digital optimal control of continuous time systems with control delay abstract this paper solves the digital stationary optimal control problem in the case of scalar linear stochastic continuous time systems with control delay quadratic integral criteria complete state information and constant sampling periods by transforming the problem to an equivalent discrete time one without control delay expressions are given for the eigenvalues of the control system and the parameters of the feedback matrix the influence of the sampling period on the cost is investigated for different values of the control delay by means of some examples

certainty equivalent control of stochastic systems stability property this work presents sufficient conditions for infinite and sliding finite horizon certainty equivalence controllers to stabilize discrete linear systems disturbed by scalar multiplicative white noise sequences these conditions also guarantee stabilizability by the optimal controllers

artificial boundary conditions for incompressible navier stokes equations a well posed result abstract numerical simulation of two dimensional incompressible viscous flows around an obstacle is considered two horizontal straight line artificial boundaries are introduced and the original flow is approximated by a flow in an infinite channel with slip boundary condition on the wall then two vertical segment artificial boundaries are introduced and a series of approximate artificial boundary conditions on them are derived by imposing the continuity of velocity and the normal stress thus the original problem is reduced to a problem defined in a bounded computational domain the well posedness of the reduced problem is proved the finite element approximation of this problem is given and error estimates are obtained furthermore numerical examples show the accuracy and efficiency of our artificial boundary conditions

a numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate reynolds numbers abstract numerical solutions have been obtained for steady uniform flow past a rotating circular cylinder results are presented for reynolds numbers based on the diameter of the cylinder 5 and 20 and the rotational parameters in the range of 0 3 to avoid the difficulties in satisfying the boundary conditions at large distances from the cylinder a new numerical technique is introduced further series expansion solutions are obtained which are valid at small values of but the results are found to be applicable over a wide range of values of the calculated values of the drag and lift coefficients and the general nature of the streamline patterns are in good agreement with the most recent time dependent calculations performed by badr and dennis

chord arc surfaces with small constant ii good parameterizations abstract in a companion paper we introduced a notion for hypersurfaces in r d 1 that is analogous to the chord arc condition with small constant for planar curves in this paper we address the problem of finding good parameterizations for these surfaces in particular we show that these surfaces must be homeomorphic to r d and we build parameterizations with l p bounds on the gradient and the gradient of the inverse with p as the chord arc constant goes to 0 when d 2 we use the uniformization theorem to find a quasisymmetric parameterization we do not know how to build bilipschitz parameterizations when d 2 or quasisymmetric parameterizations when d 3 the author conjectures that they do not exist in general however we can build bilipschitz reflections in all dimensions and these reflections will satisfy certain extra estimates in terms of carleson measures

on h on the complement of c1 α curves abstract let be a quasiconformal mapping on the plane with complex dilatation we show that if satisfies a certain carleson measure condition then one can transfer h on the upper half plane onto the corresponding space in the complement of the quasicircle r and that this condition on characterizes c 1 curves

a study of a numerical solution of the steady two dimensions navier stokes equations in a constricted channel problem by a compact fourth order method we present a numerical solution for the steady 2d navier stokes equations using a fourth order compact type method the geometry of the problem is a constricted symmetric channel where the boundary can be varied via a parameter from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular the set of non linear equations is solved by the newton method results have been obtained for reynolds number up to 500 estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method

weil petersson teichmuller space revisited abstract in our previous paper 23 it was proved that a sense preserving homeomorphism g on the unit circle s 1 belongs to the weil petersson class wp s 1 namely g can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is square integrable in the poincare metric if and only if g is absolutely continuous such that log g belongs to the sobolev class h 1 2 in this sequel to 23 we show that the smooth hilbert manifold structure on wp s 1 inherited from h 1 2 by the pullback g log g is compatible with the standard hilbert manifold structure introduced by takhtajan teo 27 this enables us to give a fast approach to some results in our previous papers 23 and 24

a cell boundary element method for viscous laminar flow solutions a cell boundary element method is developed to solve viscous fluid structure interaction problems modelled by navier stokes equations this is achieved through a hybrid approach incorporating boundary element and finite element methods in the proposed scheme cell equations are generated using the principles of the boundary element method with global equations derived following the procedures of the finite element method a primitive variable formulation with an unstructured mesh requirement forms the basis of the hybrid approach which can be applied to both two and three dimensional problems the validation of this numerical scheme of study involving analytical and numerical mathematical procedures is carried out using a number of well documented flow solutions and the accuracy and robustness of the method are demonstrated in these examples

harmonic reflection in quasicircles and well posedness of a riemann hilbert problem on quasidisks abstract a complex harmonic function of finite dirichlet energy on a jordan domain has boundary values in a certain conformally invariant sense by a construction of h osborn we call the set of such boundary values the douglas osborn space one may then attempt to solve the dirichlet problem on the complement for these boundary values this defines a reflection of harmonic functions we show that quasicircles are precisely those jordan curves for which this reflection is defined and bounded we then use a limiting cauchy integral along level curves of green s function to show that the plemelj sokhotski jump formula holds on quasicircles with boundary data in the douglas osborn space this enables us to prove the well posedness of a riemann hilbert problem with boundary data in the douglas osborn space on quasicircles

weil petersson teichmuller space iii dependence of riemann mappings for weil petersson curves the classical riemann mapping theorem implies that there exists a so called riemann mapping which takes the upper half plane onto the left domain bounded by a jordan curve in the extended complex plane the primary purpose of the paper is to study the basic problem how does a riemann mapping depend on the corresponding jordan curve we are mainly concerned with those jordan curves in the weil petersson class namely the corresponding riemann mappings can be quasiconformally extended to the whole plane with beltrami coefficients being square integrable under the poincare metric after giving a geometric characterization of a weil petersson curve we endow the space of all normalized weil petersson curves with a new real hilbert manifold structure in a geometric manner and show that this new structure is topologically equivalent to the standard complex hilbert manifold structure which implies that an appropriately chosen riemann mapping depends continuously on a weil petersson curve and vice versa this can be considered as the first result about the continuous dependence of riemann mappings on non smooth jordan curves

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

calculation of laminar separation bubbles in the wake inflation deflation regime a new interacting boundary layer method is developed for calculating two dimensional incompressible laminar separation bubbles the method relies on a completely consistent mixed boundary value treatment of the outer inviscid flow for attached flows the new method is found to converge as fast as the classical cauchy hilbert method and to yield the same solutions for separated flows the new method is found to converge two to three times faster than a comparable cauchy hilbert method the physical asymptotic theories that underlie this new numerical method will be discussed in so far as they motivate the method

direct solution of two dimensional navier stokes equations for static aeroelasticity problems a new method has been developed to calculate the steady flow and structural deformations for fluid structure interaction problems the discretized fluid dynamic and structural equations are regarded as a single set of coupled nonlinear algebraic equations the equilibrium solution is directly obtained using newton s method the governing equations used for the fluid flow are the two dimensional navier stokes equations and a finite element model is used to represent the structure this paper describes the analytical method and presents sample calculations demonstrating the technique the results show rapid convergence and good agreement with experimental data nomenclature bw half bandwidth of tangent matrix d set of structural displacement variables e set of governing equations for the aeroelastic system f flux vector in x direction g flux vector in y direction h distance from nozzle throat to centerline number of fluid dynamic control volumes in streamwise direction j number of fluid dynamic control volumes in cross stream direction l reference length total length of nozzle n total number of variables in system p pressure pe exit static pressure pt total pressure r system residual r magnitude of residual r radius at nozzle throat t tangent matrix system jacobian t wall thickness u set of fluid dynamic variables x set of variables for the aeroelastic system ax change in system variables during a newton iteration x streamwise coordinate y cross stream coordinate

l estimates for the bar partial problem in a half planeproblem in a half plane l approche de dualite pour trouver des solutions de f est suffisante pour plusieurs problemes apparaissant en theorie h p on donne des operateurs solution qui permettent de resoudre des problemes non resolubles par la dualite

newton s method applied to finite difference approximations for the steady state compressible navier stokes equations abstract newton s method is applied to finite difference approximations for the steady state compressible navier stokes equations in two spatial dimensions the finite difference equations are written in generalized curvilinear coordinates and strong conservation law form and a turbulence model is included we compute the flow field about a lifting airfoil for subsonic and transonic conditions we investigate both the requirements for an initial guess to insure convergence and the computational efficiency of freezing the jacobian matrices approximate newton method we consider the necessity for auxiliary methods to evaluate the temporal stability of the steady state solutions we demonstrate the ability of newton s method in conjunction with a continuation method to find nonunique solutions of the finite difference equations i e three different solutions for the same flow conditions

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

vorticity boundary conditions and boundary vorticity generation for two dimensional viscous incompressible flows abstract in this paper we present boundary conditions appropriate for the vorticity formulation of the two dimensional incompressible viscous navier stokes equations these boundary conditions are incorporated into a finite difference scheme and the resulting method is of the vorticity creation type i e vorticity is generated at the boundary to ensure that the tangential velocity boundary condition is satisfied the results of computations with this finite difference method are presented for flow past a circular cylinder a difference scheme and computational results for a model problem the prandtl boundary layer equations describing flow over a semi infinite flat plate are also presented

control of randomly varying systems with prescribed degree of stability the control of linear discrete time systems with stochastic parameter matrices is discussed two control techniques are particularly used infinite horizon and finite moving horizon optimal regulators it is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes in this way the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

a transformation free hoc scheme for incompressible viscous flows past an impulsively started circular cylinder in this paper we present a higher order compact scheme for the unsteady two dimensional 2d navier stokes equations on nonuniform polar grids specifically designed for the incompressible viscous flows past a circular cylinder the scheme is second order accurate in time and at least third order accurate in space the scheme very efficiently computes both unsteady and time marching steady state flow for a wide range of reynolds numbers re ranging from 10 to 9500 for the impulsively started cylinder the robustness of the scheme is highlighted when it accurately captures the vortex shedding for moderate re represented by the von karman street and the so called and s phenomena for higher re comparisons are made with established numerical and experimental results and excellent agreement is found in all the cases both qualitatively and quantitatively

new robustness bounds for discrete systems with random perturbations some new stochastic stability robustness bounds for state space models are reported nominally exponentially stable discrete time systems are assumed to be subject to random parameter perturbations and novel bounds are obtained on the maximum variances of these random perturbations to maintain stability robustness the methods employed in the analysis are the existing ones used in the deterministic framework after transforming the stochastic robustness problem to a deterministic one the results are compared with each other and with the exact stability region in an example

a generalization of the uncertainty threshold principle a generalized version of the uncertainty threshold principle is presented for discrete time systems with both jump markov parameters and independent white multiplicative noises it is shown that this threshold is not to be exceeded for the existence of the quadratically optimal steady state control for this class of systems

parametrization of all linear compensators for discrete time stochastic parameter systems abstract for discrete time stochastic parameter systems this paper presents a characterization of all state covariances assignable by a linear controller and a parametrization of all controllers that achieves a desired covariance these results indirectly provide the parametrization of all linear fixed order compensators which are mean square stabilizing for this class of systems the paper also includes robustification of the derived compensators and an example to illustrate the results

general strong conservation formulation of navier stokes equations in nonorthogonal curvilinear coordinates the selection of primary dependent variables for the solution of navier stokes equations in the curvilinear body fitted coordinates is still an unsettled issue reported formulations with primitive variables involve contravariant velocity components cartesian components and velocity projections also known as resolutes most of the formulations result in a weak conservation form of the momentum equations which contain grid line curvature and divergence related coriolis and centrifugal terms this paper presents a general strong conservation formulation of the momentum equations allowing the flexibility in choosing the various forms of the velocity components as the dependent variables ambiguous issues relating geometrical topology and forms of governing equations are discussed and clarified computational results obtained with both strong and weak forms are presented and compared to known analytical experimental data the results confirm the soundness of the formulation 19 refs

weil petersson teichmuller space ii smoothness of flow curves of h32 vector fields abstract given a continuous vector field t of sobolev class h 3 2 on the unit circle s 1 the flow maps g t of the differential equation d d t t 0 are known to be quasisymmetric homeomorphisms very recently gay balmaz ratiu 15 conjectured that the flow curve g t is in the weil petersson class wp s 1 and is continuously differentiable with respect to the hilbert manifold structure of wp s 1 introduced by takhtajan teo 40 the first assertion had already been demonstrated in our previous paper 36 in this sequel to 36 we will continue to deal with the weil petersson class wp s 1 and completely solve this conjecture in the affirmative

quasiconformal mappings and chord arc curves given a quasiconformal mapping p on the plane what conditions on its dilatation guarantee that p r is rectifiable and pir is locally abso lutely continuous we show in this paper that if satisfies certain quadratic carleson measure conditions with small norm then p r is a chord arc curve with small constant and p x p 0 g0 ea t dt for x e r with a e bmo having small norm conversely given any such map from r c we show that it has an extension to c with the right kind of dilatation similar results hold with r replaced by a chord arc curve examples are given that show that it would be hard to improve these results applications are given to conformal welding and the theorem of coifman and meyer on the real analyticity of the riemann mapping on the manifold of chord arc curves let p be a quasiconformal map of the plane onto itself thus p is a homeomorphism with locally integrable distributional derivatives and ps upz where u e l c il ul100 1 here we use the notations fz af azf 2 z id f fz 2 aa ida f this function u is called the complex dilatation of p the mapping theorem for q c maps states that for each u e l c il ul100 1 there is a q c map p on c with dilatation u and p is unique up to normalization a basic problem is to understand how geometric properties of p are reflected in u for example one would like to have natural conditions on u which imply that p r is rectifiable and p ir is absolutely continuous this question arises naturally when considering problems in conformal mappings and conformal welding in this paper we obtain such estimates for the mapping theorem and we also give some applications our results involve bmo aoo weights chord arc curves and carleson measures and so we first review the appropriate definitions a locally integrable function f on r lies in bmo if llfil sup lil if x fil dx received by the editors june 1 1986 1980 mathematics subject classification 1985 revision primary 30g60 secondary 42b20 30e20

optimal stabilizing control of a stochastic system driven by randomly correlated noise the problem of optimal stabilization of a discrete time linear system subjected to additive correlated noise disturbances with an uncertain model is considered this problem is first converted to one of stabilizing a system with multiplicative and additive noises with time wise uncorrelated characteristics a novel controller different from the infinite horizon optimal controller is then chosen from among the class or constant feedback controllers in order to stabilize the system in the mean square sense it is shown that for a special case of this problem stronger results of both mean square and almost sure asymptotic stability are possible we also present a simpler stabilizability condition to make it easier to use the particular method proposed an example is incorporated to illustrate the new technique

steady state solutions of the euler equations in two dimensions rotating and translating v states with limiting cases i numerical algorithms and results new second and third order algorithms are presented for calculating translating and rotating steady state solutions of the 2d incompressible euler equations which we call v states these are piecewise constant regions of vorticity and the contours bounding them are obtained by solving iteratively a nonlinear integro differential equation new limiting contours with corners are obtained and compared with local analytical solutions the precise results correct mistakes for limiting contours that were previously given

estimates for 8706 μ 1 and calderon s theorem on the cauchy integral etude du caractere borne de l operateur integral de cauchy a l aide d une transformation quasi conforme

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

does the stationary viscous flow around a circular cylinder exist for large reynolds numbers a numerical solution via variational imbedding we propose an approach to identifying the solutions of the steady incompressible navier stokes equations for large reynolds numbers these cannot be obtained as initial value problems for the unsteady system because of the instability of the latter our approach consists of replacing the original steady state problem for the navier stokes equations by a boundary value problem for the euler lagrange equations for minimization of the quadratic functional of the original equations this technique is called method of variational imbedding mvi and in this case it leads to a system of higher order partial differential equations which is solved by means of an operator splitting method as a featuring example we consider the classical flow around a circular cylinder which is known to lose stability as early as for re 40 we find a stationary solution with recirculation zone for reynolds numbers as large as re 200 thus new information about the possible hybrid flow regimes is obtained

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

full and reduced order observer design for discrete stochastic bilinear systems the author considers a general discrete time stochastic bilinear system model and derives the mean square optimal linear unbiased observer equations to be used in reconstructing a prespecified linear combination of state variables based on noisy output measurements

deterministic and stochastic robustness measures for discrete systems deterministic and stochastic lyapunov theorems are used to demonstrate the robustness of a stable linear time variant discrete time nominal system to both unknown deterministic and stochastic perturbations time domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system it is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed loop system is known to be stable with a certain degree e g as in the case of linear quadratic optimal control with alpha degree of prescribed stability

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

steady viscous flow in a triangular cavity by efficient numerical techniques abstract accurate and efficient calculations of the flow inside a triangular cavity are presented for high reynolds numbers the navier stokes equations expressed in a stream function and vorticity formulation are solved numerically using finite differences on a transformed geometry second order numerical boundary conditions are derived and newton s iteration is employed to solve the nonlinear system resulting from the finite difference discretization aside from solving the equilateral triangular cavity problem we have also been able to compute numerical solutions for scalene triangular cavity problems our coarse mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good

an integral equation approach to the incompressible navier stokes equations in two dimensions we present a collection of methods for solving the incompressible navier stokes equations in the plane that are based on a pure stream function formulation the advantages of this approach are twofold first the velocity is automatically divergence free and second complicated nonlocal boundary conditions for the vorticity are avoided the disadvantage is that the solution of a nonlinear fourth order partial differential equation is required by recasting this partial differential equation as an integral equation we avoid the ill conditioning which hampers finite difference and finite element methods in this environment by using fast algorithms for the evaluation of volume integrals we are able to solve the equations using o m or o m log m operations where m is the number of points in the discretization of the domain

quasiconformal mappings and ahlfors david curves we show that if p is a quasiconformal mapping of the plane whose dilatation satisfies a certain quadratic carleson measure condition relative to an ahlfors david curve f then p is differentiable almost everywhere on f and log ip l e bmo when f is chord arc we show that its image is a bishopjones curve if the carleson norm is small then we show that p is absolutely continuous on f the image of f is an ahlfors david curve and p ea where a e bmo with a small norm

performance of digital linear regulators which use logarithmic arithmetic this paper analyzes the performance of digital linear regulators which use finite precision logarithmic arithmetic a linear equation is derived which describes the steady state covariance matrix of such a closed loop regulator system the utility of this covariance matrix in designing regulators which use logarithmic arithmetic is illustrated through several numerical examples and the presentation of a regulator design methodology

stabilizing compensator design for discrete time non linear stochastic systems with incomplete state information in this work an approach to stabilizing compensator design is presented that is suitable for a large class of discrete time non linear stochastic systems with incomplete state information the non linearity is contained either in the state or the measurement equation and it involves a white noise vector sequence the proposed compensator is a combination of a constant gain observer and a constant feedback control gain the stabilizability conditions depend upon the system and chosen design parameter characteristics and are given for both mean square and almost sure stochastic boundedness and stability of the controlled system a specific subclass of these systems subject to certain control laws is shown to possess stabilizability conditions that can be tested a priori

steady viscous flow past a circular cylinder up to reynolds number 600 viscous flow past a circular cylinder becomes unstable around reynolds number re 40 with a numerical technique based on newton s method and made possible by the use of a supercomputer steady but unstable solutions have been calculated up to re 600 it is found that the wake bubble region with recirculating flow grows in length approximately linearly with re the width increases like re12 up to re 300 at which paint a transition to linear increase with re begins at the highest reynolds numbers we reached the wake resembles a pair of translating uniform vortices both touching the center line the cylinder moving in front with the same speed supplies the vorticity required to balance diffusion

on variance neutrality of systems within general random parameters a necessary condition for variance neutrality of discrete time linear systems within general random parameters and with arbitrary observations is established it is proved that this condition is sufficient as well if the observations are linear this result is of importance in connection with separability of optimal control and state estimation