brief paper a method for optimal control and filtering of multitime scale linear singularly perturbed stochastic systems in this paper we introduce a transformation for the exact closed loop decomposition of the optimal kalman filter and the linear quadratic optimal controller of multi time scale continuous time linear singularly perturbed stochastic systems the solution of the corresponding algebraic regulator and filter riccati equations are obtained in terms of solutions of reduced order subsystem algebraic riccati equations corresponding to the system time scales we have also obtained n completely independent reduced order subsystem kalman filters working in parallel in different time scales this allows parallel processing of information with lower order different rates kalman filters consistent with the system time scales

asymmetricalgebraicriccatiequation ahomeomorphicparametrizationofthesetof solutions abstract in this paper asymmetric algebraic riccati equations are analyzed in particular we derive a new parametrization of the set of solutions generalizing on the symmetric case the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related feedback matrices moreover the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo hamiltonian matrix associated with the equation we finally show that also the newly introduced parametrization is given by a homeomorphic map

monte carlo methods for exploring sensitivity to distributional assumptions in a bayesian analysis of a series of 2 x 2 tables this paper develops monte carlo methods for a bayesian analysis of a series of 2 x 2 tables under a variety of distributional assumptions i assume that the data in each table were generated from a pair of binomial distributions and the logarithm of odds of a favourable response follows a bivariate distribution with means that are linear functions of covariates and an arbitrary covariance matrix i use gibbs and importance sampling methods to obtain various characteristics of the posterior distribution of the quantities of interest i apply the method to analyse the data from a population case control study given the size of the population at risk i also derive the posterior distribution of the risk difference defined as the difference in the probabilities of disease development in the exposed and unexposed groups

the dirichlet problem for a quasilinear singularly perturbed second order system we study an equivalent form of the dirichlet problem for a quasilinear singularly perturbed second order system which is a singular singularly perturbed boundary value problem in this way we have not only eliminated the usual assumption of the existence of a vector potential function but also proved the existence and uniqueness of the exact solution of the studied problem meanwhile an asymptotic analysis and a remainder estimate of the solution are also presented

solving the matrix differential riccati equation a lyapunov equation approach in this technical note we investigate a solution of the matrix differential riccati equation that plays an important role in the linear quadratic optimal control problem unlike many methods in the literature the approach that we propose employs the negative definite anti stabilizing solution of the matrix algebraic riccati equation and the solution of the matrix differential lyapunov equation an illustrative numerical example is provided to show the efficiency of our approach

function theory random paths and covering spaces pour des varietes de riemann connexes m on etudie la relation entre la theorie de fonction harmonique sur m les proprietes statistiques des chemins aleatoires sur m et la structure geometrique globale de m

estimating the plant state from the compensator state for the system dot w sw where w x over z this note states and proves necessary and sufficient conditions under which a z is an estimate of a linear function of x i e z estimates tx or b a linear function of z is an estimate of x i e vz estimates x the mapping t has been used previously by the authors to compute the estimator controller form of a compensator whose state vector z had the same dimension as the plant state vector x

on the relation between additive and multiplicative decompositions of rational matrix functions in this paper a general frame to study relations between additive and multiplicative representations of rational matrix functions is presented various extensions of the positive real lemma as well as of other classical factorization results both in the continuous and discrete time cases are established in the case of square factorizations the map between solutions to an asymmetric algebraic riccati equation and pairs of factors is shown to be a homeomorphism in this framework we also derive a geometric characterization of non square factorizations

the recursive reduced order numerical solution of the singularly perturbed matrix differential riccati equation under stability observability conditions imposed on a singularly perturbed system an efficient numerical method for solving the corresponding matrix differential riccati equation is obtained in terms of the reduced order problems the order reduction is achieved via the use of the chang transformation applied to the hamiltonian matrix of a singularly perturbed linear quadratic control problem an efficient numerical recursive algorithm with a quadratic rate of convergence is developed for solving the algebraic equations comprising the chang transformation

a new filtering method for linear singularly perturbed systems in this paper we present a new method which allows complete decomposition of the optimal global kalman filter for linear singularly perturbed systems into pure slow and pure fast local optimal filters both driven by the system measurements the method is based on the exact decomposition of the global singularly perturbed algebraic riccati equation into pure slow and pure fast local algebraic riccati equations an f 8 aircraft example demonstrates the proposed method

how to obtain transience from bounded radial mean curvature we show that brownian motion on any unbounded submanifold p in an ambient manifold n with a pole p is transient if the following conditions are satisfied the p radial mean curvatures of p are sufficiently small outside a compact set and the p radial sectional curvatures of n are sufficiently negative the sufficiency conditions are obtained via comparison with explicit transience criteria for radially drifted brownian motion in warped product model spaces

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

new iterative algorithm for algebraic riccati equation related to h sub spl infin control problem of singularly perturbed systems we present the solution to the algebraic riccati equation are with indefinite sign quadratic term related to the h sub spl infin control problem for singularly perturbed systems by means of a kleinman type algorithm the resulting algorithm is very efficient from the numerical point of view because the are is solvable even if the quadratic term has an indefinite sign moreover the resulting iterative algorithm is quadratically convergent we also present an algorithm for solving the generalized algebraic lyapunov equation on the basis of the fixed point algorithm

decoupling and order reduction via the riccati transformation a program that dates back to riccati 1724 and that seeks to replace a given differential equation with an equivalent collection of effectively uncoupled equations of lower orders through the use

liouville green approximations via the riccati transformation the riccati transformation is used to obtain liouville green approximations along with error bounds possessing a particularly simple and explicit form for the equation u f t u the resulting error bounds involve the function f and its first derivative whereas the earlier bounds of olver 1961 1974 and taylor 1978 1982 involve also the second derivative of f the theorems given here resemble corresponding results of olver 1974 chapter 6 and indeed the present work owes a great debt to olver the riccati transformation used here is based on work of y sibuya k w chang and w a harris and can be used in a more general study of linear ordinary differential equations and systems of such equations cf smith 1984 1985

decoupling of recessive and nonrecessive solutions for a second order system abstract a riccati transformation is used to obtain liouville green approximations along with error bounds for a vector system u f t u on a real interval a subject to suitable assumptions on the n n matrix valued function f f t

stability analysis and synthesis of fuzzy singularly perturbed systems in this paper we investigate the stability analysis and synthesis problems for both continuous time and discrete time fuzzy singularly perturbed systems for continuous time case both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities lmis for discrete time case only the analysis problem can be cast in lmis while the derived stability conditions for controller design are nonlinear matrix inequalities nmis furthermore a two stage algorithm based on lmi and iterative lmi ilmi techniques is developed to solve the resulting nmis and the stabilizing feedback controller gains can be obtained for both continuous time and discrete time cases the reduced control law which is only dependent on the slow variables is also discussed finally an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures

an estimate for the curvature of bounded submanifolds 1 statement of the result all manifolds considered in this paper shall be connected of class c smooth and dimension at least 2 im mersions will also be smooth and of codimension at least 1 if m and m are riemannian manifolds and p m m is an isometric immersion with the property that sp m lies in a ball we intend to estimate the supremum of the sectional curvature k of m in terms of the sectional curvature k of m and the radius of the ball this is our result theorem a let ml be a complete riemannian manifold whose scalar curvature is bounded below let m q be a riemannian manifold with q c n 1 and bx a closed normal ball in mt4 q of radius x sup pose sp m j m q is an isometric immersion with the property that

a comparison of statistical methods for combining event rates from clinical trials we compare two statistical methods for combining event rates from several studies both methods treat each study as a separate stratum the peto modified mantel haenszel peto method estimates a combined odds ratio assuming homogeneity across strata and provides a test for heterogeneity the dersimonian and laird modified cochran method d l produces a weighted average of rate differences where the weights allow for among study variability we analyse 22 meta analyses from ten reports by both methods the pooled estimates are divided by their standard errors to produce a z statistic a t test comparing z statistics from all 22 studies suggests that the d l method tends to be more conservative d peto d l 0 29 t 2 53 p 0 02 for a subset of 14 non heterogeneous studies the difference is smaller and non significant d 0 09 t 0 72 p 0 49 the results from the methods correlate well r 0 66 for all 22 studies r 0 95 for 14 non heterogeneous studies thus the presence of heterogeneity influences our conclusion we discuss the statistical and scientific implications of these findings

generalized isoperimetric inequalities for extrinsic balls in minimal submanifolds the volume of an extrinsic ball in a minimal submanifold has a well defined lower bound when the ambient manifold has an upper bound on its sectional curvatures see e g 3 and 10 when this upper bound is non positive the second named author has shown an isoperimetric inequality for such domains see 11 this result again gives the comparison result for volumes alluded to above together with a characterization of the totally geodesic submanifolds of hyperbolic space forms in the present paper we find a corresponding sharp isoperimetric inequality for minimal submanifolds in spaces with sectional curvatures bounded from above by any constant as a corollary we find again a characterization of the totally geodesic submanifolds of spherical space forms

a new version of the chang transformation a new decoupling transformation is proposed for singularly perturbed linear systems this transformation has the advantage over the previous one in that in order to find such a transformation only one algorithm is required and the computation can be done in parallel because the transformation matrices are obtained from two independent equations that are identical in form

convergence of the time invariant riccati differential equation and lq problem mechanisms of attraction the nature of the attraction of the solution of the time invariant matrix riccati differential equation towards the stabilizing solution of the algebraic riccati equation is studied this is done on an explicit formula for the solution when the system is stabilizable and the hamiltonian matrix has no eigenvalues on the imaginary axis various aspects of this convergence are analysed by displaying explicit mechanisms of attraction and connections are made with the literature the analysis ultimately shows the exponential nature of the convergence of the solution of the riccati differential equation and of the related finite horizon lq optimal state and control trajectories as the horizon recedes computable characteristics are given which can be used to estimate the quality of approximating the solution of a large finite horizon lq problem by the solution of an infinite horizon lq problem

computing the estimator controller form of a compensator a technique is presented for finding the estimator and controller gains to implement a desired compensator in estimator controller form the technique is derived by mapping the states of the compensator to those of the estimator controller via a linear transformation using the technique involves finding the real invertible solutions of a non symmetric steady state matrix riccati equation the ricatti equation may have zero two or more real invertible solutions from each solution a set of estimator and controller gains can be computed multiple solutions correspond to the freedom to choose which closed loop system poles are associated with the controller and which are associated with the estimator this technique can be applied to multi input multi output systems in an example the technique is applied to the despin control system of a dual spin satellite

asymptotic properties of input output operators norm associated with singularly perturbed systems with multiplicative white noise in this paper we study the problem of the asymptotic property of the norm of input output operators related to a class of singularly perturbed stochastic linear systems the system is under perturbation of multiplicative white noise by using reduction order and boundary layer techniques it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation varepsilon tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma furthermore a stabilizing robust controller is designed which is independent of perturbation varepsilon

brief paper h control for fast sampling discrete time singularly perturbed systems this paper is concerned with the h control problem via state feedback for fast sampling discrete time singularly perturbed systems a new h controller design method is given in terms of solutions to linear matrix inequalities lmis which eliminates the regularity restrictions attached to the riccati based solution a method for evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is also given furthermore the results are extended to robust controller design for fast sampling discrete time singularly perturbed systems with polytopic uncertainties numerical examples are given to illustrate the validity of the proposed methods

singular perturbation modelling of large scale systems with multi time scale property the problem is investigated of singular perturbation modelling which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large scale systems in both continuous and discrete time versions modelling concepts based on structural properties are studied and computer oriented algorithms are developed the results of two time scale systems are extended to multi time scale cases furthermore in order to verify the validity of these studies some numerical examples are given

combining historical and randomized controls for assessing trends in proportions abstract a statistical method for incorporating historical control data in the analysis of proportions is proposed and illustrated the method has as its extremes logistic regressions completely pooling and completely ignoring historical controls the degree of pooling used is determined by the variability from experiment to experiment in the control incidences the fit of historical control groups to an assumed normal logistic model is assessed using probability plotting techniques monte carlo studies evaluate the adequacy of the asymptotic approximation used sensitivity analyses show that results are insensitive to alternative priors the method is applied to several sets of tumor data from animal experiments

h norm and invariant manifolds of systems with state delays abstract the problem of finding bounds on the h norm of systems with a finite number of point delays and distributed delay is considered sufficient conditions for the system to possess an h norm which is less or equal to a prescribed bound are obtained in terms of riccati partial differential equations rpde s we show that the existence of a solution to the rpde s is equivalent to the existence of a stable manifold of the associated hamiltonian system for small delays the existence of the stable manifold is equivalent to the existence of a stable manifold of the ordinary differential equations that govern the flow on the slow manifold of the hamiltonian system this leads to an algebraic finite dimensional criterion for systems with small delays

robust stabilization of two time scale systems with respect to the normalized coprime factorization the present paper has two main purposes the first is to provide an explicit state space solution of the robust stabilization problem with respect to the nlcf for two time scale systems in this construction only the solutions of the control and of the filtering riccati equations associated with the slow and with the fast dynamics of the nominal plant are used these solutions do not depend upon the singular perturbation and therefore all computations are well conditioned the second purpose of the paper is to investigate the case when an k independent robust controller can be used for the robust stabilization of a two time scale nominal system two constructions of such controllers are developed under some additional assumptions numerical examples illustrate the theoretical developments

composite control of non linear singularly perturbed systems a geometric approach using a geometric approach a composite control the sum of a slow control and a fast control is derived for a general class of non linear singularly perturbed systems a new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset the slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of e accuracy

technical communique a revised kleinman algorithm to solve algebraic riccati equation of singularly perturbed systems in this paper we show that the kleinman algorithm can be used well to solve the algebraic riccati equation are of singularly perturbed systems where the quadratic term of the are may be indefinite the quadratic convergence property of the kleinman algorithm is proved by using the newton kantorovich theorem when the initial condition is chosen appropriately in addition the numerical method to solve the generalized algebraic lyapunov equation gale appearing in the kleinman algorithm is given

torsional rigidity of submanifolds with controlled geometry we prove explicit upper and lower bounds for the torsional rigidity of extrinsic domains of submanifolds p m with controlled radial mean curvature in ambient riemannian manifolds n n with a pole p and with sectional curvatures bounded from above and from below respectively these bounds are given in terms of the torsional rigidities of corresponding schwarz symmetrization of the domains in warped product model spaces our main results are obtained using methods from previously established isoperimetric inequalities as found in e g markvorsen and palmer proc lond math soc 93 253 272 2006 extrinsic isoperimetric analysis on submanifolds with curvatures bounded from below p 39 preprint 2007 as in that paper we also characterize the geometry of those situations in which the bounds for the torsional rigidity are actually attained and study the behavior at infinity of the so called geometric average of the mean exit time for brownian motion

geometric analysis of lorentzian distance function on spacelike hypersurfaces some analysis on the lorentzian distance in a spacetime with controlled sectional or ricci curvatures is done in particular we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the omori yau maximum principle as a consequence and under appropriate hypotheses on the sectional or ricci curvatures of the ambient spacetime we obtain sharp estimates for the mean curvature of those hypersurfaces moreover we also give a sufficient condition for its hyperbolicity

singularly perturbed linear boundary value problems abstract in this paper an alternative approach to the method of asymptotic expansions for the study of a singularly perturbed linear system with multiparameters and multiple time scales is developed the method consists of developing a non singular linear transformation that transforms an arbitrary n time scale system into diagonal form this fast and slow mode decomposition provides a modern technique to find an approximate solution of the original system in terms of the solution of an auxiliary system corresponding to the decoupled system furthermore the decoupled system provides a useful mechanism to relate the asymptotic behavior of the solution of the original system and the solution of the degenerate system relative to the original system

a corrective feedback design for nonlinear systems with fast actuators recent two time scale results can be derived from a geometric framework which allows further extensions and computational improvements in this note the two time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control as an illustration we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations

necessary conditions for constant solutions of coupled riccati equations in nash games abstract the asymptotic behaviour of solutions as t for coupled matrix riccati equations occurring in open loop linear quadratic nash games is studied in this paper a general formula representing all possible solutions is given necessary conditions for constant real solutions are derived and an estimate for the rate of convergence is obtained two examples illustrate these results

general transformation for block diagonalization of multitime scale singularly perturbed linear systems in this technical note a general transformation for block diagonalization decoupling of multitime scale singularly perturbed linear systems composed of n subsystems is presented the resulting decoupling corresponds to subsystem time scales and produces n completely independent subsystems operating in different time scales

finite horizon optimal control of singularly perturbed systems a differential lyapunov equation approach in this note we study the finite time horizon optimal control problem for singularly perturbed systems the solution is obtained in terms of the corresponding solution of the algebraic riccati equation and the decomposition of the singularly perturbed differential lyapunov equation into reduced order differential lyapunov sylvester equations an illustrative numerical example is provided to show the efficiency of the proposed approach

new method for optimal control and filtering of weakly coupled linear discrete stochastic systems abstract the algebraic regulator and filter riccati equations of weakly coupled discrete time stochastic linear control systems are completely and exactly decomposed into reduced order continuous time algebraic riccati equations corresponding to the subsystems that is the exact solution of the global discrete algebraic riccati equation is found in terms of the reduced order subsystem nonsymmetric continuous time algebraic riccati equations in addition the optimal global kaiman filter is decomposed into local optimal filters both driven by the system measurements and the system optimal control inputs as a result the optimal linear quadratic gaussian control problem for weakly coupled linear discrete systems takes decomposition and parallelism between subsystem filters and controllers

unified canonical forms for matrices over a differential ring abstract linear differential equations with variable coefficients of the vector form i x a t x and the scalar form ii y n n t y n 1 2 t y 1 t y 0 can be studied as operators on a differential module over a differential ring using this differential algebraic structure and a classical result on differential operator factorizations developed by cauchy and floquet a new variable eigenvalue theory and an associated set of matrix canonical forms are developed in this paper for matrices over a differential ring in particular eight new spectral and modal matrix canonical forms are developed that include as special cases the classical companion jordan diagonal and generalized vandermonde canonical forms as traditionally used for matrices over a number ring field therefore these new matrix canonical forms can be viewed as unifications of these classical ones two additional canonical matrices that perform order reductions of a cauchy floquet factorization of a linear differential operator are also introduced general and explicit formulas for obtaining the new canonical forms are derived in terms of the new variable eigenvalues the results obtained here have immediate applications in diverse engineering and scientific fields such as physics control systems communications and electrical networks in which linear differential equations i and ii are used as mathematical models

parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights abstract let p be a submanifold properly immersed in a rotationally symmetric manifold having a pole and endowed with a weight e h the aim of this paper is twofold first by assuming certain control on the h mean curvature of p we establish comparisons for the h capacity of extrinsic balls in p from which we deduce criteria ensuring the h parabolicity or h hyperbolicity of p second we employ functions with geometric meaning to describe submanifolds of bounded h mean curvature which are confined into some regions of the ambient manifold as a consequence we derive half space and bernstein type theorems generalizing previous ones our results apply for some relevant h minimal submanifolds appearing in the singularity theory of the mean curvature flow

an algorithm for solving the singularly perturbed h algebraic riccati equation abstract the algebraic riccati equation of singularly perturbed h linear quadratic optimal control problems is decoupled into two completely independent reduced order pure slow and pure fast h algebraic riccati equations even though the algebraic riccati equations obtained are nonsymmetric they are efficiently solved in terms of lyapunov iterations by using the newton method the presented algorithm can be used for h parallel filtering and regulation of systems displaying two time scale dynamics

pole placement by performance criterion modification a procedure is presented that modifies the state weighting matrix q and introduces a degree of relative stability into the original performance criterion to shape the resulting optimal dynamics by positioning the closed loop eigenvalues along the real axis of the optimal system in the linear quadratic regulator problem it is based on the results of the algebraic riccati equation are which establish the invariance of certain eigenspaces of the associated hamiltonian matrix with respect to certain perturbations of q and the degree of relative stability

technical communique improvement of system order reduction via balancing using the method of singular perturbations in this paper we first present several alternative techniques for system order reduction based on system balancing by employing the method of singular perturbations the techniques obtained have the same robustness accuracy evaluated with respect to the h norm of the reduced order system as the two techniques existing in the control literature known as the direct truncation and balancing residualization methods the newly proposed techniques preserve the exact dc gain as the original system and produce very good to excellent accuracy at low and medium frequencies we also present a simple formula that fixes the dc gain for the direct truncation method in the second part of the paper we propose how to perform order reduction of a balanced system using theory of singular perturbations that can produce very good accuracy at high frequencies particularly for systems that have lightly damped highly oscillatory modes the result obtained for such kind of systems requires that the modes with higher hankel singular values should be neglected and those with smaller hankel singular values should be retained this is a counter intuitive result in the spirit of h theory but an intuitive result in the spirit of theory of singular perturbations the second part of the paper raises an important question about validity of the system robustness estimate based on the h norm for linear systems with lightly damped highly oscillatory modes

bounds on the optimum quadratic cost of structure constrained controllers in this note lower and upper bounds are derived on the quadratic cost of optimal output feedback controllers subject to constraints on the controller structure the use of these bounds in forming a comparative assessment of alternative controller confugurations is described and an illustrative example is given the principal advantage of these bounds arises from the fact that they can save considerable computational effort

geometric aspects of the riccati difference equation in the nonsymmetric case abstract this paper provides a collection of geometric results concerning the nonsymmetric riccati difference equation it gives representation formulas which express all the solutions in terms of a suitable number of known ones further results include geometric properties of the difference of two solutions and the generalization of some of the author s earlier results to the nonsymmetric case

invariant manifolds and projective combinations of solutions of the riccati differential equation abstract in this paper we show how families of solutions of the general riccati differential equation rde can be generated via projective combinations of a given number of reference solutions our approach is based upon the extension of the domain of the equation to the grassmannian manifold and the application of the radon lemma in this context we briefly discuss the relevance of our results to the study of the invariant manifolds of the equation and compare them to existing results concerning representation formulas for solutions of rde the results of the paper have been motivated by the recent characterization of solutions of the rde given in m pavon d d alessandro families of solution of matrix riccati differential equations siam j control optim 35 1 1997 194 204 which extends the classical results on the algebraic riccati equation due to willems coppel and shayman

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

new approach to block diagonalization of singularly perturbed systems by taylor expansion block diagonalization of a singularly perturbed system requires the solution of the riccati equation and the lyapunov equation a new approach is suggested for both equations using taylor expansions the convergence is studied in detail it is shown that it is ensured under restrictions which are less restrictive than the case of previously suggested methods

h optimal control for singularly perturbed systems part i perfect state measurements we study the h optimal control of singularly perturbed linear systems under perfect state measurements for both finite and infinite horizons using a differential game theoretic approach we show that as the singular perturbation parameter approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions furthermore we construct a composite controller based on the solution of the slow and fast games which guarantees a desired achievable performance level for the full order plant as approaches zero a slow controller however is not generally robust in this sense but still under some conditions which are delineated in the paper the fast dynamics can be totally ignored the paper also studies optimality when the controller includes a feedforward term in the disturbance and presents some numerical examples to illustrate the theoretical results

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

estimates of the first dirichlet eigenvalue from exit time moment spectra we compute the first dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the brownian motion exit times from the ball as an application of the model space theory we prove lower and upper bounds for the first dirichlet eigenvalues of extrinsic metric balls in submanifolds of ambient riemannian spaces which have model space controlled curvatures moreover from this general setting we thereby obtain new generalizations of the classical and celebrated results due to mckean and cheung leung concerning the fundamental tones of cartan hadamard manifolds and the fundamental tones of submanifolds with bounded mean curvature in hyperbolic spaces respectively

geometric properties and invariant manifolds of the riccati equation this short paper considers the general riccati matrix differential equation it reviews and extends results on the characterization and existence of equilibrium solutions establishes that the riccati equation has at most one stable equilibrium solution as t rightarrow infty or t rightarrow infty and confines the region of attraction to this unique stable equilibrium solution by identifying and utilizing linear and nonlinear invariant manifolds of the riccati equation

near optimal h sup spl infin control of linear singularly perturbed systems we consider the singularly perturbed h sup spl infin control problem under perfect state measurements for both finite and infinite horizons we suggest a construction of high order approximations to a controller that guarantees a desired performance level on the basis of the exact decomposition of the full order riccati equations to the reduced order slow and fast equations this leads to effective asymptotic and numerical algorithms we show that the high order accuracy controller improves the performance

on the mean exit time from a minimal submanifold soit m m une sous variete minimale immergee d une variete de riemann n n et on considere le mouvement brownien sur une boule reguliere r cm de rayon exterieur r le temps de sortie moyen pour le mouvement a partir d un point xe r est appele e r x on trouve des fonctions support pointues pour e r x dans plusieurs cas distincts

optimal control of discrete time singularly perturbed systems in this paper we present a new algorithm for solving the optimal control of discrete time singularly perturbed systems the main idea of this algorithm is based on two steps first the hamiltonian difference equation is reduced to the backward recursive form rather than the forward recursive form second the bilinear transformation is applied to transform the derived non symmetric discrete time riccati equations into continuous time equations in order to improve the efficiency of this scheme two matrix permutations are introduced into this algorithm by taking into account the previous work of gajic and shen 1991 therefore substantial numerical advantages are gained namely computation and memory requirements the f 8 aircraft model is used to illustrate the efficiency of the proposed method

exact design manifold control of a class of nonlinear singularly perturbed systems the integral manifold approach captures from a geometric point of view the intrinsic two time scale behavior of singularly perturbed systems an important class of nonlinear singularly perturbed systems considered in this note are fast actuator type systems for a class of fast actuator type systems which includes many physical systems an explicit corrected composite control the sum of a slow control and a fast control is derived this corrected control will steer the system exactly to a required design manifold

numerical methods for singular perturbation problems consider the two point boundary value problem for a stiff system of ordinary differential equations an adaptive method to solve these problems even when turning points are present is discussed

time scale decomposition of linear implicit singularly perturbed systems an implicit singularly perturbed system dot x a epsilon x where a 0 is singular is considered this note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales the decomposed form of the system is used to construct a uniform asymptotic approximation to exp a epsilon t

the exact slow fast decomposition of the algebraic ricatti equation of singularly perturbed systems the algebraic riccati equation for singularly perturbed control systems is completely and exactly decomposed into two reduced order algebraic riccati equations corresponding to the slow and fast time scales the pure slow and pure fast algebraic riccati equations are asymmetric ones but their o epsilon perturbations are symmetric it is shown that the newton method is very efficient for solving the obtained asymmetric algebraic riccati equations the method presented is very suitable for parallel computations due to the complete and exact decomposition of the riccati equation this procedure might produce new insight into the two time scale optimal filtering and control problems

families of solutions of matrix riccati differential equations the j c willems coppel shayman geometric characterization of solutions of the algebraic riccati equation are is extended to asymmetric riccati differential equations with time varying coefficients the coefficients do not need to satisfy any definiteness periodicity or system theoretic condition more precisely given any two solutions x 1 t and x 2 t of such equation on a given interval t 0 t 1 we show how to construct a family of solutions of the same equation of the form x t i pi t x 1 t pi t x 2 t where pi is a suitable matrix valued function even when specialized to the case of x 1 and x 2 equilibrium solutions of a symmetric equation with constant coefficients our results considerably extend the classical ones as no further assumption is made on the pair x 1 x 2 and on the coefficient matrices

a survey of nonsymmetric riccati equations abstract we survey recent and also older results on nonsymmetric matrix riccati differential equations and in the time invariant case on the corresponding algebraic riccati equations in particular we cite various applications connected with matrix riccati equations

exact slow fast decomposition of the singularly perturbed matrix differential riccati equation in this paper the hamiltonian matrix formulation of the riccati equation is used to derive the reduced order pure slow and pure fast matrix differential riccati equations of singularly perturbed systems these pure slow and pure fast matrix differential riccati equations are obtained by decoupling the singularly perturbed matrix differential riccati equation of dimension n 1 n 2 into the pure slow regular matrix differential riccati equation of dimension n 1 and the pure fast stiff matrix differential riccati equation of dimension n 2 a formula is derived that produces the solution of the original singularly perturbed matrix differential riccati equation in terms of solutions of the pure slow and pure fast reduced order matrix differential riccati equations and solutions of two reduced order initial value problems in addition to its theoretical importance the main result of this paper can also be used to implement optimal filtering and control schemes for singularly perturbed linear time invariant systems independently in pure slow and pure fast time scales

composite control of non linear singularly perturbed systems meeting a design objective using the integral manifold approach a composite control the sum of a fast control and a slow control is derived for a particular class of non linear singularly perturbed systems the fast control is designed completely at the outset thus ensuring the stability of the fast transients of the system and furthermore the existence of the integral manifold a new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy though this approach is by its very nature ad hoc the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples

exact slow fast decomposition of the nonlinear singularly perturbed optimal control problem abstract we study the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system which is nonlinear in both the slow and the fast variables it is known that the optimal controller for such problem can be designed by finding a special invariant manifold of the corresponding hamiltonian system we obtain exact slow fast decomposition of the hamiltonian system and of the special invariant manifold into the slow and the fast ones on the basis of this decomposition we construct high order asymptotic approximations of the optimal state feedback and optimal trajectory

torsional rigidity of minimal submanifolds we prove explicit upper bounds for the torsional rigidity of extrinsic domains of minimal submanifolds p m in ambient riemannian manifolds n n with a pole p the upper bounds are given in terms of the torsional rigidities of corresponding schwarz symmetrizations of the domains in warped product model spaces our main results are obtained via previously established isoperimetric inequalities which are here extended to hold for this more general setting based on warped product comparison spaces we also characterize the geometry of those situations in which the upper bounds for the torsional rigidity are actually attained and give conditions under which the geometric average of the stochastic mean exit time for brownian motion at infinity is finite

the use of historical control information in testing for a trend in proportions a problem commonly faced in biometric applications is to test for a trend in proportions in a 2 x k contingency table in which the k columns have a natural ordering for example a test compound may be administered at increasing dose levels to groups of test animals to determine if the proportion of animals developing a tumor increases with increasing dose level cochran 1954 and armitage 1955 proposed a chi square statistic for testing for a trend in proportions for problems with a large amount of historical data a test for trend incorporating the historical data would be useful this paper develops such a test based on a statistic which is closely related to that of cochran and armitage this method for binomial proportions is analogous to the method derived by pocock 1976 for normallydistributed data the problem will be developed in the context of an animal carcinogenesis experiment consider an experiment involving r 1 groups of test animals one group serves as a control group and the remaining r groups are given a test compound at increasing dose levels dld2 dr the animals are followed for a fixed period of time and the number of animals which develop a tumor at a particular organ is recorded for each group let ni denote the number of animals in the ith group and let the number of these animals which develop a tumor during the course of the experiment be denoted by xi i 0 1 r the results of this experiment can be summarized in a 2 x r 1 table such as table 1 to test for ap increase in the proportions pi xjni with increasing dose level cochran and armitage suggested the test statistic

intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds abstract let m g be a complete non compact riemannian manifold together with a function e h which weights the hausdorff measures associated to the riemannian metric in this work we assume lower or upper radial bounds on some weighted or unweighted curvatures of m to deduce comparisons for the weighted isoperimetric quotient and the weighted capacity of metric balls in m centered at a point o m as a consequence we obtain parabolicity and hyperbolicity criteria for weighted manifolds generalizing previous ones a basic tool in our study is the analysis of the weighted laplacian of the distance function from o the technique extends to non compact submanifolds properly immersed in m under certain control on their weighted mean curvature

stabilization of generalized linear systems via the algebraic riccati equation abstract this paper presents results from a study to examine the stabilization properties of linear time delay systems and systems depending on a parameter using techniques associated with the algebraic riccati equation are these classes of systems can be viewed as members of a broader class of systems called generalized linear systems gls techniques of spectral factorization for the gls play an essential role in the methods for performing this stabilization necessary and sufficient conditions for the existence of a polynomial solution to the generalized are are derived numerical examples are given in order to illustrate and clarify the results

brief paper new results on h control of discrete singularly perturbed systems this paper studies the problem of h control of discrete time singularly perturbed systems a new sufficient condition which ensures the existence of state feedback controllers such that the resulting closed loop system is asymptotically stable while satisfying a prescribed h norm bound is obtained this condition is in terms of a linear matrix inequality which is independent of the singular perturbation parameter furthermore a new condition on searching for the allowable upper bound of the singular perturbation parameter is proposed under which the discrete time singularly perturbed system is asymptotically stable with an h norm bound when the singular perturbation parameter is lower than this upper bound in these derived conditions the upper bound of the singular perturbation parameter is not required to be smaller than one the reduced conservatism of our results is demonstrated via a numerical example

improved error bounds for the liouville green or wkb approximation a variant of the gronwall bellman inequality is used to develop new bounds on solutions to the fundamental singular integral equations that arise in the error analysis of the liouville green or wkb approximation consequently new improved error bounds are obtained from the liouville green approximation to the solution of the differential equation d2wdt2 q t w 0 where the function q is real and twice continuously differentiable and does not vanish

variable structure control for singularly perturbed linear continuous systems with matched disturbances a variable structure system can be studied using the singular perturbation theory the discontinuous control that leads to a finite time reaching of the sliding surface creates fast time transients analogous to the stable boundary layer dynamics of a singularly perturbed system as the sliding mode is attained the slow time dynamics prevails just as that of a singularly perturbed system after the boundary layer dynamics fades away in this technical note the problem of sliding mode control for singularly perturbed systems in the presence of matched bounded external disturbances is investigated a composite sliding surface is constructed from solutions of algebraic lyapunov equations which are derived from both the fast and the slow subsystems the resultant sliding motion ensures lyapunov stability with disturbance rejection two proposed schemes that ensure the asymptotic stability of the system are presented the effectiveness of the proposed methods is demonstrated in a numerical example of a magnetic tape control system

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

pooling controls from different studies this paper develops a method for estimating the odds ratio in a case control study that borrows strength from the controls in similar previous studies we assume that the observations within each stratum in the current study are generated from a pair of independent binomial distributions we assume that the observations on the controls again within each stratum and from the previous studies are independent binomial random variables we use these controls to construct a prior distribution for the stratum specific log odds for the controls in the current study which we then combine with the likelihood from the current study to arrive at the posterior distribution of the target quantities of interest the adjusted or stratum specific log odds ratios we assume a diffuse prior distribution for the stratum specific log odds ratio a simulation study investigates the frequency or repeated sampling properties of the inference based upon the posterior distribution of the log odds ratio so constructed

brief paper eigenvector approach for order reduction of singularly perturbed linear quadratic optimal control problems in this paper we show how to decompose the singularly perturbed algebraic riccati equation and the corresponding linear quadratic optimal control problem at steady state in terms of reduced order pure slow and pure fast problems by using the eigenvector approach the eigenvector approach should be used for decomposition of singularly perturbed control systems in the cases when the singular perturbation parameter is not very small in such cases the decomposition methods based on series expansions fixed point iterations subspace iterations and newton iterations either fail to produce solutions of the corresponding algebraic equations or display very slow convergence

the recursive reduced order solution of an open loop control problem of linear singularly perturbed systems a reduced order method with an arbitrary degree of accuracy is obtained for solving the linear quadratic optimal open loop control problem the original two point boundary value problem is transformed into the pure slow and pure fast reduced order completely decoupled initial value problems by doing this the stiffness of the singularly perturbed two point boundary value problem is converted into the problem of an ill defined linear system of algebraic equations