almost output regulation of lft systems via gain scheduling control abstractoutput regulation of general uncertain systems is a meaningful yet challenging problem in spite of the rich literature in the field the problem has not yet been addressed adequately due to the lack of an effective design mechanism in this paper we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation lft with time varying parametric uncertainties and unknown external perturbations a novel semi lft gain scheduling output regulator structure is proposed such that the associated control synthesis conditions guaranteeing both output regulation and l2 disturbance attenuation performance are formulated as a set of linear matrix inequalities lmis plus parameter dependent linear matrix equations which can be solved separately a numerical example has been used to demonstrate the effectiveness of the proposed approach

fast gain scheduling on tracking problems using derivative information current gain scheduling practice is necessarily limited to slow variation in scheduling variables this paper proposes a control law which reflects the exogenous signal and its time derivative with assumption of its availability the proposed controller achieves better performance than the existents for tracking fast scheduling variables while rejecting exogenous signal

performance analysis of three class classifiers properties of a 3 d roc surface and the normalized volume under the surface for the ideal observer classification of a given observation to one of three classes is an important task in many decision processes or pattern recognition applications a general analysis of the performance of three class classifiers results in a complex 6 d receiver operating characteristic roc space for which no simple analytical tool exists at present we investigate the performance of an ideal observer under a specific set of assumptions that reduces the 6 d roc space to 3 d by constraining the utilities of some of the decisions in the classification task these assumptions lead to a 3 d roc space in which the true positive fraction tpf can be expressed in terms of the two types of false positive fractions fpfs we demonstrate that the tpf is uniquely determined by and therefore is a function of the two fpfs the domain of this function is shown to be related to the decision boundaries in the likelihood ratio plane based on these properties of the 3 d roc space we can define a summary measure referred to as the normalized volume under the surface nvus that is analogous to the area under the roc curve auc for a two class classifier we further investigate the properties of the 3 d roc surface and the nvus for the ideal observer under the condition that the three class distributions are multivariate normal with equal covariance matrices the probability density functions pdfs of the decision variables are shown to follow a bivariate log normal distribution by considering these pdfs we express the tpf in terms of the fpfs and integrate the tpf over its domain numerically to obtain the nvus in addition we performed a monte carlo simulation study in which the 3 d roc surface was generated by empirical optimal classification of case samples in the multidimensional feature space following the assumed distributions to obtain an independent estimate of nvus the nvus value obtained by using the analytical pdfs was found to be in good agreement with that obtained from the monte carlo simulation study we also found that under all conditions studied the nvus increased when the difficulty of the classification task was reduced by changing the parameters of the class distributions thereby exhibiting the properties of a performance metric in analogous to auc our results indicate that under the conditions that lead to our 3 d roc analysis the performance of a three class classifier may be analyzed by considering the roc surface and its accuracy characterized by the nvus

a stability property of nonlinear sampled data systems with slowly varying inputs a stability analysis is presented that deals with the response of a nonlinear sampled data system to a slowly varying exogenous input signal the main result similar to existing results for purely continuous time and discrete time systems establishes that if the system possesses a manifold of exponentially stable constant operating points equilibria corresponding to constant values of the input signal then an initial state close to this manifold and a slowly varying input signal yield a trajectory that remains close to the manifold the analysis involves casting the sampled data system as a continuous time system with discrete jumps at the sampling instants

feedback linearization families for nonlinear systems characterizations are developed for parameterized linear dynamic feedback control laws that can arise when linearizing a nonlinear dynamic feedback control law for a specified nonlinear system about a family of constant operating points such characterizations are important in applying the recently developed extended linearization design approach to various types of control problems to illustrate the input output decoupling problem is considered

a new algorithm for the design of multifunctional observers this paper presents a general algorithm for low order multifunctional observer design with arbitrary eigenvalues the feature of this algorithm is that it can generate a functional observer with different orders which are no larger but usually much less than m v 1 where m is the number of functionals and v is the observability index of a c since the order needed for the observer varies with the functionals besides other system parameters this design approach should be practical the resulting observer system matrix is in its jordan form the key step of this algorithm is the generation of the basis for the transformation matrix which relates the system and observer states the computation of this algorithm is quite reliable it is based on the block observable lower hessenberg form of a c and all its initial and major computation involves only the orthogonal operations

on a stability theorem for nonlinear systems with slowly varying inputs recently m kelemen ieee trans automat contr vol ac 31 766 768 aug 1986 presented a stability result that deals with the response of a nonlinear system to slowly varying input signals in this work a proof is given under a weaker hypothesis on the input signal by constructing a lyapunov function that is standard in the control literature this proof may be more accessible than the other approaches for completeness brief proofs of some intermediate results that are regarded as well known are included a simple example is given to show that this approach can yield explicit bounds in certain situations of interest

unknown input observer design and analysis for networked control systems the insertion of communication networks in the feedback loops of control systems is a defining feature of modern control systems these systems are often subject to unknown inputs in a form of disturbances perturbations or attacks the objective of this paper is to design and analyse an observer for networked dynamical systems with unknown inputs the network effect can be viewed as either a perturbation or time delay to the exchanged signals in this paper we 1 review an unknown input observer uio design for a non networked system 2 derive the networked unknown input observer netuio dynamics 3 design a netuio such that the effect of higher delay order terms are nullified and 4 establish stability guaranteeing bounds on the networked induced time delay and perturbation the formulation and results derived in this paper can be generalised to scenarios and applications where the signals are perturbed due to a different source of perturbation or delay

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

the existence and design of functional observers for two dimensional systems abstract this paper is concerned with functional observers for two dimensional 2d systems described by the fornasini marchesini local state space second model a necessary and sufficient condition is given for the existence of asymptotic functional observers a more tractable necessary condition for the existence of asymptotic functional observers is also presented as it helps exclude those 2d systems for which there is no asymptotic functional observer a constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality lmi technique two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method

an approximation method for the nonlinear servomechanism problem an analysis of the nonlinear servomechanism problem by the authors 1992 is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense the results are based on a kth order approximate solution for the plant zero error manifold and corresponding control law constructions are shown to yield kth order asymptotic tracking and disturbance rejection properties for the closed loop system the approach is illustrated by application to the ball and beam system

brief analysis and design of gain scheduled sampled data control systems the existence of gain scheduled sampled data controllers that meet an important linearization requirement about a family of equilibria is investigated

the hypervolume under the roc hypersurface of near guessing and near perfect observers in n class classification tasks we express the performance of the n class guessing observer in terms of the n sup 2 n conditional probabilities which make up an n class receiver operating characteristic roc space in a formulation in which sensitivities are eliminated in constructing the roc space equivalent to using false negative fraction and false positive fraction in a two class task we then show that the guessing observer s performance in terms of these conditional probabilities is completely described by a degenerate hypersurface with only n 1 degrees of freedom as opposed to the n sup 2 n 1 required in general to achieve a true hypersurface in such a roc space it readily follows that the hypervolume under such a degenerate hypersurface must be zero when n 2 we then consider a near guessing task that is a task in which the n underlying data probability density functions pdfs are nearly identical controlled by n 1 parameters which may vary continuously to zero at which point the pdfs become identical with this approach we show that the hypervolume under the roc hypersurface of an observer in an n class classification task tends continuously to zero as the underlying data pdfs converge continuously to identity a guessing task the hypervolume under the roc hypersurface of a perfect ideal observer in a task in which the n data pdfs never overlap is also found to be zero in the roc space formulation under consideration this suggests that hypervolume may not be a useful performance metric in n class classification tasks for n 2 despite the utility of the area under the roc curve for two class tasks

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

ideal observers and optimal roc hypersurfaces in n class classification the likelihood ratio or ideal observer decision rule is known to be optimal for two class classification tasks in the sense that it maximizes expected utility or equivalently minimizes the bayes risk furthermore using this decision rule yields a receiver operating characteristic roc curve which is never above the roc curve produced using any other decision rule provided the observer s misclassification rate with respect to one of the two classes is chosen as the dependent variable for the curve i e an inversion of the more common formulation in which the observer s true positive fraction is plotted against its false positive fraction it is also known that for a decision task requiring classification of observations into n classes optimal performance in the expected utility sense is obtained using a set of n 1 likelihood ratios as decision variables in the n class extension of roc analysis the ideal observer performance is describable in terms of an n sup 2 n 1 parameter hypersurface in an n sup 2 n dimensional probability space we show that the result for two classes holds in this case as well namely that the roc hypersurface obtained using the ideal observer decision rule is never above the roc hypersurface obtained using any other decision rule where in our formulation performance is given exclusively with respect to between class error rates rather than within class sensitivities

a stability property in this note we obtain a stability property not for a point of equilibrium but for a certain family of asymptotically stable equilibria of a dynamical system with an input we show that this property depends not only on the initial condition but also on the time derivative of the input function we suggest possible applications of this result to some control problems

decision strategies that maximize the area under the lroc curve for the 2 class detection problem signal absent present the likelihood ratio is an ideal observer in that it minimizes bayes risk for arbitrary costs and it maximizes the area under the receiver operating characteristic roc curve auc the auc optimizing property makes it a valuable tool in imaging system optimization if one considered a different task namely joint detection and localization of the signal then it would be similarly valuable to have a decision strategy that optimized a relevant scalar figure of merit we are interested in quantifying performance on decision tasks involving location uncertainty using the localization roc lroc methodology therefore we derive decision strategies that maximize the area under the lroc curve a sub lroc we show that these decision strategies minimize bayes risk under certain reasonable cost constraints the detection localization task is modeled as a decision problem in three increasingly realistic ways in the first two models we treat location as a discrete parameter having finitely many values resulting in an l 1 class classification problem in our first simple model we do not include search tolerance effects and in the second more general model we do in the third and most general model we treat location as a continuous parameter and also include search tolerance effects in all cases the essential proof that the observer maximizes a sub lroc is obtained with a modified version of the neyman pearson lemma a separate form of proof is used to show that in all three cases the decision strategy minimizes the bayes risk under certain reasonable cost constraints

existence conditions for functional observability from an eigenspace perspective two theorems on conditions for nonexistence and for existence of built functional observers from an eigenspace perspective are presented and proved one more theorem on functional observability in terms of constructed products of matrices a c and l0 is also presented this theorem provides an easy way to check functional observability before proceeding with the design of functional observers the existence and the nonexistence theorems are used to unify previously reported theorems on functional observability by showing their equivalence the connection between the concept of functional observability and the well known concept of state observability is also presented

tracking control of a pendulum using a numerically efficient state estimation approach for polynomic non linear systems this paper reports on the tracking control of a pendulum the particular contributions of this paper lie in the development of a numerically efficient approach for the state estimation of a class of non linear systems which fall under the extended generalized wiener model structure and its application to the pendulum system it details the estimation and control aspects for achieving the tracking control of the pendulum where attention is focused on extended kalman filtering ekf methods based on volterra series approximations of the non linearity for the estimation of the pendulum states control is then effected by the feedback linearization fl technique and the internal model principle imp it is argued that this offers accuracy benefits over linear techniques while substantially reducing the computational burden associated with the standard ekf approaches the arguments are supported by evidence from a case study system it is demonstrated that this proposed approach is significantly faster and d

confidence intervals around bayes cost in multi state diagnostic settings to estimate optimal performance a critical feature of diagnostic testing is correctly classifying subjects based upon specified thresholds of some measure the commonly employed youden index determines a test s optimal thresholds by maximizing the correct classification rates for a diagnostic scenario an alternative to the youden index is the cost function bayes cost bc bc determines a test s optimal setting by minimizing the sum of all misclassification rates from the test unlike the youden index bc can consider a priori costs of all the diagnostic outcomes including class specific misclassifications regardless of the number of classes delta method approximate confidence intervals around bc are derived under the assumption of normally distributed classes as a means for quantifying a test s performance and comparing classifiers at their optimal settings in a multi state diagnostic framework a simulation study is conducted to demonstrate the performance of the derived confidence intervals that are found to perform well especially for sample sizes of 50 or larger in each diagnostic class finally the proposed methods are applied to a four class breast tissue classification problem where four possible discriminatory features are compared under varying decision cost structures using the confidence intervals around bc the best feature for classification is selected and the optimal thresholds and their 95 confidence intervals are determined

output regulation for control systems on se n a separation principle based approach this technical note considers a solution to an output regulation problem for control systems on the special euclidean group se n the proposed solution consists of a convergent observer together with a certainty equivalence implementation of an almost globally stable state feedback law the design of the observer and the state feedback are carried out independently we show that all closed loop solutions remain bounded that the steady state solution is contained in exactly one of a finite number of isolated sets which are all unstable except one which is the desired equilibrium set and which is asymptotically stable

unknown inputs functional observers designs for delay descriptor systems new time and frequency domain designs of unknown inputs functional observers uifo for a class of descriptor systems with a constant time delay are investigated in this paper the unknown inputs are present in both the state and the measurement equations the time procedure design is based on the unbiasedness of the estimation error and the lyapunov krasovskii stability theory after given the existence condition of such observers the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities the particular cases where the observer is independent of internal delay and where it is independent of delay are also investigated a design algorithm that summarises the different steps of the uifo design is proposed then the frequency procedure design is derived from time domain results by applying the factorisation approach where we define some useful matrix fraction descriptions note that the order of this unknown input observers is equal to

efficient multiclass roc approximation by decomposition via confusion matrix perturbation analysis receiver operator characteristic roc analysis has become a standard tool in the design and evaluation of two class classification problems it allows for an analysis that incorporates all possible priors costs and operating points which is important in many real problems where conditions are often nonideal extending this to the multiclass case is attractive conferring the benefits of roc analysis to a multitude of new problems even though the roc analysis extends theoretically to the multiclass case the exponential computational complexity as a function of the number of classes is restrictive in this paper we show that the multiclass roc can often be simplified considerably because some roc dimensions are independent of each other we present an algorithm that analyzes interactions between various roc dimensions identifying independent classes and groups of interacting classes allowing the roc to be decomposed the resulting decomposed roc hypersurface can be interrogated in a similar fashion to the ideal case allowing for approaches such as cost sensitive and neyman pearson optimization as well as the volume under the roc an extensive bouquet of examples and experiments demonstrates the potential of this methodology

approximate noninteracting control with stability for nonlinear systems a notion of approximate noninteracting control with stability for nonlinear systems is introduced and the design of both static and dynamic state feedback control laws that achieve this property for a given plant is considered this approach to the problem is based on the notion of extended linearization and begins with an extension of the linearization approach pointwise to all constant operating points in an open neighborhood of the nominal under natural assumptions it is shown that obstructions to extract noninteracting control with internal stability or input state output stability can be circumvented in the context of approximate noninteraction

a stability property and its application to discrete time nonlinear system control an inequality on the solution of discrete time nonlinear systems is established a special case of this inequality leads to a stability result that is the counterpart of the kelemen theorem on continuous time systems application of this inequality gives some results on stability regulation and tracking of the discrete time nonlinear systems

existence conditions for unknown input functional observers this article presents necessary and sufficient conditions for the existence and design of an unknown input functional observer the existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions the existence of the observer does not require the satisfaction of the observer matching condition i e equation 16 in hou and muller 1992 design of observers for linear systems with unknown inputs ieee transactions on automatic control 37 871 875 is not limited to estimating scalar functionals and allows for arbitrary pole placement the proposed observer always exists when a state observer exists for the unknown input system and furthermore the proposed observer can exist even in some instances when an unknown input state observer does not exist

exact feedforward linearization based on differential flatness this article deals with the trajectory aspect of differential flatness from a feedforward point of view the notion of exact feedforward linearization based on differential flatness is introduced a differentially flat system to which a nominal feedforward deduced from flatness is applied is equivalent by change of coordinates to a linear multivariable brunovsk form if the initial condition is consistent with the one considered in the design of the nominal trajectory in its second part the new notion states that there exist unique solutions in the vicinity of the desired trajectory when applying a nominal feedforward to the corresponding flat system to the end of stabilizing the desired trajectory the information from the brunovsk form is used to design the combination of the nominal feedforward and an additional feedback part in the case of extended pid controls for the latter stability is proven using a theorem by kelemen thus the overall control structure turns out to be quite simple and e

a differential vector space approach to nonlinear system regulation nonlinear system regulation is an active research area and is important for disturbance rejection and reference signal tracking existing results using differential geometry or lyapunov theory are restricted to bounded exogenous signals the paper uses a differential vector space approach to develop solutions for nonlinear system regulation with both bounded and unbounded exogenous signals the solutions are given in terms of observable dual state spaces in the differential vector space of the system and are well suited to symbolic and numerical computation

on stability properties of nonlinear systems with slowly varying inputs systems with slowly varying inputs are discussed as a special class of two time scale systems and singular perturbation results are seen as convenient tools to analyze their properties a lemma by f c hoppensteadt trans amer math soc vol 123 p 521 35 1966 for a parameterized family of systems is restated and applied to the analysis of systems with slowly varying inputs

output regulation with derivative information output regulation for a nonlinear plant driven by an exogenous signal is addressed in this paper in the absence of the standard exosystem hypothesis we assume availability of the instantaneous values of the exogenous signal and its first time derivative for use in the control law we formulate an approximate output regulation problem and characterize solvability in terms of the existence of a certain invariant manifold the control law we obtain yields a closed loop system with output exhibiting ultimate boundedness properties with respect to both the first and the second time derivatives of the exogenous signal performance characteristics are illustrated by application to the linear case and to specific nonlinear examples

brief stability and l2 gain properties of lpv systems stability and l 2 gain properties of linear parameter varying systems are obtained under assumed bounds on either the maximum or average value of the parameter rate

stabilization analysis of discrete nonlinear systems in this paper we set a new framework for the analysis of nonlinear discrete systems to carry out the stabilization theorem and to design stable controllers of the systems within that framework this framework includes many practically important systems described for example by lipschitz functions functions with arbitrary order bounded derivatives bilinear functions and all polynomial functions an important existence theorem for stabilizing has been proven for this framework the theorem basically states that under definite rather broad conditions the zero solution of the plants can be made stable by a nonlinear output feedback in addition this nonlinear feedback is from a larger class of functions than these classes given by current literature following these stabilization theorems a new design procedure for the output feedback control law is presented all results presented are easy to use and convenient to apply the application is illustrated by several examples including the design of stabilizing control for a bilinear control system

generalized output regulation problem for a class of nonlinear systems with nonautonomous exosystem the problem of the generalized output regulation is considered here in contrast to the classical output regulation problem where the references to be tracked and disturbances to be rejected are generated by an autonomous exogeneous system for the generalized output regulation an exogenous system is driven by an unknown external reference signal in such a way the class of reference or disturbance signals is expanded presented result solves the full measurement feedback case and is based on the well known notion of the regulator equation combined with the classical concept of the invariant distribution illustrative example including matlab simulink simulations is presented to demonstrate the suggested approach

a dissipativity based approach to output regulation of non minimum phase systems abstract the present paper presents a new contribution to the design of output regulators for a class of nonlinear systems characterized by a possibly unstable zero dynamics it is shown that the problem in question can be reduced to a stabilization problem with a supplementary gain constraint for a suitably defined reduced auxiliary plant

robustness analysis with respect to exogenous perturbations for flatness based exact feedforward linearization a methodology to analyze robustness with respect to exogenous perturbations for exact feedforward linearization based on differential flatness is presented the analysis takes into consideration the tracking error equation and makes thereafter use of a stability result by kelemen coupled with results issued from interval analysis this turns exact feedforward linearization based on differential flatness into a general control methodology for flat systems

linear functional state observer for time delay systems a new linear functional state observer for time delay systems is introduced in this paper it is shown that the observer converges with any prescribed stability margin to any number of linear functionals when some conditions are met the design procedure is simple and can be easily implemented numerical examples are given to illustrate the properties of the new observer and its advantages over existing observer design techniques in the literature

three class roc analysis a decision theoretic approach under the ideal observer framework receiver operating characteristic roc analysis is well established in the evaluation of systems involving binary classification tasks however medical tests often require distinguishing among more than two diagnostic alternatives the goal of this work was to develop an roc analysis method for three class classification tasks based on decision theory we developed a method for three class roc analysis in this method the objects were classified by making the decision that provided the maximal utility relative to the other two by making assumptions about the magnitudes of the relative utilities of incorrect decisions we found a decision model that maximized the expected utility of the decisions when using log likelihood ratios as decision variables this decision model consists of a two dimensional decision plane with log likelihood ratios as the axes and a decision structure that separates the plane into three regions moving the decision structure over the decision plane which corresponds to moving the decision threshold in two class roc analysis and computing the true class 1 2 and 3 fractions defined a three class roc surface we have shown that the resulting three class roc surface shares many features with the two class roc curve i e using the log likelihood ratios as the decision variables results in maximal expected utility of the decisions and the optimal operating point for a given diagnostic setting set of relative utilities and disease prevalences lies on the surface the volume under the three class surface vus serves as a figure of merit to evaluate different data acquisition systems or image processing and reconstruction methods when the assumed utility constraints are relevant

functional observability and the design of minimum order linear functional observers the design of a minimum order linear functional observer for linear time invariant systems has been an open problem for over four decades this technical note provides a solution to this problem the technical note also introduces the concept of functional observability detectability and shows that the well known concept of observability detectability is a special case of functional observability detectability

multi modelling as new estimation schema for high gain observers the presented paper proposes a novel method of observer design a new two layer observer structure is introduced the first layer consists of multiple high gain observers the latter is built to connect the first layer observers into single one as the new contribution the new mapping is defined between an unknown state and measurable outputs allowing to explore new estimation schema hence the proposed method enhances the estimation process for linear and nonlinear systems furthermore it is shown that the introduced observation scheme improves the transients illustrative examples are calculated to show the properties of the new observation method

restrictions on the three class ideal observer s decision boundary lines we are attempting to develop expressions for the coordinates of points on the three class ideal observer s receiver operating characteristic roc hypersurface as functions of the set of decision criteria used by the ideal observer this is considerably more difficult than in the two class classification task because the conditional probabilities in question are not simply related to the cumulative distribution functions of the decision variables and because the slopes and intercepts of the decision boundary lines are not independent given the locations of two of the lines the location of the third will be constrained depending on the other two in this paper we attempt to characterize those constraining relationships among the three class ideal observer s decision boundary lines as a result we show that the relationship between the decision criteria and the misclassification probabilities is not one to one as it is for the two class ideal observer

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

neural network enhanced output regulation in nonlinear systems a neural network based approach is developed to approximate the feedforward function needed for solving the nonlinear output regulation problem the approach eliminates the need for solving the regulator equations thus applying to complex uncertain nonlinear systems

ordered multiple class roc analysis with continuous measurements receiver operating characteristic roc curves have been useful in two group classification problems in three and multiple class diagnostic problems an roc surface or hyper surface can be constructed the volume under these surfaces can be used for inference using bootstrap techniques or u statistics theory in this article roc surfaces and hyper surfaces are defined and their behaviour and utility in multi group classification problems is investigated the formulation of the problem is equivalent to what has previously been proposed in the general multi category classification problem but the definition of roc surfaces here is less complex and addresses directly the narrower problem of ordered categories in the three class and by extension the multi class problem applied to continuous and ordinal data non parametric manipulation of both continuous and discrete test data and comparison between two diagnostic tests applied to the same subjects are considered a three group classification example in the context of hiv neurological disease is presented and the results are discussed

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

minimal single linear functional observers for linear systems a constructive procedure to design a single linear functional observer for a time invariant linear system is given the proposed procedure is simple and is not based on the solution of a sylvester equation or on the use of canonical state space forms both stable observers or fixed poles observers problems are considered for minimality

asymptotic state tracking in a class of nonlinear systems via learning based inversion describes a learning approach to asymptotic state tracking in a class of nonlinear systems the tracking problem considered concerns the case when the tracking error dynamics are described by a set of time varying nonlinear differential equations which are periodic in time with a known period our iterative update scheme is based on the specific property that the learning system tends to oscillate in steady state in fact our approach extends in a very natural manner the idea of the well known iterative learning control for the case of finite time tracking problems to the case of infinite time asymptotic tracking problems the best advantage of the proposed leaning approach is that it is computationally simple and does not require one to solve any complicated equations based on full system dynamics we explore the conditions under which a periodic nonlinear system exhibits a steady state oscillation our work also can be viewed to provide a learning based solution to the input state inversion problem the generality and practicality of our work is demonstrated through rigorous performance analysis and simulation using a robot manipulator

an optimal three class linear observer derived from decision theory many attempts have been made to develop an optimal linear observer for classifying multiclass data most approaches either do not have a definite description of optimality or have regions of ambiguity in decision making in this paper we derive a three class hotelling observer 3 ho inspired by the ideal observer that results from a decision theoretic solution to the three class classification problem assuming the data vectors follow multivariate gaussian distributions with equal covariance matrices for the three classes it is shown that two two class hotelling templates construct a 3 ho which has the same performance as the three class ideal observer 3 io we show that without the gaussian and equal covariance assumptions the 3 ho is still applicable when the two class hotelling templates of each pair of the classes satisfy a certain linear relationship in this case the 3 ho simultaneously maximizes the signal to noise snr of the test statistics between each pair of the classes in conclusion we developed a three class linear mathematical observer that uses first and second order ensemble data statistics this mathematical observer which has clearly defined optimality for several data statistics conditions and has decision rules that have no ambiguous decision regions is potentially useful in the optimization and evaluation of imaging techniques for performing three class diagnostic tasks

on the order reduction of linear function observers this note analyzes a new algorithm presented in 1 for designing a linear function observer with a minimum number of arbitrary poles it shows that the maximum order of the observer of 1 is nu nu p p for p leq q and n q for p geq q instead of p nu 1 1 as suggested in 1 where nu i i 1 to p are the descending ordered observability indexes of system a c and n p and q are the order of the system the number of the functions and the number of the system outputs respectively this note also shows the significance of this result for presentational purposes only a special case of 1 is considered here however the technical properties as proved in this note are general

stabilization on zero error manifolds and the nonlinear servomechanism problem the extended linearization methodology is applied to the nonlinear servomechanism problem for the case of time varying exogenous signals this yields a novel approach to establishing exponential manifold known as the zero error manifold advantages of the approach are that the underlying theory is relatively simple and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small thus certain cases of unbounded exogenous signals can be treated a transmission zero condition for existence of the requisite zero error manifold is given

a system decomposition approach to the design of functional observers this paper reports a system decomposition that allows the construction of a minimum order functional observer using a state observer design approach the system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem functional observability indices are introduced and a closed form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices

the roc manifold for classification systems we define the roc manifold and cc manifold as duals in a given sense their analysis is required to describe the classification system we propose a mathematical definition based on vector space methods to describe both the roc manifolds for n class classification systems fully describe each system in terms of its misclassifications and by conjunction its correct classifications optimal points which minimize misclassifications can be identified even when costs and prior probabilities differ these manifolds can be used to determine the usefulness of a classification system based on a given performance criterion many performance functionals such as summary statistics preferred for cc manifolds can also be evaluated using the roc manifold under certain constraints examples using the roc manifold and performance functionals to compete classification systems are demonstrated with simulated and applied disease detection data

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

three class roc analysis the equal error utility assumption and the optimality of three class roc surface using the ideal observer previously we have developed a decision model for three class receiver operating characteristic roc analysis based on decision theory the proposed decision model maximizes the expected decision utility under the assumption that incorrect decisions have equal utilities under the same hypothesis equal error utility assumption this assumption reduced the dimensionality of the general three class roc analysis and provided a practical figure of merit to evaluate the three class task performance however it also limits the generality of the resulting model because the equal error utility assumption will not apply for all clinical three class decision tasks the goal of this study was to investigate the optimality of the proposed three class decision model with respect to several other decision criteria in particular besides the maximum expected utility meu criterion used in the previous study we investigated the maximum correctness mc or minimum error maximum likelihood ml and nyman pearson n p criteria we found that by making assumptions for both meu and n p criteria all decision criteria lead to the previously proposed three class decision model as a result this model maximizes the expected utility under the equal error utility assumption maximizes the probability of making correct decisions satisfies the n p criterion in the sense that it maximizes the sensitivity of one class given the sensitivities of the other two classes and the resulting roc surface contains the maximum likelihood decision operating point while the proposed three class roc analysis model is not optimal in the general sense due to the use of the equal error utility assumption the range of criteria for which it is optimal increases its applicability for evaluating and comparing a range of diagnostic systems

roc representation for the discriminability of multi classification markers in this paper the receiver operating characteristic roc representation and its accuracy measures are well defined and meaningful assessments for the discriminability of multi classification markers are shown given a set of classifiers c a parameterized system can be used to characterize the corresponding optimal roc manifold a connection with the decision set further leads to a better understanding of some geometric features of optimal roc manifolds and preserves the simplicity in computing the hypervolume under the roc manifold hum in addition it motivates us to address the necessary and sufficient conditions for the existence of the hum to sum up this work provides working scientists with an extension of the two class roc analysis to the multi classification roc analysis in a theoretically sound manner highlightsa proper assessment of performance probabilities is shown to be the optimal roc manifold the necessary and sufficient conditions are addressed for the existence of the hum the scientific groundwork is extended to a more general multi class roc analysis

a new polytopic approach for the unknown input functional observer design in this paper a constructive procedure to design functional unknown input observers for nonlinear continuous time systems is proposed under the polytopic takagi sugeno framework an equivalent rep

a practical functional observer scheme for interconnected time delay systems this paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems a set of easily verifiable existence conditions is established and upon its satisfaction simple distributed observers are designed using a straightforward design procedure simulation results of a numerical example are given to substantiate the feasibility of the approach

measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups this article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups we use a receiver operating characteristic roc surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed under the assumption of normal distributions of the diagnostic test from three diagnostic groups we present the maximum likelihood estimate to the volume under the roc surface and give the asymptotic variance to the estimate we further propose several asymptotic confidence interval estimates to the volume under the roc surface the performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study in addition we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate finally we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage alzheimer s disease based on the neuropsychological database of the washington university alzheimer s disease research center

feedback control of multiinput nonlinear systems by extended linearization control of a nonlinear system is addressed by considering its family of linearizations given that a family of linear state feedback controllers has been designed to meet some linear control objective it is shown how these controllers can be pieced together into an overall nonlinear state feedback controller the resulting closed loop system has the property that its linearizations are equal to the desired linearly controlled systems a similar approach can be used to design nonlinear state estimators the approach is illustrated by applying it to the control of a planar two link manipulator

brief robustness analysis of exact feedforward linearization based on differential flatness a methodology to analyze robustness with respect to parametric uncertainty for exact feedforward linearization based on differential flatness is presented the analysis takes into consideration the tracking error equation and thereafter makes use of a stability result by kelemen coupled with results issued from interval analysis theory

on output regulation for discrete time nonlinear systems output regulation for a discrete time nonlinear plant driven by an exogenous signal is addressed in the absence of the standard exosystem hypothesis we assume availability of the current and l past values of the exogenous signal for use in the control law we formulate an approximate output regulation problem and characterize solvability in terms of the existence of a certain invariant manifold the control law yields a closed loop system with output exhibiting ultimate boundedness properties with respect to the l 1 difference of the exogenous signal a perturbation analysis of robustness properties is also provided

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

optimization of restricted roc surfaces in three class classification tasks we have shown previously that an n class ideal observer achieves the optimal receiver operating characteristic roc hypersurface in a neyman pearson sense due to the inherent complexity of evaluating observer performance even in a three class classification task some researchers have suggested a generally incomplete but more tractable evaluation in terms of a surface plotting only the three ldquosensitivities rdquo more generally one can evaluate observer performance with a single sensitivity or misclassification probability as a function of two linear combinations of sensitivities or misclassification probabilities we analyzed four such formulations including the ldquosensitivityrdquo surface in each case we applied the neyman pearson criterion to find the observer which achieves optimal performance with respect to each given set of ldquoperformance description variablesrdquo under consideration in the unrestricted case optimization with respect to the neyman pearson criterion yields the ideal observer as does maximization of the observer s expected utility moreover during our consideration of the restricted cases we found that the two optimization methods do not merely yield the same observer but are in fact completely equivalent in a mathematical sense thus for a wide variety of observers which maximize performance with respect to a restricted roc surface in the neyman pearson sense that roc surface can also be shown to provide a complete description of the observer s performance in an expected utility sense

a note on functional observability in this note we propose an alternative to characterize the functional observability for linear systems the main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi functional observer of a time invariant linear system the proof of this condition is constructive and it leads to design a stable observer via a new procedure neither based on the solution of a sylvester equation nor on the use of canonical state space forms

three class roc analysis toward a general decision theoretic solution multiclass receiver operating characteristic roc analysis has remained an open theoretical problem since the introduction of binary roc analysis in the 1950s previously we have developed a paradigm for three class roc analysis that extends and unifies decision theoretic linear discriminant analysis and probabilistic foundations of binary roc analysis in a three class paradigm one critical element in this paradigm is the equal error utility eeu assumption this assumption allows us to reduce the intrinsic space of the three class roc analysis 5 d hypersurface in 6 d hyperspace to a 2 d surface in the 3 d space of true positive fractions sensitivity space in this work we show that this 2 d roc surface fully and uniquely provides a complete descriptor for the optimal performance of a system for a three class classification task i e the triplet of likelihood ratio distributions assuming such a triplet exists to be specific we consider two classifiers that utilize likelihood ratios and we assumed each classifier has a continuous and differentiable 2 d sensitivity space roc surface under these conditions we proved that the classifiers have the same triplet of likelihood ratio distributions if and only if they have the same 2 d sensitivity space roc surfaces as a result the 2 d sensitivity surface contains complete information on the optimal three class task performance for the corresponding likelihood ratio classifier