implicit schemes and lu decompositions implicit methods for hyperbolic equations are analyzed by constructing lu factorizations it is shown that the solution of the resulting tridiagonal systems in one dimension is well conditioned if and only if the lu factors are diagonally dominant stable implicit methods that have diagonally dominant factors are constructed for hyperbolic equations in n space dimesnions only two factors are required even in three space dimensions acceleration to a steady state is analyzed when the multidimensional backward euler method is used with large time steps it is shown that the scheme approximates a newton raphson iteration procedure

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

an implicit multigrid method for turbulent combustion abstract an implicit multigrid scheme for solving the navier stokes turbulence species and variance transport equations describing turbulent combustion is presented turbulence chemistry interaction is included by use of presumed probability density functions pdf to avoid stiffness problems associated with chemically reacting flows time integration is performed by an implicit lu sgs algorithm this requires the formation of a source term jacobian the complete analytically derived jacobian including assumed pdf modeling is given in the present paper thus the high numerical stability of the original algorithm is maintained convergence acceleration is accomplished by a nonlinear multigrid method strongly nonlinear source terms in species turbulence and variance conservation equations usually keep multigrid methods from converging it is shown that freezing of coarse grid source terms including spatial derivatives and restriction damping in regions of high chemical activity may remedy this problem two finite rate chemistry test cases with methane and hydrogen combustion at supersonic speed demonstrate a strong reduction in required cpu time

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

matrix dissipation for central difference schemes with combustion the effect of artificial viscosity is investigated for problems related to supersonic combustion an implicit lower upper symmetric gauss seidel finite volume method is employed for solving the full compressible two dimensional averaged navier stokes and species transport equations for the right hand side discretization central differences are used therefore some kind of artificial viscosity is necessary to reduce oscillations near shock waves and to enable convergence to machine accuracy in comparison to the standard second and fourth order scalar dissipation a matrix dissipation reduces the amount of artificial viscosity by scaling each equation individually for the necessary absolute flux jacobian matrix a new decomposition is presented keeping the additional cost moderate with an appropriate sensor the scheme also gets total variation diminishing properties calculations using different dissipation models are presented and advantages using a matrix dissipation are shown

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

mixed h 2 h control via state feedback for nonlinear systems this paper studies a mixed h 2 h control problem with internal stability by means of memoryless state feedback for smooth nonlinear control systems the problem consists of combining the performance requirements of quadratic optimal controllers with the robustness properties of h controllers it is shown that under appropriate assumptions the problem is solvable if a pair of cross coupled hamilton jacobi isaacs equations allows smooth solutions our approach to the mixed h 2 h nonlinear control problem is drawn from the concepts of non zero sum differential game lasalle s invariance principle and completion of squares analogous results are also developed for discrete time nonlinear systems by using the taylor expansion argument finally all the results obtained in affine systems are generalized to non affine nonlinear systems

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

upwind differencing and lu factorization for chemical non equilibrium navier stokes equations abstract an efficient and robust upwind method for solving the chemical non equilibrium navier stokes equations has been developed the method uses either the roe or van leer flux splitting for inviscid terms and central differencing for viscous terms in the explicit operator residual and the steger warming sw splitting and lower upper lu approximate factorization for the implicit operator this approach is efficient since the sw lu combination requires the inversion of only block diagonal matrices as opposed to the block tridiagonal inversion of the widely used adi method and is fully vectorizable the lu method is particularly advantageous for systems with large number of equations such as for chemical and thermal nonequilibrium flow formulas of the numerical method are presented for the finite volume discretization of the navier stokes equations in general coordinates numerical tests in hypersonic blunt body ramped duct shock wave boundary layer interaction and divergent nozzle flows demonstrate the efficiency and robustness of the present method

nonlinear stochastic h_2 h_ infty control with x u v dependent noise infinite horizon case for general nonlinear stochastic ito systems with state control and external disturbance dependent noise the infinite horizon mixed h2 hinfin control is studied it turns out that in order to solve the h2 hinfin control one only needs to solve four cross coupled hamilton jacobi equations a necessary condition and a sufficient condition for the existence of the solution of h2 hinfin controlis respectively presented which extends the previous results to more general models

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

necessary and sufficient conditions for mixed h sub 2 and h sub infinity optimal control it is shown that d s bernstein and w m hadad s ibid vol 34 no 3 p 293 1989 necessary condition for full order mixed h sub 2 and h sub infinity optimal control is also sufficient and that j c doyle et al s proc amer control conf p 2065 1989 sufficient condition for full order mixed h sub 2 and h sub infinity optimal control is also necessary they are duals of one another

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

analysis of incomplete repeated measurements with dependent censoring times summary a frequently encountered complication in repeated measurements data analysis is that a substantial number of subjects drop out of the study in this paper several conceptually simple methods are proposed for analysing incomplete repeated measures when the measurement times vary substantially from subject to subject and the subject s drop out time may depend on the observed and unobserved outcome variables numerical studies are conducted to examine the adequacy of our procedures under practical settings a detailed illustration with an aids clinical trial is also provided

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

brief trading robustness with optimality in nonlinear control the mixed h 2 h control problem is studied for a class of nonlinear systems a procedure providing a sub optimal solution to this problem is discussed and analyzed in detail the sub optimal state feedback control law can be obtained solving two hamilton jacobi equations and a simple one parameter static minimization problem a simple one dimensional example is discussed in detail and applications to the optimal robust stabilization of the angular velocities of a rigid body are included

exact two sample inference with missing data when comparing follow up measurements from two independent populations missing records may arise due to censoring by events whose occurrence is associated with baseline covariates in these situations inferences based only on the completely followed observations may be biased if the follow up measurements and the covariates are correlated this article describes exact inference for a class of modified u statistics under covariate dependent dropouts the method involves weighing each permutation according to the retention probabilities and thus requires estimation of the missing data mechanism the proposed procedure is nonparametric in that no distributional assumption is necessary for the outcome variables and the missingness patterns monte carlo approximation by the gibbs sampler is proposed and is shown to be fast and accurate via simulation the method is illustrated in two small data sets for which asymptotic inferential procedures may not be appropriate

two sample asymptotically distribution free tests for incomplete multivariate observations abstract asymptotically distribution free tests for equality of two multivariate distributions based on censored observations are proposed by choosing appropriate test scores we obtain the multivariate versions of the gehan and log rank tests an important application of the proposed tests is in the area in which multiple observations are collected on study subjects some of whom may have missing observations the patterns of missing observations are allowed to differ for the two groups to be compared these tests are particularly useful for longitudinal studies for example the analysis of repeated measurements and growth curves real examples are also provided for illustration

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 coupled implicit method for chemical non equilibrium flows at all speeds a time accurate coupled solution procedure is described for the chemical nonequilibrium navier stokes equations over a wide range of mach numbers this method employs the strong conservation form of the governing equations but uses primitive variables p g u v h y i as unknowns real gas properties and nonequilibrium chemistry are considered numerical tests include steady convergent divergent nozzle flows with air dissociation recombination chemistry dump combustor flows withn pentane air chemistry and nonreacting unsteady driven cavity flows numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for mach numbers ranging from the incompressible limit to supersonic speeds c 1993 academic press inc

an implicit multigrid method for the simulation of chemically reacting flows the application of multigrid methods is complicated if the set of governing equations contains strongly nonlinear source terms this is the case for finite rate chemistry as well as for turbulence conservation equations in most cases strong nonlinearities within the chemical production rates prevent convergence of standard multigrid methods this paper investigates different approaches to treating chemical and turbulent production terms on coarse grids in order to enable convergence independent of combustion supersonic flows require special care during restriction and prolongation if strong shock waves occur a full coarsening four level nested multigrid method is used for all conservation equations including those of turbulence and species transport strong convergence accelerations are achieved by a local source term dependent damping of the restricted residual error several test cases with and without combustion demonstrate the efficiency and accuracy of the proposed multigrid algorithm

state space algorithm for the computation of superoptimal matrix interpolating functions a state space algorithm is studied which generates the unique superoptimal nehari extension of a general rational matrix the procedure is to use a set of all pass transformations to sequentially minimize each frequency dependent singular value of the interpolating function in a dimension peeling algorithm these all pass transformations are determined by the maximal schmidt pairs of a sequence of hankel operators the process terminates when the original problem is reduced to one of rank one at this stage all the available degrees of freedom have been exhausted the work is an extension of that by young 1986 and gives a concrete state space implementation of his operator theoretic arguments in addition bounds are given on the minimum achievable values for s1 e sup ersi e j i 1 2 rank g0 and also the mcmillan degree of the final superoptimal extension here si denotes the ith singular value of a frequency dependent matrix and the numbering is taken to be in decrea

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

exact significance testing to establish treatment equivalence with ordered categorical data this communication concerns the problem of establishing the therapeutic equivalence of two treatments that are being compared on the basis of ordered categorical data the problem is formulated as a significance test in which the null hypothesis specifies a treatment difference an efficient numerical algorithm for computing the exact significance level is provided along with a simple method for obtaining the asymptotic significance level both methods are applied to a clinical trial of a new agent versus an active control guidelines for when to use the exact procedure and when to rely on asymptotic theory are provided

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

rank estimation of treatment differences based on repeated measurements subject to dependent censoring abstract in comparing the effectiveness of two treatments suppose that for each patient repeated measurements of an outcome variable are taken at prespecified time points but some observations may be missing due to the patient s dependent right censoring in this article a simple rank estimation procedure constructed based on an artificial censoring technique is proposed for the treatment differences over time without imposing a parametric structure on the dependence between the outcome measures and the censoring variable our method can be easily implemented and is illustrated by a dataset from an aids clinical trial

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach