two designs are aimed at enhancing h h2 performances there could even be a further adaptive loop for on line performance enhancement

optimal energy conserving local discontinuous galerkin methods for second order wave equation in heterogeneous media abstract solving wave propagation problems within heterogeneous media has been of great interest and has a wide range of applications in physics and engineering the design of numerical methods for such general wave propagation problems is challenging because the energy conserving property has to be incorporated in the numerical algorithms in order to minimize the phase or shape errors after long time integration in this paper we focus on multi dimensional wave problems and consider linear second order wave equation in heterogeneous media we develop and analyze an ldg method in which numerical fluxes are carefully designed to maintain the energy conserving property and accuracy compatible high order energy conserving time integrators are also proposed the optimal error estimates and the energy conserving property are proved for the semi discrete methods our numerical experiments demonstrate optimal rates of convergence and show that the errors of the numerical solutions do not grow significantly in time due to the energy conserving property

spectral domain decomposition methods for the solution of acoustic and elastic wave equations a new spectral domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2 d heterogeneous media starting from a variational formulation of the problem two different approaches are proposed for the spatial discretization a mixed fourier legendre and a full legendre collocation the matching conditions at subdomain interfaces are carefully analyzed and the stability and efficiency of time advancing schemes are investigated the numerical validation with some significant test cases illustrates the accuracy flexibility and robustness of our methods these allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy

reliable rm h_infty fuzzy control for continuous time nonlinear systems with actuator failures this paper is concerned with the design of reliable hinfin fuzzy controllers for continuous time nonlinear systems with actuator failures the takagi and sugeno fuzzy model is employed to represent a nonlinear system the objective is to find a stabilizing state feedback fuzzy controller such that the nominal hinfin performance is optimized while satisfying a prescribed hinfin performance constraint in the actuator failure cases based on the linear matrix inequality lmi techniques two efficient methods for the design of a suboptimal reliable hinfin fuzzy controller are proposed different lyapunov functions are used during the design for the nominal and actuator failure cases which lead to a less conservative controller design in the first method a single lyapunov function is used for the actuator failure cases the second method adopts a parameter dependent lyapunov function for the actuator failure cases which further reduces the conservatism of the design finally numerical simulations on the chaotic rossler system are given to illustrate the effectiveness of the proposed design methods

a necessary and sufficient condition for the stabilisation of a matrix and its principal submatrices abstract we present a necessary and sufficient condition for the existence of a real diagonal matrix such that its product with a given real square matrix is hurwitz together with all its principal submatrices we also give an explicit formula for a matrix which in particular supplies all the involved matrices with negative distinct eigenvalues

reliable regulation in decentralised control systems this article addresses the design of decentralised regulators which supply the control systems with signal tracking and disturbance rejection this property has to be attained to the maximum possible extent even when instrumentation faults occur thus causing the opening of some feedback loops the problem is tackled for lti asymptotically stable plants subject to perturbations under the assumption that the laplace transforms of the exogenous signals have multiple poles on the imaginary axis the proposed regulator is composed of an lti nominal controller supervised by a reconfiguration block once the actions of the reconfiguration block have been settled the synthesis of the nominal controller is reformulated as a suitable regulation problem a constructive sufficient condition for its solvability is established this condition turns out to be also necessary if the exogenous signals are polynomial in time

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

spectral methods for hyperbolic problems we review the current state of fourier and chebyshev collocation methods for the solution of hyperbolic problems with an eye to basic questions of accuracy and stability of the numerical approximations throughout the discussion we emphasize recent developments in the area such as spectral penalty methods the use of filters the resolution of the gibbs phenomenon and issues related to the solution of nonlinear conservations laws such as conservation and convergence we also include a brief discussion on the formulation of multi domain methods for hyperbolic problems and conclude with a few examples of the application of pseudospectral collocation methods for solving nontrivial systems of conservation laws

generalized dynamic programming for stochastic combinatorial optimization in stochastic versions of combinatorial optimization problems the objective is to maximize or minimize a function of random variables for many problems of this type conventionally applied dynamic programming dp may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of dp we develop a generalization of dp that guarantees optimality even in the absence of monotonicity we illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed dp algorithm e kao is potentially suboptimal due to the violation of monotonicity m sniedovich using generalized dp we are able to modify the algorithm to guarantee optimality