comparison theorems for the matrix riccati equation on deduit une inegalite matricielle a partir d une inegalite differentielle on utilise ce resultat pour deduire des inegalites pour les solutions d equations de riccati matricielles

comparison and uniqueness theorems for periodic riccati differential equations this paper presents some comparison and uniqueness theorems for periodic riccati differential equations prdes precisely it is first shown that for a prde with a positive semidefinite coefficient matrix in the quadratic term under the assumption of stabilizability the solubility of the corresponding riccati differential inequality implies that the prde admits a maximal solution furthermore for the class of prdes mentioned above a monotonicity property is given it is also proven that each stabilizing solution if any for this class of prde is just the maximal solution and thus is unique finally for a prde with a positive definite coefficient matrix in the constant term it is concluded that the stabilizing solution if any is also unique and using this uniqueness result another uniqueness theorem of the stabilizing solution for the general prde is derived

newton s method for a rational matrix equation occurring in stochastic control we study a general class of rational matrix equations which contains the continuous care and discrete dare algebraic riccati equations as special cases equations of this type were encountered in siam j control and optimization 36 1998 1504 1538 stochastics and stochastics reports 65 1999 255 297 where h type problems of disturbance attenuation for stochastic linear systems were studied we develop a unifying framework for the analysis of these equations based on the theory of resolvent positive operators and show that they can be solved by newton s method starting at an arbitrary stabilizing matrix

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

the standard h problem and the maximum principle the general linear case the classical relatively simple ideas of linear quadratic lq optimization are used in a time domain treatment of the standard h infty problem given the power of time domain analysis the problem can be solved in the general framework of linear time varying possibly infinite dimensional finite as well as infinite horizon systems under no structural restrictions such as block dimensions zero blocks in the d operator etc in the spirit of recent finite dimensional linear time invariant lti results the solution is given in terms of two coupled riccati equations it includes a criterion for suboptimality and a parametrization of all suboptimal compensators results pertinent to lti periodic and asymptotic systems are obtained as corollaries

overtaking optimal regulation and tracking of piecewise diffusion linear systems the infinite horizon optimal control of linear stochastic systems with quadratic cost integrand is studied and the tracking of a periodic signal on an infinite time interval is considered the system is exposed to three types of noises and is modeled by a nonhomogeneous linear stochastic control plant with modal and diffusion disturbances where the dynamics switch at random times within a finite number of descriptions according to a markov chain the overtaking optimality criterion is employed considering the expected cost the existence of a unique optimal control is established for the above noisy control systems with partial information this is realized as an affine feedback control of the best estimate of the state moreover in the case of partial information this feedback control is proved to be also almost surely overtaking optimal

nonparametric identification in nonseparable panel data models with generalized fixed effects abstract this paper extends the familiar notion of fixed effects to nonlinear structures with infinite dimensional unobservables like preferences the main result is that a generalized version of differencing identifies local average responses lars in nonseparable structures in contrast to existing results this does not require either substantial restrictions on functional form or independence between the persistent unobservables and the explanatory variables of interest and it requires only two time periods on the other hand the results are confined to the subpopulation of stayers chamberlain 1982 i e the population for which the explanatory variables do not change over time we extend the basic framework to include time trends and dynamics in the explanatory variables and we show how distributional effects as well as average partial effects are identified our approach also allows endogeneity in the transitory unobservables furthermore we show that this new identification principle can be applied to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects finally we suggest estimators for the local average response and average partial effect and we analyze their large and finite sample behavior

on overtaking optimal tracking for linear systems optimal tracking problems involving a time varying linear plant and infinite horizon quadratic performance index are considered in general such problems yield an unbounded performance index for every control and thus must be interpreted as so called overtaking optimal control problems a completing the square argument is used to derive the overtaking optimal control for a general problem formulation and various properties are discussed

an iterative algorithm to solve state perturbed stochastic algebraic riccati equations in lq zero sum games an iterative algorithm to solve a kind of state perturbed stochastic algebraic riccati equation sare in lq zero sum game problems is proposed in our algorithm we replace the problem of solving a sare with an indefinite quadratic term by the problem of solving a sequence of sares with a negative semidefinite quadratic term which can be solved by existing methods under some appropriate conditions we prove that our algorithm is globally convergent we give a numerical example to show the effectiveness of our algorithm our algorithm also has a natural game theoretic interpretation

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

binary response models for panel data identification and information this paper considers a panel data model for predicting a binary outcome the conditional probability of a positive response is obtained by evaluating a given distribution function f at a linear combination of the predictor variables one of the predictor variables is unobserved it is a random effect that varies across individuals but is constant over time the semiparametric aspect is that the conditional distribution of the random effect given the predictor variables is unrestricted this paper has two results if the support of the observed predictor variables is bounded then identification is possible only in the logistic case even if the support is unbounded so that from manski 1987 identification holds quite generally the information bound is zero unless f is logistic hence consistent estimation at the standard pn rate is possible only in the logistic case

sieve m inference on irregular parameters abstract this paper presents sieve inferences on possibly irregular i e slower than root n estimable functionals of semi nonparametric models with i i d data we provide a simple consistent variance estimator of the plug in sieve m estimator of a possibly irregular functional and the asymptotic standard normality of the sieve t statistic we show that for hypothesis testing of irregular functionals the sieve likelihood ratio statistic is asymptotically chi square distributed these results are useful in inference on structural parameters that may have singular semiparametric efficiency bounds a simulation study and an empirical application of heckman and singer 1984 duration model are presented

differential operators and finite dimensional algebras abstract let r be a dedekind domain that is finitely generated over k an algebraically closed field of characteristic zero let m be a torsionfree module of rank one over a subalgebra of r with integral closure r this paper investigates the structure of d m the ring of differential operators on m it is shown that d m has a unique minimal non zero ideal j m and that the factor d m j m is a finite dimensional k algebra this factor is realised as the algebra of all endomorphisms of an associated vector space that preserve certain subspaces the main result is that given any finite dimensional k algebra a there exists such an m with a d m j m

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

testing identifying assumptions in nonseparable panel data models abstract recent work on nonparametric identification of average partial effects apes from panel data require restrictions on individual or time heterogeneity identifying assumptions under the generalized first differencing category such as time homogeneity chernozhukov et al 2013 have testable equality restrictions on the distribution of the outcome variable this paper proposes specification tests based on these restrictions the bootstrap critical values for the resulting kolmogorov smirnov and cramer von mises statistics are shown to be asymptotically valid and deliver good finite sample properties in monte carlo simulations an empirical application illustrates the merits of testing nonparametric identification from an empiricist s perspective

stability radii of systems with stochastic uncertainty and their optimization by output feedback we consider linear plants controlled by dynamic output feedback which are subjected to blockdiagonal stochastic parameter perturbations the stability radii of these systems are characterized and it is shown that for real data the real and the complex stability radii coincide a corresponding result does not hold in the deterministic case even for perturbations of single output feedback type in a second part of the paper we study the problem of optimizing the stability radius by dynamic linear output feedback necessary and sufficient conditions are derived for the existence of a compensator which achieves a suboptimal stability radius these conditions consist of a parametrized riccati equation a parametrized liapunov inequality a coupling inequality and a number of linear matrix inequalities one for each disturbance term the corresponding problem in the deterministic case the optimal mu synthesis problem is still unsolved

global solutions to a game theoretic riccati equation of stochastic control abstract in this paper the existence of global solutions to game theoretic riccati equations associated to a controlled stochastic differential equation with state dependent white noise is investigated one proves that if a stabilizing and attenuating feed back exists then a matrix differential game theoretic riccati equation of stochastic control has a unique global bounded stabilizing positive semidefinite solution this solution is periodic if the coefficients are periodic functions and it solves an algebraic riccati equation if the coefficients are constant conversly if such a solution exists it allows an explicit construction of a stabilizing and disturbance attenuating state feedback

h2 optimal control for linear stochastic systems the aim of the present paper is to provide an optimal solution to the h 2 state feedback and output feedback control problems for stochastic linear systems subjected both to markov jumps and to multiplicative white noise it is proved that in the state feedback case the optimal solution is a static gain which is also optimal in the class of all higher order controllers in the output feedback case the optimal h 2 controller has the same order as the given stochastic system the realization of the optimal controllers depend on the stabilizing solutions of some appropriate systems of riccati type coupled equations an effective iterative convergent algorithm to compute these stabilizing solutions is also presented the paper gives some illustrative numerical example allowing to compare the results obtained by the proposed design approach with the ones presented in the recent control literature

a sufficient condition for linear quadratic stochastic zero sum differential games for markov jump systems in this note we consider the linear quadratic stochastic zero sum differential game lq szsdg for the markov jump system mjs driven by brownian motion unlike previous work considered in the literature the diffusion term of the mjs is dependent on the state and the control of both players and the cost parameters need not be definite matrices we obtain a sufficient condition under which a feedback saddle point for the lq szsdg exists we show that the corresponding feedback saddle point is linear in the state and can be characterized in terms of a set of coupled riccati differential equations crdes we also discuss the solvability of the crdes and verify the solvability through numerical examples under the existence condition of the saddle point

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

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

periodic strong solutions of periodically time varying matrix riccati equations abstract generalized conditions for the existence of periodic strong solutions in periodically time varying matrix riccati equations are derived first the precise structure of eigenvalues on the unit circle of the transition matrix associated with the hamil tonian matrix and that of the corresponding generalized eigenvectors are clarified in relation to the quasi detectability and quasi stabilizability of the system then such analysis is applied for deriving the conditions for the existence of a unique periodic real symmetric and non negative definite solution in the periodically time varying matrix riccati equation

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

a numerical procedure to compute the stabilising solution of game theoretic riccati equations of stochastic control in this article the problem of the numerical computation of the stabilising solution of the game theoretic algebraic riccati equation is investigated the riccati equation under consideration occurs in connection with the solution of the h control problem for a class of stochastic systems affected by state dependent and control dependent white noise and subjected to markovian jumping the stabilising solution of the considered game theoretic riccati equation is obtained as a limit of a sequence of approximations constructed based on stabilising solutions of a sequence of algebraic riccati equations of stochastic control with definite sign of the quadratic part the proposed algorithm extends to this general framework the method proposed in lanzon feng anderson and rotkowitz lanzon a feng y anderson b d o and rotkowitz m 2008 computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term viaa recursive method ieee transactions on automat

some remarks on the riccati equation arising in an optimal control problem with state and control dependent noise this paper solves a quadratic optimal control for a linear stochastic evolution equation with unbounded coefficients it is assumed that the stochastic noise depends both on the state and on the control the dynamic programming approach is used and attention is focused on the riccati equation in 5 and 6 some attractivity and maximality properties of the solutions of the algebraic riccati equation are proved and it is shown that in some special cases there exists a maximal solution

properties of the solutions of rational matrix difference equations abstract we prove a comparison theorem for the solutions of a rational matrix difference equation generalizing the riccati difference equation and existence and convergence results for the solutions of this equation moreover we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing or almost stabilizing solution

binary response correlated random coefficient panel data models abstract in this paper we consider binary response correlated random coefficient crc panel data models which are frequently used in the analysis of treatment effects and demand of products we focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors our identification conditions and estimation are based on the framework of the model with a special regressor which is a novel approach proposed by lewbel 1998 lewbel 2000 to solve the heterogeneity and endogeneity problem in the binary response models with the help of the additional information on the special regressor we can transform a binary response crc model to a linear moment relation we also construct a semiparametric estimator for the average slopes and derive the n normality result further we propose a nonparametric method to test the correlations between random coefficients and regressors simulations are given to show the finite sample performance of our estimators and test statistics

individual and time effects in nonlinear panel models with large n t fixed eects estimators of nonlinear panel data models can be severely biased because of the well known incidental parameter problem we develop analytical and jackknife bias corrections for nonlinear models with both individual and time eects under asymptotic sequences where the time dimension t grows with the cross sectional dimension n the time eects introduce additional incidental parameter bias as the existing bias corrections apply to models with only individual eects we derive the appropriate corrections the basis for the corrections are general asymptotic expansions of xed eects estimators with incidental parameters in multiple dimensions we apply the expansions to m estimators with concave objective functions in parameters for panel models with additive individual and time eects these estimators cover xed eects estimators of the most popular limited dependent variable models such as logit probit ordered probit tobit and poisson models our analysis therefore extends the use of large t bias adjustments to an important class of models we also develop bias corrections for functions of the data parameters and individual and time eects including average partial eects in this case the incidental parameter bias is asymptotically of second order in general but the corrections improve nite sample properties

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

systems of matrix rational differential equations arising in connection with linear stochastic systems with markovian jumping abstract in this paper a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled riccati differential equations arising in connection with control of some linear stochastic systems is considered the system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite dimensional hilbert space adequately choosen this allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of lyapunov type our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions conditions providing the existence of a maximal solution minimal solution respectively with respect to some classes of global solutions are presented it is shown that if the coefficients of the equations are periodic functions all these special solutions stabilizing maximal minimal are periodic functions too whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves

multiplicative error models with sample selection this paper presents a simple approach to deal with sample selection in models with multiplicative errors models for non negative limited dependent variables such as counts fit this framework the approach builds on a specification of the conditional mean of the outcome only and is therefore semiparametric in nature gmm estimators are constructed for both cross section data and for panel data we derive distribution theory and present monte carlo evidence on the finite sample performance of the estimators

static output feedback of state multiplicative systems with application to altitude control a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with stochastic multiplicative wiener type noise that achieves a minimum bound on either the stochastic h 2 or the h performance level is introduced a solution is achieved also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope the stochastic uncertainties appear in both the dynamic and the measurement matrices of the system the problems are solved using the expected value of the standard performance index over the stochastic parameters the theory developed is applied to an altitude control example

average and quantile effects in nonseparable panel models nonseparable panel models are important in a variety of economic settings including discrete choice this paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument partial identification results for average and quantile effects are given for discrete regressors under static or dynamic conditions in fully nonparametric and in semiparametric models with time effects it is shown that the usual linear fixed effects estimator is not a consistent estimator of the identified average effect and a consistent estimator is given a simple estimator of identified quantile treatment effects is given providing a solution to the important problem of estimating quantile treatment effects from panel data bounds for overall effects in static and dynamic models are given the dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity the impact of t the number of time periods is shown by deriving shrinkage rates for the identified set as t grows we also consider semiparametric discrete choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds computationally convenient methods for semiparametric models are presented we propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples we give empirical illustrations

nonlinear overtaking optimal control sufficiency stability and approximation the authors consider infinite horizon nonlinear optimal control problems with unbounded performance indexes using notions of overtaking optimality in the framework of optimal control new sufficient conditions of caratheodory hamilton jacobi type for both weak overtaking and overtaking optimality are presented and compared with known results from the calculus of variations setting using local structural properties of a related control hamiltonian conclusions are drawn on aspects of existence of overtaking and weak overtaking optimal controls stability of optimal trajectories and approximation of weak overtaking optimal controls both similarities and differences among alternative approaches to overtaking weak overtaking and strong optimal control problems are discussed the formulation and results are illustrated in the classical linear quadratic tracking problem and in an optimization approach to gain scheduling

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

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

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

heterogeneity and selection in dynamic panel data abstract the data generating process dgp for generic dynamic panel data consists of a law of state dynamics g a selection or attrition rule h and an initial condition f i study nonparametric identifiability of this complete dgp g h f using short unbalanced panel data allowing for nonseparability between observed states and unobserved heterogeneity in each of g h and f for t 3 the dgp is identified by using a proxy variable for t 6 the three additional periods construct a proxy and thus the dgp is identified without an auxiliary variable

quadratic control for linear time varying systems an infinite dimensional linear time varying system on the interval infty infty is considered we introduce three quadratic problems the infinite horizon problem and one sided and two sided average cost problems a riccati equation on infty infty is considered first and sufficient conditions for the existence and uniqueness of a bounded solution are given then by dynamic programming the quadratic problems are solved similar problems in the stochastic case are considered

endomorphisms of right ideals of the weyl algebra let a a k be the first weyl algebra over an infinite field k let p be any noncyclic projective right ideal of a and set s end p we prove that as k algebras s f a in contrast there exists a noncyclic projective right ideal q of s such that s end q thus despite the fact that they are morita equivalent s and a have surprisingly different properties for example under the canonical maps autk a pick a pick s in contrast autk s has infinite index in pick s introduction given a comnmutative domain r the first weyl algebra a r is defined to be the associative r algebra thus r is central subring generated by elements x and y subject to the relation xy yx 1 when no ambiguity is possible we write a for a r let f be a field of characteristic zero then a a f is a simple ring and indeed may be thought of as one of the nicest and most important examples of simple noetherian rings the initial motivation for this paper was the following result of smith if p is the noncyclic right ideal p x2a xy 1 a of a then end p t a as f algebras 11 note that as char f 0 a is a simple hereditary ring and so end p is automatically morita equivalent to a even worse as pedp ada 17 the full matrix rings m2 a and m2 end p are isomorphic thus any proof of smith s result must be fairly subtle and may therefore provide useful invariants for a the first main aim of this paper is to generalize smith s result to an arbitrary projective right ideal of a while the proof of this is harder than that of smith s result it does provide a more informative proof in the sense that unlike smith we do not and cannot require an explicit description of end p for the rest of this introduction k will denote a field of arbitrary characteristic and all isomorphisms of rings will be k algebra isomorphisms theorem a let p be a projective right ideal of a a k then end p a if and only if p is a cyclic right ideal of a see theorem 3 1 this has some easy corollaries corollary b let p and q be projective right ideals of a a k then end p end q if and only if p to q for some t e d k the division ring of fractions of a and a e autk a the group of k automorphisms of a received by the editors february 13 1986 1980 mathematics subject classification 1985 revision primary 16a65 16a72 16a19 supported in part by an nsf grant 1987 american mathematical society 0002 9947 87 1 00 25 per page

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

an optimal stochastic production planning problem with randomly fluctuating dem and this paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous time markov chain the problems with control production and state inventory constraints are treated it is shown that a unique optimal feedback solution exists after first showing that convex viscosity solutions to the associated dynamic programming equation are continuously differentiable

brief paper soft constrained stochastic nash games for weakly coupled large scale systems in this paper we discuss infinite horizon soft constrained stochastic nash games involving state dependent noise in weakly coupled large scale systems first we formulate linear quadratic differential games in which robustness is attained against model uncertainty it is noteworthy that this is the first time conditions for the existence of robust equilibria have been derived based on the solutions of sets of cross coupled stochastic algebraic riccati equations csares after establishing an asymptotic structure with positive definiteness for csares solutions we derive a recursive algorithm by means of newton s method so that it can be used to obtain solutions for csares as another important feature we propose a high order approximate nash strategy based on iterative solutions finally we provide a numerical example to verify the efficiency of the proposed algorithms

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

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

a note on an lqg regulator with markovian switching and pathwise average cost we study a linear system with a markovian switching parameter perturbed by white noise the cost function is quadratic under certain conditions we find a linear feedback control which is almost surely optimal for the pathwise average cost over the infinite planning horizon

solvability and asymptotic behavior of generalized riccati equations arising in indefinite stochastic lq controls the optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential riccati equation in this paper we provide general necessary and sufficient conditions for the solvability of this generalized differential riccati equation furthermore its asymptotic behavior is investigated along with its connection to the generalized algebraic riccati equation associated with the linear quadratic control problem in finite time horizon examples are presented to illustrate the results established

the linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and markovian jumping in this paper the linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and markovian jumping is investigated two classes of admissible controls are considered one of these classes contains controls with additional property that corresponding trajectories tend to zero in mean square when tends to spl infin while concerning the controls contained in the second class of admissible controls there is not any stability assumption in the optimization problem over the first class of admissible controls the cost functional could have indefinite sign of weights matrices an iterative procedure to compute the maximal solution of the systems of generalized riccati equations is provided a numerical example to illustrate the applicability of the iterative procedure is given

comparison theorems for the matrix riccati equation abstract we derive comparison theorems for the matrix valued riccati equations of the form r i z b i z a i z r i z r i z d i z r i z c i z r i z r i 0 r 0 i i 1 2 such equations arise in transport problems and other applications sufficient conditions under which r 1 z r 2 z 0 and r 1 z r 2 z 0 in the componentwise sense for all z are given respectively the comparison theorems in which the positivity is defined in terms of positive semidefiniteness were obtained by royden because of the intrinsic disparity in the nature of positivity structure the techniques developed there cannot be applied to our problem

robust h control with maximal decay rate for linear discrete time stochastic systems abstract the problems of robust stabilization and robust h control with maximal decay rate are investigated for discrete time stochastic systems with time varying norm bounded parameter uncertainties for the robust stabilization problem an optimal state feedback controller is designed which ensures that the closed loop system is robustly stochastically stable with maximal decay rate while for the robust h control problem the designed state feedback controller guarantees that the resulting closed loop system is with a specified h performance level besides robust stochastic stability with maximal decay rate the method based on the convex optimization and linear matrix inequality is developed to solve these problems two examples are provided to show the effectiveness of the proposed approach

rings of operators on modules over commutative rings and their right ideals suppose that there is an inclusion ofk algebrasr e endkmwithrcommutative andenon commutative we introduce and impose conditions under which the finitely generated essential right ideals ofemay be classified in terms ofk submodules ofm this yields a classification of the domains morita equivalent toewheneis a noetherian domain for example a special case of our results is theorem let r be a commutative noetherian k algebra which is domain let e be a simple ore extension of r of the form r x x 1 or r x in the latter case we must also assume r 3 then for a certain sublatticelof the lattice of k submodules of r a every non zero right ideal of e is isomorphic to one of the form formula for some v l b every domain morita equivalent to e is isomorphic to formula for some v l conversely if r is dedekind then e v is morita equivalent to e for v l