nonlinear state feedback for l 1 optimal control this paper considers l1 optimal control problems with full state feedback in contrast to h optimal control previous work has shown that linear l1 optimal controllers can be dynamic and arbitrarily high order however this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback the derivation which is nonconstructive relies on concepts from viability theory

feedback control for linear time invariant systems with state and control bounds in the presence of disturbances the problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered the only information required about the disturbances is a finite convex polyhedral bound discrete and continuous time systems are considered the property of positive d invariance of a region is introduced and it is proved that a solution of the problem is achieved by the selection of a polyhedral set s and the computation of a feedback matrix k such that s is positively d invariant for the closed loop system it is shown that if polyhedral sets are considered the solution involves simple linear programming algorithms however the procedure suggested requires a great amount of computational work offline if the state space dimension is large because the feedback matrix k is obtained as a solution of a large set of linear inequalities all of the vertices of s are required

the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

linear nonquadratic optimal control we consider the optimization of nonquadratic measures of the transient response we present a computational implementation of dynamic programming recursions to solve finite horizon problems in the limit the finite horizon performance converges to the infinite horizon performance we provide conditions based on finite horizon computations which only assure that a receding horizon implementation of the finite horizon optimal control is stabilizing and within a specified tolerance of the infinite horizon performance

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

brief optimal induced l1 norm state feedback control state feedback synthesis is considered for linear discrete time systems to minimize an upper bound of the closed loop induced l 1 norm a sufficient condition called generalized bounded real inequality gbri is presented to establish such a bound an algorithm similar to the invariant kernel algorithm shamma ieee trans automat control 41 1996 533 544 and the contractive set algorithm blanchini ieee trans automat control 39 1994 428 433 reduces the analysis and synthesis problems to linear programming if the problem is feasible our algorithm gives a polyhedral set that induces a closed loop lyapunov function and leads to feasible control laws an example is given for which the optimal induced l 1 norm achieved by a linear controller is achieved by our synthesis approach

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

further results on linear nonquadratic optimal control continues an investigation by the authors of minimizing the transient response of a linear system as measured by nonquadratic penalty functions in particular penalty functions which have linear growth first this note shows that the optimal state feedback which minimizes the transient response in the case of no exogenous inputs also minimizes the induced l sup 1 norm in case exogenous inputs are present second it considers the case of constrained systems and derives bounds which establish the stability and performance of receding horizon control laws finally this note illustrates the results for scheduling of reliable manufacturing systems

posterior likelihood methods for multivariate survival data this article deals with the semiparametric analysis of multivariate survival data with random block group effects survival times within the same group are correlated as a consequence of a frailty random block effect the standard approaches assume either a parametric or a completely unknown baseline hazard function this paper considers an intermediate solution that is a nonparametric function that is reasonably smooth this is accomplished by a bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard the posterior likelihood based on data as well as the prior process is similar to the discretized penalized likelihood for the frailty model the methodology is exemplified with the recurrent kidney infections data of mcgilchrist and aisbett 1991 biometrics 47 461 466 in which the times to infections within the same patients are expected to be correlated the reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

tests for variation over groups in survival data abstract when survival data can be divided into natural groups such as in a clinical trial with patients from a number of different institutions the question arises whether effects are different for the different groups for situations where one is concerned with a random pattern of variation over groups this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups these tests are closely related to the locally most powerful tests of liang for testing for variation across a large number of strata the tests are applied to data from a lung cancer trial conducted by the eastern cooperative oncology group

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

probabilistic output admissible set for systems with time varying uncertainties this paper considers time varying uncertain constrained systems and develops a method for computing a probabilistic output admissible poa set this set consists of the initial states probabilistically assured to satisfy the constraint the time invariant counterpart has already been investigated in hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear we first define the poa set for time varying uncertainties with finite dimensional probability space then we show that an algorithm similar to hatanaka and takaba computations of probabilistic output admissible set for uncertain constrained systems automatica 44 2 2008 to appear provides the poa set also in the time varying case as long as an upper bound of a what we call future output admissibility foa index is available we moreover present two methods for computing the upper bound of the foa index probabilistic and deterministic methods a numerical simulation demonstrates the effectiveness of our algorithm

computation of maximal safe sets for switching systems the problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models given the practical and theoretical relevance of the problem finding implementable procedures that could at least approximate the maximal safe set is important to this end we begin by restricting our attention to a special class of hybrid systems switching systems we exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set this procedure requires the computation of a maximal controlled invariant set we then restrict our attention to linear discrete time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets however even for this class of systems the computation may not converge in a finite number of steps we then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained a tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set our procedure is applied to the idle speed regulation problem in engine control to demonstrate its efficiency

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

bayesian tests and model diagnostics in conditionally independent hierarchical models abstract consider the conditionally independent hierarchical model cihm in which observations yi are independently distributed from f yi i the parameters i are independently distributed from distributions g and the hyperparameters are distributed according to a distribution h the posterior distribution of all parameters of the cihm can be efficiently simulated by markov chain monte carlo mcmc algorithms although these simulation algorithms have facilitated the application of cihms they generally have not addressed the problem of computing quantities useful in model selection this article explores how mcmc simulation algorithms and other related computational algorithms can be used to compute bayes factors that are useful in criticizing a particular cihm in the case where the cihm models a belief that the parameters are exchangeable or lie on a regression surface the bayes factor can measure the consistency of the data with the structural prior belief bayes factors can also be u

computation of minimum time feedback control laws for discrete time systems with state control constraints the problem of finding a feedback law that drives the state of a linear discrete time system to the origin in minimum time subject to state control constraints is considered algorithms are given to obtain facial descriptions of the m step admissible sets these descriptions are then used to characterize the complete class of minimum time feedback laws moreover the characterization leads to a conceptually simple on line implementation the main ideas are illustrated with two simple examples

a quadratic programming approach for solving the l sub 1 multiblock problem the authors present a new method to compute solutions to the general multiblock l sub 1 control problem the method is based on solving a standard h sub 2 problem and a finite dimensional semidefinite quadratic programming problem of appropriate dimension the new method has most of the properties that separately characterize many existing approaches in particular as the dimension of the quadratic programming problem increases this method provides converging upper and lower bounds on the optimal l sub 1 norm and for well posed multiblock problems ensures the convergence in norm of the suboptimal solutions to an optimal l sub 1 solution the new method does not require the computation of the interpolation conditions and it allows the direct computation of the suboptimal controller

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

on nonlinear state feedback controllers for persistent disturbance rejection abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant in the state feedback case there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance in the case of d 12 square and invertible we show that it is enough to have the nonlinearity on a particular substate which can be used to significantly simplify the design problem

l sub 2 state feedback control with a prescribed rate of exponential convergence in this paper we consider the l sub 1 state feedback problem with an internal stability constraint in particular we establish the connection between controlled invariant contractive sets and static control laws that achieve a level of l sub 1 performance as well as a desired unforced rate of convergence we outline two algorithms for computing controlled invariant contractive sets the first is a modification of standard recursive techniques used in the literature whereas the second is based on dynamic games and involves solving an appropriate discrete isaacs recursion the latter approach results in a min max characterization of l sub 1 state feedback controllers we point out that the isaacs recursion provides a one shot as opposed to iterative computation of the optimal l sub 1 performance

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

brief set valued methods for linear parameter varying systems we consider stability analysis and state feedback synthesis for linear parameter varying lpv systems lpv systems are defined as linear systems whose dynamics depend on exogenous time varying parameters stability analysis of lpv systems involves testing the stability of a family of possible parameter trajectories similarly stabilization and optimal control of lpv systems involves constructing feedback for a family of possible parameter trajectories a further constraint is that the feedback depends on parameter trajectories in a causal manner previous work has considered lpv systems with unconstrained i e arbitrarily fast parameter variations we consider the utilization of known constraints on the parameter variations such as rate constraints for discrete time lpv systems whose parameters take on a finite set of values we provide constructive computational algorithms which nonconservatively assess stabilizability these algorithms lead to parameter dependent lyapunov functions for stability and parameter dependent nonlinear state feedback for stabilization we further provide algorithms to construct whenever possible nonlinear feedback to achieve a specified level of disturbance rejection as measured by signal magnitude we also consider the dynamic game of minimizing a transient response as measured by a norm summation and provide algorithms to construct the optimal cost and near optimal nonlinear feedback

semiparametric bayesian analysis of multiple event time data abstract multiple event time data e g carcinogenic growths in different times and locations multiple attacks of cardiac arrest arise in various medical studies a bayesian analysis of such data based on proportional intensity model of multiple event time data is presented in this paper the bayesian structure is somewhat analogous to that used by kalbfleisch in a proportional hazard model an unobserved random frailty component is used in the proportional intensity model to take care of heterogeneity among the intensity processes in different subjects the monte carlo method of sampling from multivariate distributions the so called gibbs sampler is used to sample from the joint posterior distribution of the unknown parameters the methodology developed here is exemplified with the well known data set on rat tumors of gail santner and brown

minimization of the worst case peak to peak gain via dynamic programming state feedback case considers the problem of designing a controller that minimizes the worst case peak to peak gain of a closed loop system in particular we concentrate on the case where the controller has access to the state of a linear plant and it possibly knows the maximal disturbance input amplitude we apply the principle of optimality and derive a dynamic programming formulation of the optimization problem under mild assumptions we show that at each step of the dynamic program the cost to go has the form of a gauge function and can be recursively determined through simple transformations we study both the finite horizon and the infinite horizon case under different information structures the proposed approach allows us to encompass and improve earlier results based on viability theory in particular we present a computational scheme alternative to the standard bisection algorithm or gamma iteration that allows us to compute the exact value of the worst case peak to peak gain for any finite horizon we show that the sequence of finite horizon optimal costs converges as the length of the horizon goes to infinity to the infinite horizon optimal cost the sequence of such optimal costs converges from below to the optimal performance for the infinite horizon problem we also show the existence of an optimal state feedback strategy that is globally exponentially stabilizing and derive suboptimal globally exponentially stabilizing strategies from the solutions of finite horizon problems

optimization of the l sup spl infin induced norm under full state feedback this paper considers the l sup spl infin optimal control problem i e minimization of the effects of disturbances as measured by the l sup spl infin induced norm earlier work showed that even in the case of full state feedback optimal and near optimal linear controllers may be dynamic and of arbitrarily high order however previous work by the author derived the existence of near optimal nonlinear controllers which are static this paper presents a constructive algorithm for such nonlinear controllers the main idea is to construct a certain subset of the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to this set a construction of this subset requires the solution of several finite linear programs with the number of variables being at least the number of states but less than the number of states plus the number of controls the concept of controlled invariance plays a central role throughout

selecting factors predictive of heterogeneity in multivariate event time data in multivariate survival analysis investigators are often interested in testing for heterogeneity among clusters both overall and within specific classes we represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models ranging from a null model with no random effects to a full model having random effects for each class following a bayesian approach we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse gamma densities since frailties with zero variance effectively drop out of the model this prior allocates probability to each model in the sequence including the overall null hypothesis of homogeneity using a counting process formulation the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms posterior computation proceeds via a data augmentation gibbs sampling algorithm a single run of which can be used to obtain model averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure the methods are illustrated using data from a lung cancer trial

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

constrained regulation of linear systems abstract in this paper the linear constrained regulation problem without an assigned set of initial states is investigated this problem consists of the determination of a linear state feedback control law and of a set of admissible initial states d so that every trajectory of the resulting closed loop system which emanates from the set converges asymptotically to the origin without violation of the control constraints by applying well known results on the positive invariance of polyhedral sets an eigenstructure assignment approach to this problem is established if the number of unstable open loop eigenvalues does not exceed the number of control variables then this approach enables one to derive a linear state feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant this positively invariant set is the maximal admissible set of initial states for the control law under consideration for the case where the number of control variables is greater than the number of the unstable open loop eigenvalues a modified algorithm is proposed

some necessary and sufficient conditions for admitting a continuous sphere order representation of two dimensional space times a space time may be regarded as a partially ordered set by causal relations recently as a poset a sphere order representation of a space time is considered and some interesting results are obtained in this paper we define a weakly causally convex open set and characterize connected open subsets of the n dimensional minkowski space time which admit a continuous n sphere order representation then some necessary and sufficient conditions for admitting a continuous two sphere order representation of two dimensional space times are given as a result it is shown that any simply connected and causally simple space time of dimension two can be causally isomorphically imbedded into the two dimensional minkowski space time

sphere orderings representation of space time a space time may be regarded as a partially ordered set by causal relations r j low considered a continuous sphere order representation of a space time and obtained some interesting results however some important questions about the conditions of continuity of this representation are still left unanswered in this paper we considered the problem of continuity and presented a partial solution for the set of all discontinuity points of a sphere order representation and constructed an example of a space time which could not admit a sphere order representation with a special dimension we also showed that for a poset the definition of the 2 sphere ordering dimension is equivalent to the definition of the 2 euclidian dimension

an algorithm to find maximal state constraint sets for discrete time linear dynamical systems with bounded controls and states an algorithm to find a polyhedral approximant to the maximal state constraint set given state and input bounds is suggested for linear discrete time dynamical systems

set valued observers and optimal disturbance rejection a set valued observer also called guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals we consider the guaranteed state estimation problem for linear time varying systems with a priori magnitude bounds on exogenous signals we provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l sup spl infin induced norm sense we then consider the utility of set valued observers for disturbance rejection with output feedback and derive the following general separation structure an optimal controller can consist of a set valued observer followed by a static nonlinear function on the observed set of possible states a general construction of this function is provided in the scalar control case furthermore in the special case of full control i e the number of control inputs equals the number of states optimal output feedback controllers can take the form of an optimal estimate of the full state feedback controller

the geometry of the space of null geodesics the topology and geometry of the space of null geodesics n of a space time m are used to study the causal structure of the space time itself in particular the question of whether the topology of n is hausdorff or admits a compatible manifold structure carries information on the global structure of m and the transversality properties of the intersections of skies of points tell whether the points are conjugate points on a null geodesic

worst case analysis of nonlinear systems the authors work out a framework for evaluating the performance of a continuous time nonlinear system when this is quantified as the maximal value at an output port under bounded disturbances the disturbance problem this is useful in computing gain functions and l sub spl infin induced norms which are often used to characterize performance and robustness of feedback systems the approach is variational and relies on the theory of viscosity solutions of hamilton jacobi equations convergence of euler approximation schemes via discrete dynamic programming is established the authors also provide an algorithm to compute upper bounds for value functions differences between the disturbance problem and the optimal control problem are noted and a proof of convergence of approximation schemes for the control problem is given case studies are presented which assess the robustness of a feedback system and the quality of trajectory tracking in the presence of structured uncertainty

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

generalized score test of homogeneity based on correlated random effects models summary we present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing in these models each subject has a particular random effect but the random effects between subjects are correlated we derive the general form of the score statistic for testing that the random effects have a variance equal to 0 we apply this result to both parametric and semiparametric models in both cases we show that under certain conditions the score statistic has an asymptotic normal distribution we consider several applications of this theory including overdispersion heterogeneity between groups spatial correlations and genetic linkage

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

a goodness of fit test for cox s proportional hazards model based on martingale residuals a goodness of fit test for cox s proportional hazards model is proposed on the basis of martingale residuals the test is derived as the score test for the presence of an extra random effect in the exponential part of the hazard function assumptions about the distribution of the random effects are not made only the correlation matrix must be specified this can be done on the basis of an existing division of individuals into groups such as families or on the basis of the distance between observed covariates the variance of the test statistic is derived using a counting process approach corrections for the estimation of parameters are available the test is demonstrated in a simulated data set as well as in a real data set on ovarian cancer

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

optimization over state feedback policies for robust control with constraints this paper is concerned with the optimal control of linear discrete time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input it is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence this implies that a broad class of constrained finite horizon robust and optimal control problems where the optimization is over affine state feedback policies can be solved in a computationally efficient fashion using convex optimization methods this equivalence result is used to design a robust receding horizon control rhc state feedback policy such that the closed loop system is input to state stable iss and the constraints are satisfied for all time and all allowable disturbance sequences the cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance free state and input sequences the value of the receding horizon control law can be calculated at each sample instant using a single tractable and convex quadratic program qp if the disturbance set is polytopic or a tractable second order cone program socp if the disturbance set is given by a 2 norm bound

three measures of explained variation for correlated survival data under the proportional hazards mixed effects model measures of explained variation are useful in scientific research as they quantify the amount of variation in an outcome variable of interest that is explained by one or more other variables we develop such measures for correlated survival data under the proportional hazards mixed effects model because different approaches have been studied in the literature outside the classical linear regression model we investigate three measures r 2 rres2 and 2 that quantify three different population coefficients we show that although the three population measures are not the same they reflect similar amounts of variation explained by the predictors among the three measures we show that r 2 which is the simplest to compute is also consistent for the first population measure under the usual asymptotic scenario when the number of clusters tends to infinity the other two measures on the other hand all require that in addition the cluster sizes be large we study the properties of the measures both analytically and through simulation studies we illustrate their different usage on a multi center clinical trial and a recurrent events data set copyright 2016 john wiley sons ltd

a decomposition approach to distributed control of spatially invariant systems this note considers the decentralized control of spatially invariant systems i e systems of homogeneous interacting components the main idea is for individual components to model interactions with neighbors as disturbances that satisfy certain magnitude bounds while simultaneously self imposing symmetric magnitude bounds these magnitude bounds can be interpreted as negotiated levels of interaction among components it turns out that this approach is equivalent to constructing a feedback that is robustly stabilizing with structured uncertainties

on positively invariant sets for discrete time linear systems with disturbance an application of maximal disturbance sets this note concerns the investigation of maximal sets with respect to which a set is positively invariant and given a set a some properties of spl delta p i sets are analyzed the approach uses one step of the backward recursion introduced in d alessandro and de santis 1991 where feasibility and optimality conditions for linear dynamical input and or state constrained systems were analyzed in section ii the author gives the main definitions and some basic results in the subsequent section iii some properties of spl delta p i sets are investigated the particular case of polyhedral sets is analyzed in section iv in section v the author shows an application to linear systems with parametric uncertainties in the dynamic matrix a the author develops a technique to determine a set in the parameters space such that for any value of the parameter in the set a given set in the state space is positively invariant in the last section a numerical example is developed

relatively optimal control and its linear implementation motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality roughly optimality for a specific nominal plant initial condition we consider a generic discrete time finite horizon constrained optimal control problem for linear systems and we seek for a state feedback possibly dynamic controller as a fundamental requirement we do not admit preactions or controller state initialization based on the plant initial state and we assume our controller to be time invariant in particular we do not consider controllers simply achieved by the feedforward and tracking of the optimal trajectory a relatively optimal control is a stabilizing controller such that if initialized at its zero state produces the optimal constrained trajectory for the nominal initial condition of the plant we show that one of such controllers is linear dead beat and its order is equal to the length of the horizon minus the plant order thus of complexity which is known a priori some additional features such as the assignment of the compensator poles to achieve strong stabilization are proposed we show that by means of the proposed approach we can face several problems such as optimal point to point operations optimal impulse response and optimal tracking

comparison principle positive invariance and constrained regulation of nonlinear systems abstract in this paper the comparison principle is applied to the design of feedback controllers for nonlinear discrete time systems subject to physical constraints first the connection between the comparison principle and the existence of positively invariant sets of a special form is established and polyhedral positively invariant sets for nonlinear systems are obtained then these results are applied to the determination of state feedback control laws that transfer to the origin all initial states of a prespecified region of the state space without violation of physical constraints on the control vector

admissible sets and feedback control for discrete time linear dynamical systems with bounded controls and states for linear discrete time dynamical systems necessary and sufficient conditions are given for a control sequence belonging to a polyhedral constraint set to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set a variable structure linear state feedback controller given in terms of the controls at the vertices of the polyhedral state constraint set is presented

convergence of an algorithm to find maximal state constraint sets for discrete time linear dynamical systems with bounded controls and states in 1 an algorithm was presented to find an approximant to the maximal state constraint set for a linear discrete time dynamical system with polyhedral state and input hounds here it is shown that the algorithm will yield an approximant arbitrarily close to the maximal state constraint set and the number of iterations is given as a function of the prescribed precision of the approximant

brief doubly invariant equilibria of linear discrete time games in this paper the notion of doubly invariant di equilibrium is introduced the concept extends controlled and robustly controlled invariance notions to the context of two person dynamic games each player tries to keep the state in a region of state space independently of the actions of the rival player the paper gives existence conditions criteria and algorithms for the determination of di equilibria of linear dynamic games in discrete time two examples illustrate the results the first one is in the area of fault tolerant controller synthesis the second is an application to macroeconomics

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

continuous causal representation of space time via sphere orderings a space time can be regarded as a partially ordered set or poset where the partial ordering is causal precedence the question of when this poset can be represented by spheres in euclidean space is investigated and it is shown that spaces which can be so represented are rare if the position and radius of the spheres are required to be continuous functions on the space time

internal behaviour provided by nonlinear l1 optimal controllers abstract an l 1 optimal linear time invariant lti compensator may have an order significantly higher than that of the plant even when the state is measurable recently there has been work exploring the use of nonlinear static feedback controllers which provide near optimal performance here we consider a class of nonlinear state feedback controllers and derive superposition like bounds on both the plant state and the controlled output in the event that the plant initial condition the disturbance and the noise are all non zero

brief paper computations of probabilistic output admissible set for uncertain constrained systems this paper considers uncertain constrained systems and develops two algorithms for computing a probabilistic output admissible poa set which is a set of initial states probabilistically assured to satisfy the constraint the first algorithm is inspired by an existing randomized sequential technique the second algorithm alleviates the computational effort based on heuristics the present algorithms terminate in a finite number of iterations and provide a poa set additionally we can obtain information on the size of the resulting set a posteriori a numerical simulation demonstrates the applicability of the poa set to a control system design scheme

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

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

bayesian semiparametric dynamic frailty models for multiple event time data many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly such as infection hospitalization recurrence of disease or tumor onset to analyze such data it is necessary to account for within subject dependency in the multiple event times motivated by data from studies of palpable tumors this article proposes a dynamic frailty model and bayesian semiparametric approach to inference the widely used shared frailty proportional hazards model is generalized to allow subject specific frailties to change dynamically with age while also accommodating nonproportional hazards parametric assumptions on the frailty distribution are avoided by using dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty by centering the semiparametric model on a conditionally conjugate dynamic gamma model we facilitate posterior computation and lack of fit assessments of the parametric model our proposed method is demonstrated using data from a cancer chemoprevention study

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

state feedback e 1 optimal controllers can be dynamic abstract this paper considers l 1 optimal control problems given by discrete time systems with full state feedback scalar control and scalar disturbance motivation stems from the central role that this problem structure played in the development of the h 2 and h theories first systems with a scalar regulated output are studied singular problems sufficient conditions are given based on the non minimum phase zeros of the transfer function from the control to the regulated output for the existence of a static l 1 optimal controller a simple way to compute the static gain is provided using pole placement ideas it is shown however that having full state information does not prevent the l 1 optimal controller from being dynamic in general and that examples with arbitrarily high order optimal controllers can be easily constructed second problems with two regulated outputs one of them being the scalar control are considered non singular problems it is shown by means of a class of fairly general examples for which exact l 1 optimal solutions are constructed that such problems may not have static controllers that are l 1 optimal thus concluding that a separation structure does not occur in these problems in general

random effects selection in linear mixed models nous presentons le probleme pratique important de la selection des effets aleatoires dans un modele lineaire mixte un modele bayesien hierarchique est utilise pour identifier tout effet aleatoire devariance nulle l approche proposee reparametrise le modele mixte de telle sorte que les fonctions des parametres de covariance de la distribution des effets aleatoires soient incorporees comme des coefficients de regression pour des variables latentes normales nous permettons aux effets aleatoires de sortir du modele en choisissant des melanges d a priori avec des masses ponctuelles en zero pour les variances des effets aleatoires du fait de la reparametrisation le modele prend une structure lineaire conditionnelle qui facilite l utilisation de lois a priori conjuguees et normales nous demontrons que les calculs a posteriori peuvent etre effectues via un algorithme simple et efficace de monte carlo par chaine de markov les methodes sont illustrees par des donnees simulees et par des donnees reelles d exposition prenatale au polychlorobiphenile et des donnees sur le developpement psychomoteur des enfants

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

nonlinear l 1 optimal controllers for linear systems in this paper we study the l sub 1 optimal control problem for linear systems we show that by allowing the class of controllers to include nonlinear controllers we can make the closed loop l sub 1 norm strictly smaller than we could do using only linear controllers

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest