cheap control for a class of non linear systems for a class of non linear dynamic systems a quadratic regulator problem is considered in which the cost functional contains a small parameter multiplied to the control term in the analysis of the problem an appropriate transformation of the state variables and an eigenvector technique are utilized which were devised originally for analysing complex linear cheap control problems and for solving a lyapunov type system of linear equations respectively in so doing the class of nonlinear systems is characterized and extended in a mathematically simple way for which the optimal cost becomes zero as the small parameter goes to zero

differential geometric methods in variable structure control this article presents a differential geometric approach for the design of sliding modes in non linear variable structure feedback systems coordinate free characterizations of local existence conditions for sliding regimes and a geometric reformulation of some of its most salient features are presented the approach uses basic notions from differential geometry involving vector fields distributions and 1 forms both single and multiple input cases are treated with some illustrative examples

a multivariate two sample test based on the number of nearest neighbor type coincidences for independent d variate random samples x 1 cdots x n 1 i i d f x y 1 cdots y n 2 i i d g x where the densities f and g are assumed to be continuous a e consider the number t of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample we show that if f g a e the limiting normal distribution of t as min n 1 n 2 rightarrow infty n 1 n 1 n 2 rightarrow tau 0 tau 1 does not depend on f an omnibus procedure for testing the hypothesis h 0 f g a e is obtained by rejecting h 0 for large values of t the result applies to a general distance generated by a norm on mathbb r d for determining nearest neighbors and it generalizes to the multisample situation

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

a model reference adaptive control scheme for pure feedback nonlinear systems a model reference adaptive control mrac scheme is presented for nonlinear systems in a pure feedback canonical form with unknown parameters the present of parameter uncertainty in the system causes imperfect linearization i e it introduces nonlinear additive terms in the transformed coordinates under some mild technical assumptions global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

singular pdes and the single step formulation of feedback linearization with pole placement the present work proposes a new formulation and approach to the problem of feedback linearization with pole placement the problem under consideration is not treated within the context of geometric exact feedback linearization where restrictive conditions arise from a two step design method transformation of the original nonlinear system into a linear one in controllable canonical form with an external reference input and the subsequent employment of linear pole placement techniques in the present work the problem is formulated in a single step using tools from singular pde theory in particular the mathematical formulation of the problem is realized via a system of first order quasi linear singular pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the system of singular pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law computed through the solution of the system of singular pdes both feedback linearization and pole placement design objectives may be accomplished in a single step effectively overcoming the restrictions of the other approaches by bypassing the intermediate step of transforming the original system into a linear controllable one with an external reference input

state feedback control of non linear systems a design method for state feedback controllers for single input non linear systems is proposed the method makes use of the transformations of the non linear system into controllable like canonical forms the resulting non linear state feedback is designed in such a way that the eigenvalues of the linearized closed loop model are invariant with respect to any constant operating point the method constitutes an alternative approach to the design methodology recently proposed by baumann and rugh also a review of different transformation methods for non linear systems is presented an example and simulation results of different control strategies are provided to illustrate the design technique

aggregation of a class of interconnected linear dynamical systems abstract in this paper we introduce the notion of a meaningful average of a collection of dynamical systems as distinct from an ensemble average such a notion is useful for the study of a variety of dynamical systems such as traffic flow power systems and econometric systems we also address the associated issue of the existence and computation of such an average for a class of interconnected linear time invariant dynamical systems such an average dynamical system is not only attractive from a computational perspective but also represents the average behavior of the interconnected dynamical systems the problem of analysis and control of heirarchical large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system

nonlinear control via uniform system approximation abstract we introduce the notion of uniform system approximation and use it to solve the following problem given a single input nonlinear system f g x f x g x u that is linearly controllable on a manifold e of equilibrium points find vector fields f g such that f g and f g agree to first order on e and f g is input to state linearizable on a neighborhood of e the solution proceeds by constructing a linearizable uniform system approximation and yields as a by product a feedback control law that can be used to guarantee stable operation of the given system in a neighborhood of e this includes for example smooth transitions between operating points that are not necessarily close to each other a simple example is given to illustrate the approach

linearization of discrete time nonlinear systems and a canonical structure linearizable nonlinear discrete time systems are described as a composition of diffeomorphisms linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms

robust tracking in nonlinear systems a nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system the tracking error is measured by a general function of system state and the input command the controller is robust in the sense that the tracking error is ultimately bounded in the presence of modeling errors free parameters which affect the form of the controller allow flexibility in determining such factors as the size of the ultimate bound the rate of error decay excursion of the control conditions on the class of modeling errors and the level of system gain restrictive assumptions on the structure of the model and the modeling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature these assumptions hold for robotic manipulators this application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature

global inverse optimal control with guaranteed convergence rates of input affine nonlinear systems in earlier works global inverse optimal controllers were proposed for input affine nonlinear systems with given control lyapunov functions however these controllers do not provide information about the convergence rates if the systems have local homogeneous approximations we can employ homogeneous controllers which locally asymptotically stabilize the origin and specify the convergence rates however homogeneous controllers generally do not attain global stability for nonhomogeneous systems in this paper we design global inverse optimal controllers with guaranteed local convergence rates by utilizing local homogeneity of input affine nonlinear systems if we do not consider inverse optimality we can liberally adjust the sector margins we also clarify that local convergence rates and sector margins are invariant under coordinate transformations

nilpotent bases for distributions and control systems abstract let v m be the lie algebra infinite dimensional of real analytic vector fields on the n dimensional manifold m necessary conditions that a real analytic k dimensional distibution on m have a local basis which generates a nilpotent subalgebra of v m are derived two methods for sufficient conditions are given the first depending on the existence of a solution to a system of partial differential equations the second using darboux s theorem to give a computable test for an n 1 dimensional distribution a nonlinear control system in which the control variables appear linearly can be transformed into an orbit equivalent system whose describing vector fields generate a nilpotent algebra if the distribution generated by the original describing vector fields admits a nilpotent basis when this is the case local analysis of the control system is greatly simplified

an exact distribution free test comparing two multivariate distributions based on adjacency summary a new test is proposed comparing two multivariate distributions by using distances between observations unlike earlier tests using interpoint distances the new test statistic has a known exact distribution and is exactly distribution free the interpoint distances are used to construct an optimal non bipartite matching i e a matching of the observations into disjoint pairs to minimize the total distance within pairs the cross match statistic is the number of pairs containing one observation from the first distribution and one from the second distributions that are very different will exhibit few cross matches when comparing two discrete distributions with finite support the test is consistent against all alternatives the test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks comparing brains that are impaired by arteriovenous abnormalities with normal controls a second exact distribution free test is also discussed it ranks the pairs and sums the ranks of the cross matched pairs

an input output characterization for linearization by feedback for a stationary initially relaxed single input single output bilinear realizable system that is described by a sequence of regular transfer functions the relative degrees of the individual transfer functions are defined in a manner similar to the linear case these relative degrees are used to characterize the region where linear input output behavior can be obtained by state feedback in a bilinear realization of the system

ensemble subsampling for imbalanced multivariate two sample tests some existing nonparametric two sample tests for equality of multivariate distributions perform unsatisfactorily when the two sample sizes are unbalanced in particular the power of these tests tends to diminish with increasingly unbalanced sample sizes in this article we propose a new testing procedure to solve this problem the proposed test based on the nearest neighbor method by schilling employs a novel ensemble subsampling scheme to remedy this issue more specifically the test statistic is a weighted average of a collection of statistics each associated with a randomly selected subsample of the data we derive the asymptotic distribution of the test statistic under the null hypothesis and show that the new test is consistent against all alternatives when the ratio of the sample sizes either goes to a finite limit or tends to infinity via simulated data examples we demonstrate that the new test has increasing power with increasing sample size ratio when the size of the smaller sample is fixe

a kernel two sample test we propose a framework for analyzing and comparing distributions which we use to construct statistical tests to determine if two samples are drawn from different distributions our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel hilbert space rkhs and is called the maximum mean discrepancy mmd we present two distribution free tests based on large deviation bounds for the mmd and a third test based on the asymptotic distribution of this statistic the mmd can be computed in quadratic time although efficient linear time approximations are available our statistic is an instance of an integral probability metric and various classical metrics on distributions are obtained when alternative function classes are used in place of an rkhs we apply our two sample tests to a variety of problems including attribute matching for databases using the hungarian marriage method where they perform strongly excellent performance is also obtained when comparing distributions over graphs for which these are the first such tests

gap metric based robustness analysis of nonlinear systems with full and partial feedback linearisation abstractthis paper uses gap metric analysis to derive robustness and performance margins for feedback linearising controllers distinct from previous robustness analysis it incorporates the case of output unstructured uncertainties and is shown to yield general stability conditions which can be applied to both stable and unstable plants it then expands on existing feedback linearising control schemes by introducing a more general robust feedback linearising control design which classifies the system nonlinearity into stable and unstable components and cancels only the unstable plant nonlinearities this is done in order to preserve the stabilising action of the inherently stabilising nonlinearities robustness and performance margins are derived for this control scheme and are expressed in terms of bounds on the plant nonlinearities and the accuracy of the cancellation of the unstable plant nonlinearity by the controller case studies then confirm reduced conservatism compared with standard methods

on the extension of the korobov s class of linearizable triangular systems by nonlinear control systems of the class c1 abstract we give the complete description of nonlinear control systems of the class c 1 with one dimensional control which are feedback linearizable by means of a change of the control of the class c 1 and a change of variables of the class c 2 as well as the control systems which are linearizable by means of a change of variables only the both results are originated from the approach proposed by v i korobov in 1973 for the linearization of triangular control systems

the control of robot manipulators with bounded input the problem of tracking a desired trajectory in the state space of an n link robotic manipulator with bounds on the allowable input torque is considered using a so called optimal decision strategy ods a pointwise optimal control law is derived which at each time t minimizes the deviation between the vector of joint accelerations and a desired joint acceleration vector subject to the input constraints the design of the optimal control law is reduced to the solution of a quadratic programming problem which is solved using the primal dual method the solution gives an on line feedback control scheme for trajectory following in the presence of input constraints in addition we extend the above optimal decision strategy to the case where the controller design is based on a simplified model or where the plant itself is imprecisely known the resulting torque optimization scheme may be incorporated into any existing control scheme to account for input bounds this has important implications for the problem of deriving robust control schemes that take into account parameter uncertainty and model simplification simulations are presented for the case of a three link manipulator with bounded torque and our results are compared to the computed torque method our simulations show that by optimally adjusting the input torque to each joint when one or more of them saturates significant improvement in tracking performance can result

distortion of effects caused by indirect confounding summary undetected confounding may severely distort the effect of an explanatory variable on a response variable as defined by a stepwise data generating process the best known type of distortion which we call direct confounding arises from an unobserved explanatory variable common to a response and its main explanatory variable of interest it is relevant mainly for observational studies since it is avoided by successful randomization by contrast indirect confounding which we identify in this paper is an issue also for intervention studies for general stepwise generating processes we provide matrix and graphical criteria to decide which types of distortion may be present when they are absent and how they are avoided we then turn to linear systems without other types of distortion but with indirect confounding for such systems the magnitude of distortion in a least squares regression coefficient is derived and shown to be estimable so that it becomes possible to recover the effect of the generating process from the distorted coefficient

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

conditionally specified continuous distributions a distribution is conditionally specified when its model constraints are expressed conditionally for example besag s 1974 spatial model was specified conditioned on the neighbouring states and pseudolikelihood is intended to approximate the likelihood using conditional likelihoods there are three issues of interest existence uniqueness and computation of a joint distribution in the literature most results and proofs are for discrete probabilities here we exclusively study distributions with continuous state space we examine all three issues using the dependence functions derived from decomposition of the conditional densities we show that certain dependence functions of the joint density are shared with its conditional densities therefore two conditional densities involving the same set of variables are compatible if their overlapping dependence functions are identical we prove that the joint density is unique when the set of dependence functions is both compatible and complete in addition a joint density apart from a constant can be computed from the dependence functions in closed form since all of the results are expressed in terms of dependence functions we consider our approach to be dependence based whereas methods in the literature are generally density based applications of the dependence based formulation are discussed

permutation tests for equality of distributions in high dimensional settings motivated by applications in high dimensional settings we suggest a test of the hypothesis h 0 that two sampled distributions are identical it is assumed that two independent datasets are drawn from the respective populations which may be very general in particular the distributions may be multivariate or infinite dimensional in the latter case representing for example the distributions of random functions from one euclidean space to another our test uses a measure of distance between data this measure should be symmetric but need not satisfy the triangle inequality so it is not essential that it be a metric the test is based on ranking the pooled dataset with respect to the distance and relative to any fixed data value and repeating this operation for each fixed datum a permutation argument enables a critical point to be chosen such that the test has concisely known significance level conditional on the set of all pairwise distances

a functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

discriminant adaptive nearest neighbor classification nearest neighbour classification expects the class conditional probabilities to be locally constant and suffers from bias in high dimensions we propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality we use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods we determine the local decision boundaries from centroid information and then shrink neighbourhoods in directions orthogonal to these local decision boundaries and elongate them parallel to the boundaries thereafter any neighbourhood based classifier can be employed using the modified neighbourhoods the posterior probabilities tend to be more homogeneous in the modified neighbourhoods we also propose a method for global dimension reduction that combines local dimension information in a number of examples the methods demonstrate the potential for substantial improvements over nearest neighbour classification

ensemble subsampling for imbalanced multivariate two sample tests chen l dou w w and qiao z 2013 journal of the american statistical association 108 1308 1323

exact and approximate feedback linearization without the linear controllability assumption the feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable in this paper the assumption of linear controllability is removed necessary and sufficient conditions are given through lie orbital symmetries thus giving a geometric characterization of the problem in the analytic case both the exact and the approximate linearization problems are considered in the analytic case

large rotations revisited application of lie algebra abstract the paper presents an elementary introduction and application of lie algebra to compound groups of large rotations following an elementary overview of the foundations of lie algebra the authors discuss the rotational groups lo 3 and the exponential form of the rotation matrix these yield a practical link between the elegance of lie group theory and engineering kinematics some illustrative examples as the standard stanford manipulator indicate interesting possibilities on enlarged applications concerning robotic mechanisms vehicles and biosystems

on the limiting distributions of multivariate depth based rank sum statistics and related tests a depth based rank sum statistic for multivariate data introduced by liu and singh j amer statist assoc 88 1993 252 260 as an extension of the wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies those applications however are based on a conjectured limiting distribution provided by liu and singh j amer statist assoc 88 1993 252 260 the present paper proves the conjecture under general regularity conditions and therefore validates various applications of the rank sum statistic in the literature the paper also shows that the corresponding rank sum tests can be more powerful than hotelling s t 2 test and some commonly used multivariate rank tests in detecting location scale changes in multivariate distributions

feedforward and feedback linearization of non linear systems with disturbances the problem of transforming non linear systems with input disturbances to their linear equivalents is investigated a characterization of the class of non linear systems with disturbances that are equivalent to controllable quasi linear systems with disturbances z az bv z d is given the necessary transformations state space coordinate changes and control input space coordinate changes by non linear feedforward and feedback are presented and their implications for control system synthesis are discussed finally a numerical example is given

instrumental variables as bias amplifiers with general outcome and confounding drawing causal inference with observational studies is the central pillar of many disciplines one sufficient condition for identifying the causal effect is that the treatment outcome relationship is unconfounded conditional on the observed covariates it is often believed that the more covariates we condition on the more plausible this unconfoundedness assumption is this belief has had a huge impact on practical causal inference suggesting that we should adjust for all pretreatment covariates however when there is unmeasured confounding between the treatment and outcome estimators adjusting for some pretreatment covariate might have greater bias than estimators without adjusting for this covariate this kind of covariate is called a bias amplifier and includes instrumental variables that are independent of the confounder and affect the outcome only through the treatment previously theoretical results for this phenomenon have been established only for linear models we fill in this gap in the literature by providing a general theory showing that this phenomenon happens under a wide class of models satisfying certain monotonicity assumptions we further show that when the treatment follows an additive or multiplicative model conditional on the instrumental variable and the confounder these monotonicity assumptions can be interpreted as the signs of the arrows of the causal diagrams

gir based ensemble sampling approaches for imbalanced learning abstract this paper presents two adaptive ensemble sampling approaches for imbalanced learning one is the undersampling based approach and the other one is the oversampling based approach with the objectives of bias reduction and adaptive learning both of these two approaches are based on a novel class imbalance metric termed generalized imbalance ratio gir instead of the conventional sample size ratio specifically these two sampling based approaches adaptively split the imbalanced learning problem into multiple balanced learning subproblems in a probabilistic way which forces the classifiers trained in the subproblems focus on those difficult to learn samples in each subproblem several weak classifiers are trained in a boosting manner a final stronger classifier is further built by combining all these weak classifiers in a bagging manner extensive experiments are conducted on real life uci imbalanced data sets to evaluate the performance of the proposed methods the superior performance demonstrates the effectiveness of the proposed methods and indicates wide potential applications in data mining

on the global linearization on nonhomogeneous bilinear systems abstract the problem of finding a global state space transformation to transform a given single input nonhomogeneous bilinear system to a controllable linear system on r n is considered here it is shown that this global state space transformation exists if and only if there exists a local one that carries the above bilinear system locally to a controllable linear system defined on a neighbourhood of the origin in r n to obtain this result the matrix representation of the lie algebra of affine vector fields on r n is used this is equivalent to considering the nonhomogenous bilinear system as the homogenous one in the state space of higher dimension

stabilization and feedback equivalence to linear coupled oscillators sufficient conditions for the system xdot f x u t g x x r2n to be stabilized via a smooth state feedback are given it is also shown that certain lie algebraic conditions are necessary and sufficient for the system to be feedback equivalent to a system of controlled linear coupled oscillators which is feedback stabilizable and which is proposed as a reference model for stabilization problems two overlapping sets of sufficient conditions which guarantee the existence and the explicit construction of stabilizing smooth state feedback controls are therefore given and their connections are discussed

on the multivariate runs test for independent d variate random variables x 1 x m with common density f and y 1 y n with common density g let r m n be the number of edges in the minimal spanning tree with vertices x 1 x m y 1 y n that connect points from different samples friedman and rafsky conjectured that a test of h 0 f g that rejects h 0 for small values of r m n should have power against general alternatives we prove that r m n is asymptotically distribution free under h 0 and that the multivariate two sample test based on r m n is universally consistent

collapsibility of relative risk in contingency tables with a response variable we consider the collapsibility of relative risks in contingency tables with a polytomous response variable simple collapsibility of relative risks means that they are consistent over all levels of a collapsed variable and also coincide with the corresponding marginal relative risk strong collapsibility of relative risks means that they retain simple collapsibility no matter how the variable is partially collapsed we present necessary and sufficient conditions for simple and strong collapsibilities of relative risks

on a generalization of a result of w g cochran summary a relationship due to w g cochran showing the effect on least squares regression coefficients of marginalizing over or conditioning on an explanatory variable is generalized to quantile regression coefficients the condition under which conditioning does not induce interaction or effect reversal is shown examples are given the discussion is simplest when all variables are continuous the extension to discrete variables is outlined

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

exact linearization in switched mode dc to dc power converters three popular dc to dc switched mode power converters buck boost and buck boost are shown to be in the same orbit of structural equivalence as a second order controllable circuit in brunovsky canonical form the equivalence is achievable under non linear feedback and explicit local difleomorphic state coordinate transformations the implications of local exact linearizability of this class of systems in the design of variable structure feedback control laws or pulse width modulation strategies is thoroughly discussed

on marginal and conditional parameters in logistic regression models a fundamental research question is how much a variation in a covariate influences a binary response variable in a logistic regression model both directly or through mediators we derive the exact formula linking the parameters of marginal and conditional regression models with binary mediators when no conditional independence assumptions can be made the formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish thereby recovering well known results as particular cases it also permits to quantify the distortion induced by omission of some relevant covariates opening the way to sensitivity analysis also in this case as the parameters of the conditional models are multiplied by terms that are always positive or bounded the formula may be used to construct reasonable bounds on the parameters of interest we assume that conditionally on a set of covariates the data generating process can be represented by a directed acyclic graph we also show how the results here presented lead to the extension of path analysis to a system of binary random variables

some comments on global linearization of nonlinear systems it is shown that even in the case of a single input system on r 2 it will be rather difficult to find conditions sufficient to guarantee existence of a global linearization and that local conditions alone will definitely not be enough a class of examples which is fairly typical and it is hoped useful is discussed

on the global linearization of bilinear systems abstract the problem of finding a global state space transformation to transform a given single input homogeneous bilinear system to a controllable linear system on r n is considered here we show that the existence of a solution of the above problem is equivalent to the existence of a local state space transformation that carries the corresponding bilinear system locally to a controllable linear one the complete analysis of the globally state linearizable bilinear systems in r 2 and r 3 is also included

a general condition for avoiding effect reversal after marginalization summary the paper examines the effect of marginalizing over a possibly unobserved background variable on the conditional relation between a response and an explanatory variable in particular it is shown that some conclusions derived from least squares regression theory apply in general to testing independence for arbitrary distributions it is also shown that the general condition of independence of the explanatory variable and the background ensures that monotonicity of dependence is preserved after marginalization relations with effect reversal and with collapsibility are sketched

on the largest feedback linearizable subsystem abstract a feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs it is shown to be the set of controllability indices of the largest feedback linearizable subsystem i e the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations

string stability of interconnected systems introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems intuitively string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded it is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input output stable the authors derive sufficient weak coupling conditions which guarantee the asymptotic string stability of a class of interconnected systems under the same weak coupling conditions string stable interconnected systems remain string stable in the presence of small structural singular perturbations in the presence of parameter mismatch these weak coupling conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient based parameter adaptation law is used and that the states of all the systems go to zero asymptotically

state observers and state feedback controllers for a class of non linear systems a design methodology for observers and controllers for a class of single input single output non linear systems is developed a non linear observer form is defined and a corresponding observer using non linear observer gains is specified the resulting error dynamics which are non linear are asymptotically stable for a proper choice of those gains and bounded inputs and outputs a non linear controller form is defined and a corresponding controller which results in linear closed loop dynamics with arbitrary eigenvalue placement is devised transformations from the class of interest to the defined forms are derived in the observer case the transformation to the observer form and the non linear entries in the state matrix of that form can be determined separately leading to a system of linear partial differential equations a major simplification in the controller case a simple well known system of linear partial differential equations is obtained the efficacy of the developed methodology is sho

the effect of pooling across strata in perfectly balanced studies pair matching frequency matching and stratification are used to obtain perfect exposure balance within strata defined by levels of confounders we consider the consequences of pooling such balanced data across strata in the analysis we examine model based inference for a variety of response variables and generalized linear regressions as well as for the cox 1972 journal of the royal statistical society series b 34 187 220 model if the data are pooled so that stratum effects are omitted from the regression certain models retain nominal size including all poisson models and all normal models with known variance the model based tests have supranominal size for all exponential models and subnominal size for all bernoulli models and for the cox model these results contrast with a previous analysis of simple randomization which only ensures exposure balance on average with simple randomization omission of stratum effects from these models leads to model based significance tests with supranominal size except for the cox and bernoulli models which retain nominal size just as for simple randomization however it is wise to include stratum effects in the analysis of perfectly balanced data to avoid biased estimation of exposure effects and to increase the efficiency of the comparison though motivated by cohort data these results also apply to balanced case control data under the logistic model

n dimensional controllability with n 1 controls let m be a connected real analytic n dimensional manifold f g 1 g n 1 be complete real analytic vector fields on m which are linearly independent at some point of m and u 1 u n 1 be real valued controls consider the controllability of the system dot x t f x t sum min i 1 max n 1 u i t g i x t x 0 x 0 in m necessary and sufficient conditions are given so that this system is controllable on any simply connected domain d contained in m on which g 1 g n 1 are linearly independent these conditions depend on the computation of lie brackets at those points where f g 1 g n 1 are linearly dependent

exact nonlinear control of large angle rotational maneuvers the rigid body attitude control problem with external torques is transformed into an equivalent linear form implementable by three double integrators the linearizing transformations themselves are formulated in vector algebra requiring no integrators for implementation it is thereby shown that optimal command generation for fast slewing maneuvers can be carried out exactly in the transformed system together with regulator design without gain scheduling for correction of unmodeled disturbances in particular a general rest to rest maneuver is computed in closed form and coupled with a previously obtained exact detumbling maneuver so that arbitrary initial conditions can be accommodated an illustrative simulation is appended

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

remarks on nonlinear planar control systems which are linearizable by feedback abstract the possibility that certain nonlinear systems can be linearized by the nonlinear feedback group has recently attracted a great deal of attention in the literature at least for mechanical systems the apparent ubiquity of linearizable systems is often accounted for by the claim that scalar control systems defined on r 2 are generically linearizable since there are several possible interpretations of the term generic and since until now no rigorous proof of genericity for any use of the term has been offered i thought it worthwhile to investigate in what sense if any this folklore theorem is valid contrary to the prevailing intuition linearizable systems fail to be dense in any topology for which evaluation of vector fields at points is a continous operation this includes for example both the weak and strong c topologies what then are the global properties of the class of linearizable systems in this note it is also shown that this class has no interior points in any reasonable complete topology making feedback operations continuous in particular linearizable systems in r 2 are far from being structurally stable in the weak c topology in the other hand one of the main results presented here is that globally linearizable systems are open in the strong or whitney topology thus globally linearizable planar systems are structurally stable if the well known local conditions actually implied global linearizability this result would be trivial recent work of boothby shows however that global linearization is far more subtle for this reason in the course of the proof it is necessary to modify the existing global linearization criteria in particular a nonvanishing criterion for irjectivity of smooth maps on r sharpening the so called ratio condition is presented this result appears to be of independent interest and leads to improvements of the global linearization condition in r due to hunt su and meyer and of the global non linear observability conditions in r due to kou elliott and tarn

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

stabilization of feedback linearizable systems using a radial basis function network the main obstacle in the practical use of the feedback linearization is the difficulty in obtaining a linearizing feedback and a coordinate transformation map finding a desired transformation map and feedback turns out to be finding an integrating factor for an annihilating one form in this work we develop numerical algorithms for an integrating factor and the corresponding zero form employing a radial basis function rbf neural network as an interpolation method for the data resulted from the numerical algorithms the authors obtained an approximate integrating factor and zero form in closed forms finally they construct a stabilizing controller based on a linearized system with the use of the approximate integrating factor and zero form

galerkin approximations of the generalized hamilton jacobi bellman equation in this paper we study the convergence of the galerkin approximation method applied to the generalized hamilton jacobi bellman ghjb equation over a compact set containing the origin the ghjb equation gives the cost of an arbitrary control law and can be used to improve the performance of this control the ghjb equation can also be used to successively approximate the hamilton jacobi bellman equation we state sufficient conditions that guarantee that the galerkin approximation converges to the solution of the ghjb equation and that the resulting approximate control is stabilizing on the same region as the initial control the method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the lqr design method

multivariate two sample tests based on nearest neighbors abstract a new class of simple tests is proposed for the general multivariate two sample problem based on the possibly weighted proportion of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample large values of the test statistics give evidence against the hypothesis h of equality of the two underlying distributions asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction probabilities simple infinite dimensional approximations are supplied the unweighted version yields a distribution free test that is consistent against all alternatives optimally weighted statistics are also obtained and asymptotic efficiencies are calculated each of the tests considered is easily adapted to a permutation procedure that conditions on the pooled sample power performance for finite sample sizes is assessed in simulations

nonlinear control of a swinging pendulum we propose a nonlinear controller to regulate the swinging energy of the pendulum for a cart and pendulum system roughly speaking the controller is designed to regulate an output the swing energy while providing internal stability regulating the cart position it is difficult to apply many of the standard nonlinear control design techniques since the output zeroing manifold does not contain any equilibrium points and the relative degree of the system is not constant in contrast to controllers that use a command generator and possibly a time varying feedback our control law is a simple autonomous nonlinear controller we analyze the stability of the closed loop system using an lv small gain approach on a transverse linearization of the system about the desired periodic orbit one can easily extend this approach to analyze the robustness of the control system with respect to disturbances and parameter variations experimental results demonstrate the effectiveness of the nonlinear controller

feedback control of linear systems by multirate pulse width modulation in this note sampled data methods for modeling and control design of pulse width modulated systems are examined both single rate and multirate approaches are considered local controllability and observability analyses of the sampled data models are performed and feedback linearizability conditions for the sampled data models are derived multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking

linearization of attitude control error dynamics some useful properties of direction cosine and quaternion attitude formulations that include specification of attitude error and the inversion of rigid body rotational dynamics are reviewed the inversion procedure is then applied to a measure of attitude error to realize a new model follower control system that exhibits linear attitude error dynamics error analyses and simulation results for spacecraft attitude control systems are presented to demonstrate the more robust performance obtainable from an exact linear error formulation over that obtained from either direction cosine or quaternion formulations with simple linear feedback control laws

collapsibility of distribution dependence summary cox and wermuth proposed that the partial derivative of the conditional distribution function of a random variable y given another x is used for measuring association between two variables with arbitrary distributions the paper presents a necessary and sufficient condition for uniform collapsibility of this association measure over a third variable w

a quality index based on data depth and multivariate rank tests let f and g be the distribution functions of two given populations on rp p 1 we introduce and study a parameter q q f g which measures the overall outlyingness of population g relative to population f the parameter q can be defined using any concept of data depth its value ranges from 0 to 1 and is 5 when f and g are identical we show that within the dass of elliptical distributions when g departs from f in location or g has a larger spread or both the value of q dwindles down from 5 hence q can be used to detect the loss of accuracy or precision of a manufacturing process and thus it should serve as an important measure in quality assurance this in fact is the reason why we refer to q as a quality index in this article in addition to studying the properties of q we provide an exact rank test for testing q 5 vs q 5 this can be viewed as a multivariate analog of wilcoxon s rank sum test the tests proposed here have power against location change and scale increase simultaneo

criteria for surrogate end points summary a surrogate end point is often used to evaluate the effects of treatments or exposures on the true end point in medical researches various criteria for the statistical surrogate principal surrogate and strong surrogate have been proposed we first illustrate that with a surrogate end point that is defined by these criteria it is possible that a treatment has a positive effect on the surrogate which in turn has a positive effect on the true end point but the treatment has a negative effect on the true end point we define such a phenomenon as a surrogate paradox the surrogate paradox also means that the sign of the treatment effect on the true end point is unpredictable by the effect signs of both the treatment on the surrogate and the surrogate on the true end point then we propose two notions for a consistent surrogate and a strictly consistent surrogate to avoid the surrogate paradox with the causal network that was presented by lauritzen we discuss the conditions for a strong surrogate to be a consistent surrogate and a strictly consistent surrogate

a new method of normal approximation we introduce a new version of stein s method that reduces a large class of normal approximation problems to variance bounding exercises thus making a connection between central limit theorems and concentration of measure unlike skorokhod embeddings the object whose variance must be bounded has an explicit formula that makes it possible to carry out the program more easily as an application we derive a general clt for functions that are obtained as combinations of many local contributions where the definition of local itself depends on the data several examples are given including the solution to a nearest neighbor clt problem posed by p bickel

asymptotic linearization on uncertain systems by variable structure control abstract a nonlinear control system with uncertain dynamics described by a single ordinary differential equation with scalar control and available state is given based on knowledge of upper and lower estimates of the unknown dynamics we show that the system can be transformed to an asymptotically equivalent linear model arbitrarily fixed described by a single linear ordinary differential equation of the same order by using an explicitly described discontinuous feedback control law of variable structure type the linear behaviour is obtained up to an arbitrarily fast exponentially decaying error term

non linear observer design by approximate error linearization abstract for a given non linear system an observer that provides exactly linear error dynamics can be computed by solving the so called generalized characteristic equation gce unfortunately the existence of a solution to the gce is not a generic property for unforced scalar output systems we show how spline functions may be used to construct approximate solutions that minimize a norm of the non linear terms obstructing linearization of the error dynamics the resulting error dynamics are shown to be locally exponentially stable a numerical example illustrates the design and performance of the observer

ball divergence nonparametric two sample test in this paper we first introduce ball divergence a novel measure of the difference between two probability measures in separable banach spaces and show that the ball divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption using ball divergence we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples it is therefore robust to outliers or heavy tail data we show that this multivariate two sample test statistic is consistent with the ball divergence and it converges to a mixture of 2 distributions under the null hypothesis and a normal distribution under the alternative hypothesis importantly we prove its consistency against a general alternative hypothesis moreover this result does not depend on the ratio of the two imbalanced sample sizes ensuring that can be applied to imbalanced data numerical studies confirm that our test is superior to several existing tests in terms of type i error and power we conclude our paper with two applications of our method one is for virtual screening in drug development process and the other is for genome wide expression analysis in hormone replacement therapy

linear model following control and feedback equivalence to linear controllable systems the sufficient conditions developed in the area of model reference adaptive control which guarantee the existence of a linear model following control for a non linear plant are given a geometric interpretation they are compared with recent results developed in the area of non linear geometric control on global feedback equivalence to linear controllable systems the comparison gives more insight into the model following control problem and suggests the generalization of the usual control scheme to a more convenient one which admits solutions for a larger class of plants

global properties of the triangular systems in the singular case we introduce a new class of the triangular multi input and multi output control systems of o d e which are not feedback linearizable and investigate its global behavior the triangular form introduced is a generalization of the classes of triangular systems considered before for our class we solve the problem of global robust controllability combining our main result with that of f h clarke yu s ledyaev e d sontag a i subbotin asymptotic controllability implies feedback stabilization ieee trans automat control 42 1997 1394 1407 we obtain a corollary on the global discontinuous sampled stabilization an example showing that global smooth stabilization can be irrelevant to the singular case is considered to prove our main result we apply a certain back stepping algorithm and combine the technique proposed in v i korobov s s pavlichkov w h schmidt global robust controllability of the triangular integro differential volterra systems j math anal appl 309 2005 743 760 with solving a specific problem of global practical stabilization by means of a discontinuous time varying feedback law

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction