adaptive pole positioning in mimo linear systems by periodic multirate input controllers abstract in this paper the certainty equivalence principle is used to combine the identification method with a control structure derived from the pole placement problem which rely on periodic multirate input controllers the proposed adaptive pole placers contain a sampling mechanism with different sampling period to each system input and rely on a periodically varying controller which suitably modulates the sampled outputs and reference signals of the plant under control such a control strategy allows us to arbitrarily assign the poles of the sampled closed loop system in desired locations and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system and the knowledge of a set of structural indices namely the locally minimum controllability indices of the continuous time plant an indirect adaptive control scheme is derived which estimates the unknown plant parameters and consequently the controller parameters on line from sequential data of the input and outputs of the plant which are recursively updated within the time limit imposed by a fundamental sampling period t0 using the proposed algorithm the controller determination is based on the transformation of the discrete analogous of the system under control to a phase variable canonical form prior to the application of the control design procedure the solution of the problem can then be obtained by a quite simple utilization of the concept of state similarity transformation known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial diophantine equation thus introducing high order exogenous dynamics in the control loop moreover in many cases the solution of the diophantine equation for a desired set of closed loop eigenvalues might yield an unstable controller and the overall adaptive pole placement scheme is unstable with unstable compensators because their outputs are unbounded the proposed control strategy avoids these problems since here gain controllers are essentially needed to be designed moreover persistency of excitation and therefore parameter convergence of the continuous time plant is provided without making any assumption either the richness of the reference signals or on the existence of specific convex sets in which the estimated parameters belong or finally on the coprimeness of the polynomials describing the arma model as in known adaptive pole placement schemes

invertibility and inversion of linear periodic systems abstract in this paper the invertibility properties of periodic discrete time systems are studied necessary and sufficient conditions for the existence and a synthesis procedure for constructing left and right inverses are given

objective bayes model selection in probit models we describe a new variable selection procedure for categorical responses where the candidate models are all probit regression models the procedure uses objective intrinsic priors for the model parameters which do not depend on tuning parameters and ranks the models for the different subsets of covariates according to their model posterior probabilities when the number of covariates is moderate or large the number of potential models can be very large and for those cases we derive a new stochastic search algorithm that explores the potential sets of models driven by their model posterior probabilities the algorithm allows the user to control the dimension of the candidate models and thus can handle situations when the number of covariates exceed the number of observations we assess through simulations the performance of the procedure and apply the vari able selector to a gene expression data set where the response is whether a patient exhibits pneumonia software needed to run the procedures is available in the r package varselectip copyright 2011 john wiley sons ltd categorical responses often appear in the analysis of the effect of a medical treatment which is applied to a collection of patients these patients are typically characterized by a set of p potential covariates and a first important statistical problem in the presence of covariates is to reduce the dimension of the model by retaining from the original p covariates those that have some influence in the observed responses thus we have a model selection problem in the class of 2 p models in this paper we describe a new variable selection procedure applicable to dichotomous responses that are modeled with a probit regression although under the 0 1 loss function an optimal solution is the model having the highest posterior probability the 0 1 loss function might not be realistic for many applications one potential shortcoming is that submodels different from the true one are assigned the same loss regardless of how far or close to the true one they are therefore it seems appropriate to not choose a single optimal model but a subset of them having posterior probabilities over a given threshold thus the output of our model selection procedure will be a ranking of the models according to their posterior probabilities the literature on variable selection in logistic or probit models is not large researchers have car ried out variable selection in logistic regression with lasso type procedures for instance meier et al 1 used a group lasso for logistic regression whereas kyung et al 2 used the latent variable probit model for bayesian lasso variable selection the bayesian approaches tend to dominate and researchers typically solve the main difficulties in its formulation the choice of the prior for the models involved and for the model parameters by using subjective priors swartz and shete 3 did a simulation study of the five types of variable selection in case control logistic regression and found that a bayesian stochastic search based on a spike and slab prior was the best performer chen and dey 4 also used a bayesian approach and were particularly concerned with correlated binary responses in multivariate logistic regression in their study the researchers developed subjective priors and selected models on the

single loop stability margins for multirate and periodic control systems it is shown how to compute the stability margin of periodic systems with respect to compatible periodic perturbations of such systems it is suggested that the nonstandard time invariant model for periodic systems introduced by the author syst contr lett vol 17 pp 9 14 1991 leads to a simpler computation although the standard model gives the same result

lqg optimal control of multirate sampled data systems an lqg control synthesis technique for multirate sampled data systems where each input has its own frequency of updating and each output has its own frequency of measurement is presented the skew of the output sampling mechanism renders the prediction problem singular for the lack of measures at some time instants an ad hoc prediction algorithm is derived by enlarging the dimension of the state vector to be estimated and feeding the state filter with a combination of measured outputs over a past and finite interval of time the constraints on the input updating mechanism are dealt with by inserting a dynamical system corresponding to a zero order hold into the loop

some qualitative properties of multirate digital control systems the authors consider multirate digital control systems which consist of an interconnection of a continuous time nonlinear plant described by ordinary differential equations a digital controller described by ordinary difference equations which has quantizers but is otherwise linear along with the required interface elements a d and d a converters the input to the digital controller consists of the multirate sampled output of the plant in the present paper the authors show that when quantizer nonlinearities are neglected then under reasonable conditions which exclude the critical cases the stability properties in the lyapunov sense of the trivial solution of a nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization for such systems we also present a result concerning the existence and construction of stabilizing multirate output digital controllers in the present paper the authors also show that the solutions of a multirate digital feedback control system with nonlinear plant and quantizers are uniformly ultimately bounded if the trivial solution of the corresponding linear system consisting of the linearization of the plant and with the quantization removed from the digital controller is asymptotically stable we also provide a result which compares the response of multirate digital control systems with nonlinear plant and quantizers in the controller with the response of the corresponding nonlinear multirate digital control systems without quantizers in the digital controller

dynamics of predator prey system with fading memory abstract a predator prey model with fading memory for general holling type functional response is proposed the fading memory term is used with the hypothesis that the predator s growth rate at present depends on the recent past quantities of prey the effects of predator harvesting is also considered in the model the model is analysed theoretically as well as numerically two parameter bifurcation analysis are done and the existence of hopf point bifurcation is identified both supercritical and subcritical hopf bifurcations are obtained with the variation of system parameters maximum sustainable yield with respect to harvesting effort is also determined it is to be observed that the system dynamics is very rich in presence of fading memory the obtained results may be useful in the field of agriculture and fishery

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

an estimation algorithm for multirate sampled digital control systems abstract this paper presents an optimization based algorithm for state estimation of multirate digital control systems the algorithm features a predictor estimator structure and it is derived by employing a time invariant modelling approach to multirate systems special care is taken to ensure the causality of the derived estimation algorithm and to reduce the dimensionality inherent in multirate system modelling while maintaining a reasonably simple implementation the proposed algorithm is developed to ensure convergence in state estimation between base sampling instants as well as between model rate sampling instants

the effects of harvesting and time delay on predator prey systems with holling type ii functional response in this paper the effects of harvesting and time delay on two different types of predator prey systems with delayed predator specific growth and holling type ii functional response are studied by applying the normal form theory of retarded functional differential equations developed by faria and magalhaes j differential equations 122 1995 pp 181 200 j differential equations 122 1995 pp 201 224 hopf bifurcations are demonstrated in models with harvesting of the prey at a constant rate by taking the delay as a bifurcation parameter and numerical examples supporting our theoretical prediction are also given furthermore bifurcation analysis indicates that delayed predator prey systems with predator harvesting exhibit bogdanov takens bifurcation the versal unfoldings of the models at the bogdanov takens singularity are obtained and numerical simulations and bifurcation diagrams are given to illustrate the obtained results

model order selection based on information theoretic criteria design of the penalty information theoretic criteria itc have been widely adopted in engineering and statistics for selecting among an ordered set of candidate models the one that better fits the observed sample data the selected model minimizes a penalized likelihood metric where the penalty is determined by the criterion adopted while rules for choosing a penalty that guarantees a consistent estimate of the model order are known theoretical tools for its design with finite samples have never been provided in a general setting in this paper we study model order selection for finite samples under a design perspective focusing on the generalized information criterion gic which embraces the most common itc the theory is general and as case studies we consider a the problem of estimating the number of signals embedded in additive white gaussian noise awgn by using multiple sensors b model selection for the general linear model glm which includes e g the problem of estimating the number of sinusoids in awgn the analysis reveals a trade off between the probabilities of overestimating and underestimating the order of the model we then propose to design the gic penalty to minimize underestimation while keeping the overestimation probability below a specified level for the considered problems this method leads to analytical derivation of the optimal penalty for a given sample size a performance comparison between the penalty optimized gic and common aic and bic is provided demonstrating the effectiveness of the proposed design strategy

stochastic model specification search for gaussian and partial non gaussian state space models model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time varying to this aim a new model space mcmc method is developed in this paper it is based on extending the bayesian variable selection approach which is usually applied to variable selection in regression models to state space models for non gaussian state space models stochastic model search mcmc makes use of auxiliary mixture sampling we focus on structural time series models including seasonal components trend or intervention the method is applied to various well known time series

objective bayesian comparison of constrained analysis of variance models in the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints for instance when examining three group means mu 1 mu 2 mu 3 through an analysis of variance anova a model may specify that mu 1 mu 2 mu 3 while another one may state that mu 1 mu 3 mu 2 and finally a third model may instead suggest that all means are unrestricted this is a challenging problem because it involves a combination of nonnested models as well as nested models having the same dimension we adopt an objective bayesian approach requiring no prior specification from the user and derive the posterior probability of each model under consideration our method is based on the intrinsic prior methodology suitably modified to accommodate equality and inequality constraints focussing on normal anova models a comparative assessment is carried out through simulation studies we also present an application to real data collected in a psychological experiment

pursuing a maneuvering target which uses a random process for its control since a pursuer pursuing a maneuvering target does not know what maneuvers an evading target will make the maneuvers the target s control law appear as a random process to the pursuer however he has opinions about what the evader will do from these he can assign a prior probability distribution to the evader s maneuvers for a linear pursuit evasion problem in which the evader s control law is modeled as a random process in which the pursuer has partial noisy linear measurements of his own and the evader s relative position and a quadratic optimality criterion is used past results of the authors imply that the optimal control is a linear function of the predicted miss determining the predicted miss involves estimating the evader s terminal position from past system measurements nonlinear filtering techniques are used to give expressions for computing the conditional expectation of the evader s terminal position even in the presence of the random unknown maneuvers of the evader

criteria for bayesian model choice with application to variable selection in objective bayesian model selection no single criterion has emerged as dominant in defining objective prior distributions indeed many criteria have been separately proposed and utilized to propose differing prior choices we first formalize the most general and compelling of the various criteria that have been suggested together with a new criterion we then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models this results in a new model selection objective prior with a number of compelling properties

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

a new bayesian test to test for the intractability countering hypothesis abstractwe present a new test of hypothesis in which we seek the probability of the null conditioned on the data where the null is a simplification undertaken to counter the intractability of the more complex model that the simpler null model is nested within with the more complex model rendered intractable the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data bayes factors are shown to be known only up to a ratio of unknown data dependent constants a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to bayes factor computation by noninformative priors thus a new test is needed in which we can circumvent bayes factor computation in this test we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalized posterior of the model parameter given the measured data to that gi

time invariant representation of discrete periodic systems a large number of results from linear time invariant system theory can be extended to periodic systems provided an equivalent time invariant system can be found this paper presents a simple and numerically reliable procedure to achieve the same it is shown that using a stacked representation of periodic systems under system equivalence a minimal order generalized state space description can always be obtained

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

a two species competitive system under the influence of toxic substances the effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view in this paper we have studied the dynamical behaviours of a two species competitive system affected by toxic substances boundedness local and global stabilities are addressed we have also studied the stability of this system with diffusion around the non trivial stable in the deterministic case equilibrium point in a random environment extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

the deviance information criterion 12 years on summary the essentials of our paper of 2002 are briefly summarized and compared with other criteria for model comparison after some comments on the paper s reception and influence we consider criticisms and proposals forimprovement made by us and others

a periodic fixed structure approach to multirate control we develop an approach to designing reduced order multirate controllers a discrete time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically time varying dynamics using discrete time stability theory the optimal projection approach to fixed order i e full and reduced order dynamic compensation is generalized to obtain reduced order periodic controllers that account for the multirate architecture it is shown that the optimal reduced order controller is characterized by means of a periodically time varying system of equations consisting of coupled riccati and lyapunov equations in addition the multirate static output feedback control problem is considered for both problems the design equations are presented in a concise unified manner to facilitate their accessibility for developing numerical algorithms for practical applications

state space solution to the periodic multirate h sub spl infin control problem a lifting approach a two riccati equation solution to the h sub spl infin control problem for periodic multirate systems is derived via the lifting method the solution is expressed in terms of two algebraic riccati equations the causality constraints are represented by a set of positive definiteness conditions and coupling criteria as a by product the study shows that there is a close connection between the solution of the causally constrained lifted problem and the solution obtained by solving the problem directly as a periodic h sub spl infin problem defined for the multirate system

bayes variable selection in semiparametric linear models there is a rich literature on bayesian variable selection for parametric models our focus is on generalizing methods and asymptotic theory established for mixtures of g priors to semiparametric linear regression models having unknown residual densities using a dirichlet process location mixture for the residual density we propose a semiparametric g prior which incorporates an unknown matrix of cluster allocation indicators for this class of priors posterior computation can proceed via a straightforward stochastic search variable selection algorithm in addition bayes factor and variable selection consistency is shown to result under a class of proper priors on g even when the number of candidate predictors p is allowed to increase much faster than sample size n while making sparsity assumptions on the true model size

inference from intrinsic bayes procedures under model selection and uncertainty in this article we present a fully coherent and consistent objective bayesian analysis of the linear regression model using intrinsic priors the intrinsic prior is a scaled mixture of g priors and promotes shrinkage toward the subspace defined by a base or null model while it has been established that the intrinsic prior provides consistent model selectors across a range of models the posterior distribution of the model parameters has not previously been investigated we prove that the posterior distribution of the model parameters is consistent under both model selection and model averaging when the number of regressors is fixed further we derive tractable expressions for the intrinsic posterior distribution as well as sampling algorithms for both a selected model and model averaging we compare the intrinsic prior to other mixtures of g priors and provide details on the consistency properties of modified versions of the zellner siow prior and hyper g priors supplementary materials for this arti

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

cost translation and a lifting approach to the multirate lqg problem it is shown how to translate an instance of a multirate sampled data lqg problem into an equivalent modified single rate shift invariant problem via a lifting isomorphism approach using this approach one can solve the multirate lqg problem without using periodic system theory or solving periodic riccati equations and without suffering any increases in state dimension this translation procedure shows the correct way to translate rms noise specification to the lifted domain for a multirate q design computer aided design package

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

a bioeconomic modeling of two prey and one predator fishery model with optimal harvesting policy through hybridization approach abstract this paper introduces an imprecise prey predator model by using interval and fuzzy number in modeling of prey and predator interaction in a prey predator system values of the biological parameter are based on the collection of data by the experts from nature therefore we consider them as interval numbers the proposed prey predator model is consisting of two species which are not only affected by the harvesting of the species but also by the present of predator species all possible existence of the biological and bionomic equilibrium points of the model are discussed under impreciseness we derive the conditions for local and global stability the optimal harvesting policy is studied by considering instantaneous annual rate of discount under fuzziness by logically hybridizing the interval and fuzzy number methodologies we find the optimal equilibrium points and harvesting efforts in the form of interval finally numerical examples are illustrated to support the proposed approach

optimal treatments in cost effectiveness analysis in the presence of covariates improving patient subgroup definition abstract in the presence of covariates the cost effectiveness analysis of medical treatments shows that the optimal treatment varies across the patient population subgroups and hence to accurately define the subgroups is a crucial step in the analysis a patient subgroup definition using only influential covariates within the potential set of patients covariates established by the expert has recently been proposed and the influential covariates were chosen from the univariate distributions of the effectiveness and the cost conditional on the effectiveness in this paper we argue that the bayesian variable selection procedure should be developed using the bivariate distribution of the cost and the effectiveness which is not the usual practice this new approach provides results with wider applicability and more understandable without a significative increase in the complexity of the procedure for real and simulated data sets optimal treatments for subgroups are found and compared with that from previous methods

multi 2 rate control from a 2 periodic perspective generalized 2 rate control this technical note finds that a conventional 2 rate controller which receives feedback at t but provides control at 2t intervals has a 2 periodic core and augments this core to have a generalized 2 rate control that has complete loop zero and pole placement capability an algorithm for controller parameter evaluation for pole zero placement using only linear algebraic steps has been developed the controller also ensures zero steady state and improved transient ripples its superiority in respect of gain margin compensation is illustrated for a third order plant with an unstable pole and a non minimum phase zero

multirate control a new approach abstract a new multirate digital control of linear periodic and time invariant systems is proposed an explicit multirate law is given which transforms the overall control design into that of a relatively small dimensional discrete time invariant system for which standard design techniques can be used it is shown that the proposed multirate scheme is in general more effective as a design tool than current multirate designs the controllability properties of the multirate system are studied consequently necessary and sufficient conditions for pole placement and stabilizability of the multirate system are given in terms of the continuous plant matrices moreover the multirate lqr problem is solved in this case the solution is obtained by solving an algebraic discrete riccati equation here necessary and sufficient conditions for the existence of a unique nonnegative definite solution of the riccati equation and the asymptotic stability of the corresponding closed loop multirate system are obtained these conditions are given in terms of the continuous time parameters

selective harvesting of two competing fish species in the presence of toxicity with time delay abstract in this paper we have considered a two competing fish species with the delay due to gestation each of which obeys the law of logistic growth and releases a substance toxic to the other we also consider the selective harvesting of fishes above a certain age or size by incorporating a time delay in the harvesting term the dynamical behavior of the exploited system is examined in the presence and absence of delay boundedness local and global stabilities are addressed the possibility of the existence of a dynamic equilibrium and the optimal harvesting policy is studied in the absence of delay it is shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values

objective bayesian variable selection a novel fully automatic bayesian procedure for variable selection in normal regression models is proposed the procedure uses the posterior probabilities of the models to drive a stochastic search the posterior probabilities are computed using intrinsic priors which can be considered default priors for model selection problems that is they are derived from the model structure and are free from tuning parameters thus they can be seen as objective priors for variable selection the stochastic search is based on a metropolis hastings algorithm with a stationary distribution proportional to the model posterior probabilities the procedure is illustrated on both simulated and real examples

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

testing hardy weinberg equilibrium an objective bayesian analysis we analyze the general multiallelic hardy weinberg equilibrium problem from an objective bayesian testing standpoint we argue that for small or moderate sample sizes the answer is rather sensitive to the prior chosen and this suggests to carry out a sensitivity analysis with respect to the prior this goal is achieved through the identification of a class of priors specifically designed for this testing problem in this paper we consider the class of intrinsic priors under the full model indexed by a tuning quantity the training sample size these priors are objective satisfy savage s continuity condition and have proved to behave extremely well for many statistical testing problems we compute the posterior probability of the hardy weinberg equilibrium model for the class of intrinsic priors assess robustness over the range of plausible answers as well as stability of the decision in favor of either hypothesis copyright 2010 john wiley sons ltd

existence uniqueness and stability analysis of allelopathic stimulatory phytoplankton model in this paper we consider the two species competitive delay plankton allelopathy stimulatory model system we show the existence and uniqueness of the solution of the deterministic model moreover we study the persistence of the model and the stability properties of its equilibrium points we illustrate the theoretical results by some numerical simulations

a new shift invariant representation for periodic linear systems abstract this paper presents a new family of shift invariant representations for periodic linear discrete time systems this representation has the advantages over the standard representation 5 of preserving the time step of the original system and of preserving causality under arbitrary feedback the disadvantage is that the realization is not minimal an application in attitude determination is presented

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

the optimal projection equations for fixed order sampled data dynamic compensation with computation delay for an lqg type sampled data regulator problem which accounts for computational delay and utilizes an averaging a d device the equivalent discrete time problem is shown to be of increased order due to the inclusion of delayed measurement states the optimal projection equations for reduced order discrete time compensation are applied to the augmented problem to characterize low order controllers the design results are illustrated on a tenth order flexible beam example

training samples in objective bayesian model selection central to several objective approaches to bayesian model selection is the use of training samples subsets of the data so as to allow utilization of improper objective priors the most common prescription for choosing training samples is to choose them to be as small as possible subject to yielding proper posteriors these are called minimal training samples when data can vary widely in terms of either information content or impact on the improper priors use of minimal training samples can be inadequate important examples include certain cases of discrete data the presence of censored observations and certain situations involving linear models and explanatory variables such situations require more sophisticated methods of choosing training samples a variety of such methods are developed in this paper and successfully applied in challenging situations

consistent model selection criteria on high dimensions asymptotic properties of model selection criteria for high dimensional regression models are studied where the dimension of covariates is much larger than the sample size several sufficient conditions for model selection consistency are provided non gaussian error distributions are considered and it is shown that the maximal number of covariates for model selection consistency depends on the tail behavior of the error distribution also sufficient conditions for model selection consistency are given when the variance of the noise is neither known nor estimated consistently results of simulation studies as well as real data analysis are given to illustrate that finite sample performances of consistent model selection criteria can be quite different

a stability criterion for asynchronous multirate linear systems a stability criterion is developed for linear asynchronous multirate sampled data systems such systems typically include a linear time variant continuous time plant and several unsynchronized digital controllers the analysis method uses a time domain approach based on the closed loop state transition matrix the result is sufficient stability criterion which gives an objective measure of long term and short term stability a simple example illustrates the method

structural properties of a class of linear hybrid systems and output feedback stabilization in this paper we deal with the problem of output feedback stabilization for a class of linear hybrid systems this problem is addressed by characterizing the structural properties of such a class of systems namely reachability controllability stabilizability observability constructibility and detectability are framed in terms of algebraic and geometric conditions on the data of the system two canonical forms recalling the classical kalman decompositions with respect to reachability and observability are given by taking advantage of this characterization duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time invariant output feedback compensator are stated compared with previous results no assumption is needed on the plant about minimum phaseness relative degree or squareness

an intrinsic limiting procedure for model selection and hypotheses testing abstract improper priors typically arise in default bayesian estimation problems in the bayesian approach to model selection or hypothesis testing the main tool is the bayes factor when improper priors for the parameters appearing in the models are used the bayes factor is not well defined the intrinsic bayes factor introduced by berger and pericchi is an interesting method for overcoming that difficulty that method is of particular interest as a means for generating proper prior distributions intrinsic priors for model comparison from the improper priors typically used in estimation the goal of this article is to develop a limiting procedure that provides a solid justification for the use of bayes factor with intrinsic priors the procedure is formalized and discussed for nested and nonnested models illustrations and comparisons with other approximations to bayes factors such as the bayesian information criterion of schwarz and the fractional bayes factor of o hagan are provided

a new class of shift varying operators their shift invariant equivalents and multirate digital systems a class of linear shift varying operators that generalize the notion of n periodicity is defined it is shown that shift invariant equivalents for these operators exist and that the equivalence is in a strong sense preserving both algebraic and analytic system properties it is shown that multirate sampled data systems although not generally periodic fall into this class kranc vector switch decomposition and block filter implementations for single input single output multirate systems are connected under the unifying framework of shift invariant equivalents and this framework provides a way to extend them both to multi input multi output systems

ripple free robust output regulation and tracking for multirate sampled data control the problem of the robust continuous time asymptotic tracking and disturbance rejection for a multivariable multirate sampled data system is studied the necessity of a continuous time internal model of the exogenous signals except for the constant ones if any for obtaining a ripple free zero error response is proven the conditions are given for the existence of a hybrid control system including possibly a continuous time subcompensator for which the exponential stability and a continuous time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters this in particular both for when the dead beat convergence of the state free response and the continuous time error response is required at the nominal parameters and for when an exponential convergence with a prescribed rate of decay is required including design procedures of the continuous time and the discrete time subcompensators both for when the available description of the plant has a

a class of subspace model identification algorithms to identify periodically and arbitrarily time varying systems abstract subspace model identification algorithms that allow the identification of a linear time varying ltv state space model from an ensemble set of input output measurements are presented in this paper each pair of input and output sequences in this ensemble is recorded when the underlying system to be identified undergoes the same time varying behavior the algorithms operate directly on the available ensemble of input output data and are a generalization of the recently proposed multivariable output error state space moesp class of algorithms to this ensemble type of identification problems a special case is considered in this paper where the repetition of this time varying behavior is intrinsic namely in periodically time varying systems an example of identifying a multirate sampled data system from a recorded input and output sequence demonstrates some of the capabilities of the presented subspace model identification algorithms

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

qualitative analysis on a diffusive predator prey model with toxins abstract this paper is concerned with the diffusive predator prey model with toxins subject to dirichlet boundary conditions the uniform persistence of positive solution is given under certain conditions in addition by the liapunov schmidt method the existence and stability of the bifurcation solution from a double eigenvalues are investigated moreover by the fixed point index theory and perturbation theory of eigenvalues the uniqueness stability and multiplicity of coexistence states are analyzed when some key parameter changes finally some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states

consistency of bayesian procedures for variable selection it has long been known that for the comparison of pairwise nested models a decision based on the bayes factor produces a consistent model selector in the frequentist sense here we go beyond the usual consistency for nested pairwise models and show that for a wide class of prior distributions including intrinsic priors the corresponding bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models we find that the asymptotics of the bayes factors for intrinsic priors are equivalent to those of the schwarz bic criterion also recall that the jeffreys lindley paradox refers to the well known fact that a point null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity this implies that some limiting forms of proper prior distributions are not necessarily suitable for testing problems intrinsic priors are limits of proper prior distributions and for finite sample sizes they have been proved to behave extremely well for variable selection in regression a consequence of our results is that for intrinsic priors lindley s paradox does not arise

coexistence region and global dynamics of a harvested predator prey system the study of populational dynamics with harvesting is related to the optimal man agement of renewable resources in this paper we consider a predator prey model in which two ecologically interacting species are harvested independently with constant rates the main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria it is also proved that the harvested predator prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles

hopf bifurcation and harvesting control of a bioeconomic plankton model with delay and diffusion terms abstract in this paper we study the dynamics of a bioeconomic plankton model with delay and diffusion terms in which phytoplankton is assumed to undergo exploitation some sufficient conditions ensuring the stability and bifurcation for the model are provided by using stability and bifurcation theory our results show that harvest effort can control bifurcation and resume system s stability in the case of positive economic profit and over exploitation will result in the extinction of the population which is in line with reality finally some numerical simulations are given to verify the analytical results of nutrient phytoplankton zooplankton fish model

consistent model selection criteria for quadratically supported risks in this paper we study asymptotic properties of model selection criteria for high dimensional regression models where the number of covariates is much larger than the sample size in particular we consider a class of loss functions called the class of quadratically supported risks which is large enough to include the quadratic loss huber loss quantile loss and logistic loss we provide sufficient conditions for the model selection criteria which are applicable to the class of quadratically supported risks our results extend most previous sufficient conditions for model selection consistency in addition sufficient conditions for pathconsistency of the lasso and nonconvex penalized estimators are presented here pathconsistency means that the probability of the solution path that includes the true model converges to 1 pathconsistency makes it practically feasible to apply consistent model selection criteria to high dimensional data the data adaptive model selection procedure is proposed which is selection consistent and performs well for finite samples results of simulation studies as well as real data analysis are presented to compare the finite sample performances of the proposed data adaptive model selection criterion with other competitors

decoupling with stability for linear periodic systems in this paper the classical row by row decoupling problem with stability through the use of a dynamic compensator is studied for linear periodic discrete time systems the necessary and sufficient conditions for the existence of a solution are found and a design procedure of the dynamic compensator is provided by the sufficiency proof and also for the case of a dead beat requirement for the state free response

consistency of objective bayes factors as the model dimension grows in the class of normal regression models with a finite number of regressors and for a wide class of prior distributions a bayesian model selection procedure based on the bayes factor is consistent casella and moreno j amer statist assoc 104 2009 1261 1271 however in models where the number of parameters increases as the sample size increases properties of the bayes factor are not totally understood here we study consistency of the bayes factors for nested normal linear models when the number of regressors increases with the sample size we pay attention to two successful tools for model selection schwarz ann statist 6 1978 461 464 approximation to the bayes factor and the bayes factor for intrinsic priors berger and pericchi j amer statist assoc 91 1996 109 122 moreno bertolino and racugno j amer statist assoc 93 1998 1451 1460 we find that the the schwarz approximation and the bayes factor for intrinsic priors are consistent when the rate of growth of the dimension of the bigger model is o n b for b 1 when b 1 the schwarz approximation is always inconsistent under the alternative while the bayes factor for intrinsic priors is consistent except for a small set of alternative models which is characterized

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

moment matching model reduction for multiratc linear systems aerospace systems are described by high order dynamic models which include phenomena covering a wide range of characteristic frequencies and sensor sampling rates in order to accommodate these multiple information rates and to complete the control computations within the time available control systems are designed to operate at multiple sampling rates model reduction methods are available for single rate linear systems to preserve the first q markov parameters and the first q covariance parameters this paper extends these ideas to multirate systems