decentralized fuzzy observer based output feedback control for nonlinear large scale systems an lmi approach this paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large scale systems that use an observer based output feedback scheme a takagi sugeno t s fuzzy model is adopted for the nonlinear large scale system which has unknown interconnection terms and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities finally numerical examples are provided to verify the effectiveness of the proposed techniques

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

a class of the first order impulsive dynamic equations on time scales abstract in this paper the first order impulsive dynamic equations on time scales is considered the existence and uniqueness of solution for a class of nonlinear impulsive dynamic equations on time scales is proved

a bayesian machine learning approach for optimizing dynamic treatment regimes medical therapy often consists of multiple stages with a treatment chosen by the physician at each stage based on the patient s history of treatments and clinical outcomes these decisions can be formalized as a dynamic treatment regime this paper describes a new approach for optimizing dynamic treatment regimes that bridges the gap between bayesian inference and existing approaches like q learning the proposed approach fits a series of bayesian regression models one for each stage in reverse sequential order each model uses as a response variable the remaining payoff assuming optimal actions are taken at subsequent stages and as covariates the current history and relevant actions at that stage the key difficulty is that the optimal decision rules at subsequent stages are unknown and even if these decision rules were known the relevant response variables may be counterfactual however posterior distributions can be derived from the previously fitted regression models for the optimal decision rules and the counterfactual response variables under a particular set of rules the proposed approach averages over these posterior distributions when fitting each regression model an efficient sampling algorithm for estimation is presented along with simulation studies that compare the proposed approach with q learning

robust observer based tracking control of hodgkin huxley neuron systems under environmental disturbances a nervous system consists of a large number of highly interconnected nerve cells nerve cells communicate by generation and transmission of short electrical pulses action potential in addition membrane voltage is the only measurable state in nervous systems a robust observer based model reference tracking control is proposed for hodgkin huxley hh neuron systems to generate a desired reference response in spite of environmental noises uncertain initial values and diffusion currents from other interconnected nerve cells in order to simplify the robust tracking control design of nonlinear stochastic hh neuron systems a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic hh neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality lmi technique with the help of robust control toolbox in matlab the proposed robust observer based tracking control scheme can provide new methods for desired action potential generation suppression of oscillations and blockage of action potential transmission under environmental noise and diffusion currents these new methods are useful for patients with different neuron system dysfunctions finally three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method

interpretable dynamic treatment regimes abstractprecision medicine is currently a topic of great interest in clinical and intervention science a key component of precision medicine is that it is evidence based i e data driven and consequently there has been tremendous interest in estimation of precision medicine strategies using observational or randomized study data one way to formalize precision medicine is through a treatment regime which is a sequence of decision rules one per stage of clinical intervention that map up to date patient information to a recommended treatment an optimal treatment regime is defined as maximizing the mean of some cumulative clinical outcome if applied to a population of interest it is well known that even under simple generative models an optimal treatment regime can be a highly nonlinear function of patient information consequently a focal point of recent methodological research has been the development of flexible models for estimating optimal treatment regimes however in many settings estimati

adaptive hybrid type 2 intelligent sliding mode control for uncertain nonlinear multivariable dynamical systems a new adaptive hybrid interval type 2 fuzzy neural network fnn controller incorporating sliding mode and lyapunov synthesis approaches is proposed in this paper to handle the training data corrupted by noise or rule uncertainties for a class of uncertain nonlinear multivariable dynamic systems the hybrid adaptive fnn controller the free parameters of which can be tuned on line by an output feedback control law and adaptive laws is a combination of interval type 2 indirect and direct adaptive fnn controllers to meet the requirement of sufficient reach for the sliding mode control a weighting factor which can be adjusted based on the trade off between plant knowledge and control knowledge is included when combining the control efforts of the indirect adaptive fnn controller and the direct adaptive fnn controller the overall adaptive control scheme guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded the mass spring damper nonlinear system is fully illustrated to track sinusoidal signals the resulting adaptive hybrid interval type 2 fnn control system shows better performance than the adaptive hybrid type 1 fnn control system it reduces both the tracking error and the control effort and it is more flexible in the design process

structural nested mean models for assessing time varying effect moderation this article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment or exposure is time varying and so are the covariates said to moderate its effect intermediate causal effects that describe time varying causal effects of treatment conditional on past covariate history are introduced and considered as part of robins structural nested mean model two estimators of the intermediate causal effects and their standard errors are presented and discussed the first is a proposed two stage regression estimator the second is robins g estimator the results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators and on the bias variance trade off between the two estimators are presented the methodology is illustrated using longitudinal data from a depression study

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

stability of moving invariant sets and uncertain dynamic systems on time scales abstract in this paper we study the stability of moving invariant sets and uncertain dynamic systems on time scale a control application is considered

design of nonlinear interconnections guaranteeing the absence of periodic solutions abstract in this paper a novel methodology for scheming interconnection structure for a class of nonlinearly interconnected systems is proposed to guarantee the absence of a specific kind of periodic solutions those types of systems can be viewed as an interconnection of single input single output isolated subsystems with the interconnection structure specified by a square matrix frequency domain inequalities conditions as well as linear matrix inequalities lmis conditions for nonexistence of limit cycles of the second kind in the entire interconnected system are established the main results also define the frequency range on which cycles of the second kind of the system cannot exist based on this lmi approach an estimate of the largest bound of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem numerical results show the effect of the nonlinear interaction on system behavior and the applicability and validity of the proposed method

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

hamilton jacobi theory over time scales and applications to linear quadratic problems abstract in this paper we first derive the verification theorem for nonlinear optimal control problems over time scales that is we show that the value function is the only solution of the hamilton jacobi equation in which the minimum is attained at an optimal feedback controller applications to the linear quadratic regulator problem lqr problem gives a feedback optimal controller form in terms of the solution of a generalized time scale riccati equation and that every optimal solution of the lqr problem must take that form a connection of the newly obtained riccati equation with the traditional one is established problems with shift in the state variable are also considered as an important tool for the latter theory we obtain a new formula for the chain rule on time scales finally the corresponding lqr problem with shift in the state variable is analyzed and the results are related to previous ones

breaking the curse of nonregularity with subagging inference of the mean outcome under optimal treatment regimes precision medicine is an emerging medical approach that allows physicians to select the treatment options based on individual patient information the goal of precision medicine is to identify the optimal treatment regime otr that yields the most favorable clinical outcome prior to adopting any otr in clinical practice it is crucial to know the impact of implementing such a policy although considerable research has been devoted to estimating the otr in the literature less attention has been paid to statistical inference of the otr challenges arise in the nonregular cases where the otr is not uniquely defined to deal with nonregularity we develop a novel inference method for the mean outcome under an otr the optimal value function based on subsample aggregating subagging the proposed method can be applied to multi stage studies where treatments are sequentially assigned over time bootstrap aggregating bagging and subagging have been recognized as effective variance reduction techniques to improve unstable estimators or classifiers buhlmann and yu 2002 however it remains unknown whether these approaches can yield valid inference results we show the proposed confidence interval ci for the optimal value function achieves nominal coverage in addition due to the variance reduction effect of subagging our method enjoys certain statistical optimality specifically we show that the mean squared error of the proposed value estimator is strictly smaller than that based on the simple sample splitting estimator in the nonregular cases moreover under certain conditions the length of our proposed ci is shown to be on average shorter than cis constructed based on the existing state of the art method luedtke and van der laan 2016 and the oracle method which works as well as if an otr were known extensive numerical studies are conducted to back up our theoretical findings

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

adaptive observers for ts fuzzy systems with unknown polynomial inputs a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents however in practical applications the process under consideration may be affected by unknown inputs such as disturbances faults or unmodeled dynamics in this paper we consider the problem of simultaneously estimating the state and unknown inputs in ts systems the inputs considered in this paper are 1 polynomials in time such as a bias in the model or an unknown ramp input acting on the model and 2 unmodeled dynamics the proposed observer is designed based on the known part of the fuzzy model conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal the results are illustrated on a simulation example

multiobjective tracking control design of t s fuzzy systems in this study a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal h 2 and h reference tracking performance simultaneously first the takagi and sugeno t s fuzzy model is used to represent the nonlinear dynamic system then based on the t s fuzzy model multiobjective h 2 h tracking control design problem is formulated as a multiobjective problem mop to minimize the h 2 tracking error and h disturbance attenuation level for the fuzzy system at the same time since it is not easy to solve this mop directly an indirect method is proposed for the multiobjective h 2 h tracking control design finally in order to achieve the simultaneous optimization of the mop linear matrix inequality lmi based multiobjective evolution algorithm lmi based moea is developed based on non dominating sorting scheme to efficiently search the set of pareto optimal solutions for the mop from which designer can select one design according to his own preference further the multiobjective h 2 h fuzzy control design problem based on the weighted sum method is also solved as an alternative choice finally a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method

robustness of perturbed large scale systems with local constant state feedback the robustness problem of perturbed large scale systems is considered the nominal large scale system is stabilized by a local constant state feedback ui t kixi t and the local optimal control law ui t r i 1 bi tpixi t respectively in the above two cases bounds are obtained for an allowable non linear time invariant or time varying perturbation such that the resulting closed loop large scale system remains stable the special case of a linear perturbation is also treated here

decentralized dynamic output feedback control for affine fuzzy large scale systems with measurement errors this paper investigates the decentralized output feedback control problem for affine fuzzy large scale systems with unknown interconnections a decentralized piecewise dynamic output feedback controller is constructed and the measurement errors between actual outputs and measured outputs are considered in control synthesis by introducing the s procedure and a cyclic small gain condition novel controller design conditions in terms of linear matrix inequalities lmis are derived which allow for reducing the worst case peak output due to measurement errors with satisfying an l norm constraint finally two examples are given to illustrate the effectiveness and superiority of the new results

h_ infty fuzzy control synthesis for a large scale system with a reduced number of lmis this paper introduces an h infty fuzzy control synthesis method for a nonlinear large scale system with a reduced number of linear matrix inequalities lmis it is well known that a nonlinear large scale system can be transformed to a takagi sugeno t s fuzzy system by using sector nonlinearity or local approximation in fuzzy partition spaces methods next in order to achieve the fuzzy control design for this t s fuzzy system we solve the stabilization conditions that are represented by the lmis however if the number of lmis is large the control design process may become very complicated in this study based on the lyapunov method and s procedure several theorems are proposed for the synthesis of parallel distributed compensation pdc type fuzzy control such that the nonlinear large scale system achieves h infty control performance and the number of lmis to be solved is reduced explicitly as a result the control design process will become much easier furthermore if the modeling error between the nonlinear system and t s fuzzy system exists the robust h infty control performance and the number reduction of lmis are also achieved by the proposed theorem several examples are presented in this paper to show the number reduction effect of lmis and the effectiveness of the proposed controller synthesis

nonlinear decentralized state feedback controller for uncertain fuzzy time delay interconnected systems abstract in this paper the perturbed continuous time interconnected system with time delay is represented by an equivalent takagi sugeno type fuzzy model having r i rules for each subsystem based on lyapunov stability theorem and razumikhin theorem the nonlinear decentralized state feedback fuzzy controllers are proposed to stabilize the whole perturbed fuzzy time delay interconnected system asymptotically under using this nonlinear controller the design methods only consider the r i fuzzy rules rather than r i r i rules for each subsystem that is we can remove the negative effect of the coupled terms therefore these approaches can be less conservative moreover if all the time delays of each subsystem are the same for all rules we shall propose less conservative criteria these criteria do not need the solution of a lyapunov equation or a riccati equation we also do not need to find a common positive matrix p to satisfy any inequality the so called matching condition for the interconnection matrices and perturbations are not needed finally a numerical example is given to illustrate the control design and its effectiveness

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

sequential stability analysis and observer design for distributed ts fuzzy systems many complex physical systems are the interconnection of lower dimensional subsystems for such systems distributed stability analysis and observer design presents several advantages with respect to centralized approaches such as modularity easier analysis and design and reduced computational complexity applications include distributed process control traffic and communication networks and economic systems in this paper we propose sequential stability analysis and observer design for distributed systems where the subsystems are represented by takagi sugeno ts fuzzy models the analysis and design are done sequentially for the subsystems allowing for the online addition of new subsystems the conditions are formulated as lmis and are therefore easy to solve the approach is illustrated on simulation examples

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

estimation and evaluation of linear individualized treatment rules to guarantee performance summary in clinical practice an informative and practically useful treatment rule should be simple and transparent however because simple rules are likely to be far from optimal effective methods to construct such rules must guarantee performance in terms of yielding the best clinical outcome highest reward among the class of simple rules under consideration furthermore it is important to evaluate the benefit of the derived rules on the whole sample and in pre specified subgroups e g vulnerable patients to achieve both goals we propose a robust machine learning method to estimate a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules we then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods we provide theoretical justification for the proposed method and its inference procedure and we demonstrate via simulations its superior performance when compared to existing methods lastly we apply the method to the sequenced treatment alternatives to relieve depression star d trial on major depressive disorder and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack of fit for moderately depressed patients

concordance assisted learning for estimating optimal individualized treatment regimes in this article we propose a new concordance assisted learning for estimating optimal individualized treatment regimes we first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function we then find treatment regimes up to a threshold to maximize the concordance function named prescriptive index finally within the class of treatment regimes that maximize the concordance function we find the optimal threshold to maximize the value function we establish the convergence rate and asymptotic normality of the proposed estimator for parameters in the prescriptive index an induced smoothing method is developed to estimate the asymptotic variance of the proposed estimator we also establish the n1 3 consistency of the estimated optimal threshold and its limiting distribution in addition a doubly robust estimator of parameters in the prescriptive index is developed under a class of monotonic index models the practical use and effectiveness of the proposed methodology are demonstrated by simulation studies and an application to an aids data

tree based methods for individualized treatment regimes individualized treatment rules recommend treatments on the basis of individual patient characteristics a high quality treatment rule can produce better patient outcomes lower costs and less treatment burden if a treatment rule learned from data is to be used to inform clinical practice or provide scientific insight it is crucial that it be interpretable clinicians may be unwilling to implement models they do not understand and black box models may not be useful for guiding future research the canonical example of an interpretable prediction model is a decision tree we propose a method for estimating an optimal individualized treatment rule within the class of rules that are representable as decision trees the class of rules we consider is interpretable but expressive a novel feature of this problem is that the learning task is unsupervised as the optimal treatment for each patient is unknown and must be estimated the proposed method applies to both categorical and continuous treatments and produces favourable marginal mean outcomes in simulation experiments we illustrate it using data from a study of major depressive disorder

initial value problem for first order integro differential equation of volterra type on time scales abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear integro differential equations on time scales several important lemmas and existence criteria are obtained

on estimation of optimal treatment regimes for maximizing t year survival probability a treatment regime is a deterministic function that dictates personalized treatment based on patients individual prognostic information there is increasing interest in finding optimal treatment regimes which determine treatment at one or more treatment decision points so as to maximize expected long term clinical outcome where larger outcomes are preferred for chronic diseases such as cancer or hiv infection survival time is often the outcome of interest and the goal is to select treatment to maximize survival probability we propose two nonparametric estimators for the survival function of patients following a given treatment regime involving one or more decisions i e the so called value based on data from a clinical or observational study we estimate an optimal regime by maximizing these estimators for the value over a prespecified class of regimes because the value function is very jagged we introduce kernel smoothing within the estimator to improve performance asymptotic properties of the proposed estimators of value functions are established under suitable regularity conditions and simulations studies evaluate the finite sample performance of the proposed regime estimators the methods are illustrated by application to data from an aids clinical trial

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

positive solutions for nonlinear first order periodic boundary value problems of impulsive dynamic equations on time scales in this paper existence criteria of positive solutions to a class of nonlinear first order periodic boundary value problems of impulsive dynamic equations on time scales are obtained the main tool used in this paper is the well known guo krasnoselskii fixed point theorem

high dimensional a learning for optimal dynamic treatment regimes precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information for many complex diseases such as cancer treatment decisions need to be tailored over time according to patients responses to previous treatments such an adaptive strategy is referred as a dynamic treatment regime a major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors such as patient s genetic information demographic characteristics medical history and clinical measurements over time are available but not all of them are necessary for making treatment decision this makes variable selection an emerging need in precision medicine in this paper we propose a penalized multi stage a learning for deriving the optimal dynamic treatment regime when the number of covariates is of the non polynomial np order of the sample size to preserve the double robustness property of the a learning method we adopt the dantzig selector which directly penalizes the a leaning estimating equations oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the star d study

some pachpatte type inequalities on time scales in this paper using the comparison theorem we investigate some pachpatte type integral inequalities on time scales which provide explicit bounds on unknown functions our results extend some known dynamic inequalities on time scales unify and extend some continuous inequalities and their corresponding discrete analogues some applications of the main results are given in the end of this paper

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

greedy outcome weighted tree learning of optimal personalized treatment rules summary we propose a subgroup identification approach for inferring optimal and interpretable personalized treatment rules with high dimensional covariates our approach is based on a two step greedy tree algorithm to pursue signals in a high dimensional space in the first step we transform the treatment selection problem into a weighted classification problem that can utilize tree based methods in the second step we adopt a newly proposed tree based method known as reinforcement learning trees to detect features involved in the optimal treatment rules and to construct binary splitting rules the method is further extended to right censored survival data by using the accelerated failure time model and introducing double weighting to the classification trees the performance of the proposed method is demonstrated via simulation studies as well as analyses of the cancer cell line encyclopedia ccle data and the tamoxifen breast cancer data

l2 spaces and boundary value problems on time scales abstract in this paper we consider a second order sturm liouville type boundary value operator of the form l u p u q u on an arbitrary bounded time scale t for suitable functions p q together with suitable boundary conditions operators of this type on time scales have normally been considered in a setting involving banach spaces of continuous functions on t in this paper we introduce a space l 2 t of square integrable functions on t and sobolev type spaces h n t n 1 consisting of l 2 t functions with nth order generalised l 2 t type derivatives we prove some basic functional analytic results for these spaces and then formulate the operator l in this setting in particular we allow p h 1 t while q l 2 t this generalises the usual conditions that p c rd 1 t q c rd 0 t 2 we give some immediate applications of the functional analytic results to l such as positivity injectivity invertibility and compactness of the inverse we also construct a green s function for l the analogues of these results on real intervals are well known and are fundamental to the usual sturm liouville theory on such intervals

constructing dynamic treatment regimes over indefinite time horizons summaryexisting methods for estimating optimal dynamic treatment regimes are limited to cases where a utility function is optimized over a fixed time period we develop an estimation procedure for the optimal dynamic treatment regime over an indefinite time period and derive associated large sample results the proposed method can be used to estimate the optimal dynamic treatment regime in chronic disease settings we illustrate this by simulating a dataset corresponding to a cohort of patients with diabetes that mimics the third wave of the national health and nutrition examination survey and examining the performance of the proposed method in controlling the level of haemoglobin a1c

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

robust estimation of optimal dynamic treatment regimes for sequential treatment decisions a dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient s history q and a learning are two main approaches for estimating the optimal regime i e that yielding the most beneficial outcome in the patient population using data from a clinical trial or observational study q learning requires postulated regression models for the outcome while a learning involves models for that part of the outcome regression representing treatment contrasts and for treatment assignment we propose an alternative to q and a learning that maximizes a doubly robust augmented inverse probability weighted estimator for population mean outcome over a restricted class of regimes simulations demonstrate the method s performance and robustness to model misspecification which is a key concern

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

weak maximum principle and accessory problem for control problems on time scales abstract in this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state endpoints equality constraints using the first variation a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the dubois reymond lemma to the optimal control setting and time scales a second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions the control problem is studied under a controllability assumption and with or without the shift in the state variable these two forms of the problem are shown to be equivalent

fuzzy mixed h 2 h infty optimization based decentralized model reference control and application to piezo driven xy table systems in this paper a decentralized model reference control via fuzzy mixed h2 hinfin optimization design was developed each subsystem contained l linear pulse transfer function systems lptfss the reference model for every lptfs was first designed to shape the response of the ith closed loop subsystem then the h2 norm of the output error i e the difference between the output of the reference model and the system and weighted control input of the jth lptfs was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the jth lptfs was achieved however an output disturbance of the jth lptfs caused by the interactions among the lptfss the interconnections among the subsystems modeling errors and external loads deteriorated system performance or even resulted in instability in this situation the h infin norm of weighted sensitivity between output disturbance and output error of the jth lptfs was minimized to attenuate its effect a nonlinear control based on output error for every lptfs was also established to improve robust performance the stability of the overall system was then verified by lyapunov stability criterion the application to piezo driven xy table system pd xy ts was carried out to confirm the usefulness of the proposed control

nonlinear integro differential equations and optimal control problems on time scales this paper is mainly concerned with a class of optimal control problems of a system governed by the nonlinear integro differential equation on time scales using the contraction mapping principle the existence and uniqueness of a weak solution of the nonlinear integro differential equation on time scales are proved discussing l t 1 strong weak lower semicontinuity of integral functional on time scales we give sufficient conditions for the existence of optimal control by the virtue of the integration by parts formula on time scales the necessary conditions of optimality are derived

decentralized fuzzy control of nonlinear interconnected dynamic delay systems via mixed h_2 h_ infty optimization with smith predictor each subsystem of a nonlinear interconnected dynamic delayed system is approximated by a weighted combination of l transfer function delayed systems tfdss the h2 norm of the difference between the transfer function of a reference model and the closed loop transfer function of the kth tfds of subsystem i is then minimized to obtain a suitable frequency response without incurring oscillating and sluggish phenomena because of the existence of the disturbance at the output of the kth tfds which is not only large but also contains various frequency components the h norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth tfds is simultaneously minimized to reduce its effect furthermore with proper selection of weighted sensitivity functions certain specific modes of the output disturbance can be eliminated finally two simulations are performed one is the simulation of our designed tfdss with different delays or nonminimum phases and the other is the simulation of an internet based intelligent space for the trajectory tracking of a car like wheeled robot system we demonstrate the effectiveness and efficiency of the proposed control the main contributions of this paper are twofold first the control can simultaneously attain robust performance through the mixed h2 h optimization with a smith predictor and achieve the robust stability via l2n stable with finite gain second fuzzy observer is not needed

integration on time scales in this paper we study the process of riemann and lebesgue integration on time scales the relationship of the riemann and lebesgue integrals is considered and a criterion for riemann integrability is established

theory of the fuzzy controller abstract we first introduce notation in an attempt to standardize the description of a basic fuzzy controller if r 1 r 2 r n are the real number inputs to the fuzzy controller and is its defuzzified output then f r 1 r n for some function f by the theory of the fuzzy controller we mean in this paper the study of the structure of f for elementary fuzzy controllers using this standardized notation we first survey the known results on the theory of the fuzzy controller and then discuss important future research topics in this area

h synchronization of chaotic systems using output feedback control design this article investigates the h synchronization problem for a general class of chaotic systems based on lyapunov theory linear matrix inequality lmi and linear matrix equality lme formulation the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an h norm constraint two illustrative examples are provided to demonstrate the effectiveness of the developed theoretical results

a systematic method for design of multivariable fuzzy logic control systems this paper proposes a systematic method to design a multivariable fuzzy logic controller for large scale nonlinear systems in designing a fuzzy logic controller the major task is to determine fuzzy rule bases membership functions of input output variables and input output scaling factors in this work the fuzzy rule base is generated by a rule generated function which is based on the negative gradient of a system performance index the membership functions of isosceles triangle of input output variables are fixed in the same cardinality and only the input output scaling factors are generated from a genetic algorithm based on a fitness function as a result the searching space of parameters is narrowed down to a small space the multivariable fuzzy logic controller can quickly constructed and the fuzzy rules and the scaling factors can easily be determined the performance of the proposed method is examined by computer simulations on a puma 560 system and a two inverted pendulum system

model reference output feedback fuzzy tracking control design for nonlinear discrete time systems with time delay in this study a model reference fuzzy tracking control design for nonlinear discrete time systems with time delay is introduced first the takagi and sugeno ts fuzzy model is employed to approximate a nonlinear discrete time system with time delay next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs the advantage of proposed tracking control design is that only a simple fuzzy observer based controller is used in our approach without feedback linearization technique and complicated adaptive scheme by the proposed method the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem lmip the lmip can be efficiently solved using the convex optimization techniques simulation example is given to illustrate the design procedures and tracking performance of the proposed method

a fuzzy decentralized variable structure tracking control with optimal and improved robustness designs theory and applications to begin with each subsystem of a nonlinear interconnected system was approximated by a weighted combination of l linear pulse transfer function systems lptfss for every nominal lptfs of the mth subsystem a dead beat to its switching surface was first designed the output disturbance of the mth lptfs included the interconnections coming from the other subsystems the approximation error of the mth subsystem and the interactions resulting from the other lptfss in general this output disturbance was not small and contains various frequencies under this circumstances the h sup spl infin norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized in addition an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance although the effect of the output disturbance is attenuated and partially rejected a better performance could be enhanced by a switching control based on the lyapunov redesign in addition the stability of the overall system was verified by lyapunov stability theory the simulations for the lptfss with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control finally the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control

brief paper delay dependent robust stability of uncertain fuzzy large scale systems with time varying delays this paper addresses the stability problem of fuzzy large scale systems flsss with uncertainties and arbitrary time varying delays the stability conditions which are less conservative and more applicable than the existing results are derived by a novel lyapunov krasovskii functional method and expressed in terms of linear matrix inequalities lmis two examples are given to demonstrate the correctness and advantage of our theoretical results

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

robust stabilization in an observer controller feedback system under nonlinear time varying perturbations or unmodeled dynamics in this note a new robust criterion is proposed to analyze multivariable observer controller compensator feedback systems under additive nonlinear perturbations in order to stabilize these systems a more general parameterized observer controller compensator is introduced and a design algorithm is proposed for robust stabilization against the nonlinear perturbations finally an example is given to illustrate our results

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

a new approach to fuzzy modeling this paper proposes a new approach to fuzzy modeling the suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as takagi and sugeno s model 1985 because it has the same structure as that of takagi and sugeno s model it is also as easy to implement as sugeno and yasukawa s model 1993 because its identification mimics the simple identification procedure of sugeno and yasukawa s model the suggested algorithm is composed of two steps coarse tuning and fine tuning in coarse tuning fuzzy c regression model fcrm clustering is used which is a modified version of fuzzy c means fcm in fine tuning gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models finally some examples are given to demonstrate the validity of this algorithm

interval type 2 fuzzy adaptive tracking control design for pmdc motor with the sector dead zones we propose it2fac scheme to reduce the sector dead zone nonlinearities this scheme integrates variable structure to achieve the h tracking performance this scheme uses the lyapunov criterion to ensure the boundedness of all states this scheme exhibits faster tracking responses for the pmdc motor systems this paper deals with the permanent magnet dc motor system with sector dead zones and external disturbances via interval type 2 fuzzy adaptive tracking control scheme to achieve h tracking performance the type 2 fuzzy dynamic model is used to approximate the motor dynamics without constructing sector dead zone inverse where the parameters of the fuzzy model are obtained both from the fuzzy inference and online update laws based on the lyapunov criterion and riccati inequality the control scheme is derived to stabilize the closed loop system such that all states of the system are guaranteed to be bounded and h tracking performance is achieved due to uncertainties dead zone nonlinearities and external disturbances the advantage of the proposed control scheme is that it can better handle the vagueness or uncertainties inherent in linguistic words using fuzzy set membership functions with adaptation capability by linear analytical results instead of estimating non linear system functions as the system parameters are unknown finally the simulations of the pmdc motor system with sector dead zone nonlinearities are used to illustrate the effectiveness of the proposed control scheme and the performance comparisons with the three dimensional autonomous r o ssler system wang and chua 2008 are used to validate the h tracking performance of the pmdc motor system

properties of certain iterated dynamic integrodiffetential equation on time scales abstract the main objective of this paper is study the existence uniqueness and other properties of solution of some iterated dynamic integrodifferential on time scales the main tools employed are banach fixed point theorem and an inequality with explicit estimates are used for proving our results

interactive q learning for quantiles abstracta dynamic treatment regime is a sequence of decision rules each of which recommends treatment based on features of patient medical history such as past treatments and outcomes existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable however the mean may not always be the most appropriate summary of performance we derive estimators of decision rules for optimizing probabilities and quantiles computed with respect to the response distribution for two stage binary treatment settings this enables estimation of dynamic treatment regimes that optimize the cumulative distribution function of the response at a prespecified point or a prespecified quantile of the response distribution such as the median the proposed methods perform favorably in simulation experiments we illustrate our approach with data from a sequentially randomized trial where the primary outcome is remission of depression symptoms supplementary materials for this arti

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

decentralized pdc for large scale t s fuzzy systems this paper studies the decentralized stabilization problem for a large scale system the considered large scale system comprises of a number of subsystems and each subsystem is represented by a takagi sugeno t s fuzzy model the interconnection between any two subsystems may be nonlinear and satisfies some matching condition by the concept of parallel distributed compensation pdc the decentralized fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections maximal number of the fired rules in each subsystem and the common positive matrix p sub i based on lyapunov criterion and riccati inequality some sufficient conditions are derived and the common p sub i is solved by linear matrix inequalities lmi so that the whole closed loop large scale fuzzy system with the synthesized fuzzy control is asymptotically stable finally a numerical example is given to illustrate the control synthesis and its effectiveness

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

bayesian nonparametric estimation for dynamic treatment regimes with sequential transition times abstractwe analyze a dataset arising from a clinical trial involving multi stage chemotherapy regimes for acute leukemia the trial design was a 2 2 factorial for frontline therapies only motivated by the idea that subsequent salvage treatments affect survival time we model therapy as a dynamic treatment regime dtr that is an alternating sequence of adaptive treatments or other actions and transition times between disease states these sequences may vary substantially between patients depending on how the regime plays out to evaluate the regimes mean overall survival time is expressed as a weighted average of the means of all possible sums of successive transitions times we assume a bayesian nonparametric survival regression model for each transition time with a dependent dirichlet process prior and gaussian process base measure ddp gp posterior simulation is implemented by markov chain monte carlo mcmc sampling we provide general guidelines for constructing a prior using empirical baye

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

necessary conditions of optimality for a class of optimal control problems on time scales a class of optimal control problems of a system governed by linear dynamic equations on time scales with quadratic cost functional is considered by the lebesgue d integral theory and the sobolev type space h 1 on time scales the weak solution of linear dynamic equations on time scales for both initial value problem and backward problem are introduced therefore the necessary conditions of optimality are presented some typical examples are given for demonstration

affine ts model based fuzzy regulating servo control design an affine t s fuzzy system is derived naturally from linearizing a nonlinear system or from some data driven identification techniques for example cluster based algorithms or soft computation learning structures little research is proposed for the intrinsic analysis of an affine type fuzzy system further the controllers to regulate or to achieve servo control of affine ts based nonlinear systems are also few both affine type fuzzy regulation and servo control design scheme are theoretically derived a simple lyapunov based stability criterion and some extra conditions are proposed to guarantee the global stability of the generated closed loop fuzzy systems the exponential stability of the feedback fuzzy system is ensured under some conditions the performance of the proposed fuzzy controllers and fuzzy servo controllers is examined by three case studies simulation results show that the proposed controllers can stabilize these affine fuzzy systems and the proposed servomechanism can adapt itself to various incoming signals in very short time spans