hybrid feedback laws for a class of cascade nonlinear control systems a stabilization problem for a class of nonlinear control systems is considered systems in this class can be viewed as a cascade connection of a linear time invariant subsystem a nonlinear time periodic static subsystem and an integrator hybrid logic based feedback controllers are constructed to globally stabilize these systems to the origin the controllers operate by switching between various time periodic control functions at discrete time instants as specific applications we consider stabilization of nonholonomic control systems in power form to the origin and stabilization of trajectories for a class of nonlinear control systems numerical examples of global stabilization and tracking are reported

exponential stabilization of nonholonomic chained systems this paper presents a feedback control scheme for the stabilization of two input driftless chained nonholonomic systems also called chained form these systems are controllable but not asymptotically stabilizable by a smooth static state feedback control law in addition exponential stability cannot be obtained with a smooth time varying feedback control law here global asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth time varying feedback control law the control law depends in addition to the state and time on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state the inputs are differentiable with respect to time and tend exponentially toward zero for use in the analysis a lemma on the exponential convergence of a stable time varying nonlinear system perturbed by an exponentially decaying signal is presented simulation results are also shown

finite time stabilization of a class of cascade nonlinear switched systems under state dependent switching this paper investigates finite time stabilization fts problem for a class of cascade nonlinear switched systems unlike the existing approach based on time dependent switching strategy in which the switching instants must be given in advance largest region function strategy i e state dependent switching strategy is adopted to design the switching signal based on multiple lyapunov like functions method sufficient conditions for fts of cascade nonlinear switched systems are derived and the corresponding sliding motion problems are also considered finally an example is given to illustrate the applicability and the effectiveness of the proposed method

a new approach to the perfect regulation and the bounded peaking in linear multivariable control systems this paper presents a new approach to the perfect regulation p r and the bounded peaking b p in linear multivariable control systems based on the pole and the eigenvector assignment technique roughly speaking the p r represents an ideal control action which reduces the settling time to 0 while the b p simply means the bounded overshoot in this ideal situation simple frequency domain characterizations of the p r and the b p are derived they reveal some invariance properties of the p r and the b p that provide a powerful tool for achieving the p r and the b p the existence condition for the p r is derived which turns out to be identical to the result obtained in the optimal regulator theory this result is extended to a more general control objective of attaining the p r for one output while keeping the b p for another output a condition on which the p r is realized by an output feedback is also derived a simple design algorithm is proposed for achieving the p r which is essentially the eigenvector assignment procedure finally an application to a real system is discussed

on the accuracy of bonferroni significance levels for detecting outliers in linear models at present the first order bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely we present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use the application to analyses of 2 m factorial experiments and regression models is illustrated with several examples

perfect and subperfect regulation in linear multivariable control systems this paper is concerned with the synthesis of a high gain feedback control called perfect regulation p r for linear multivariable systems with external signals the existence condition for p r is derived in which the minimum phase property plays an essential role the use of an observer is discussed for achieving p r under restricted state observation some asymptotically ideal feedback properties are demonstrated such as the complete desensitization the complete servo performance with decoupling and the complete disturbance rejection which formulate the loop tightness for multivariable systems a design method for applying p r to non minimum phase systems called subperfect regulation s p r is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non minimum phase part it is a multivariable extension of a well known design technique for scalar systems to overcome the difficulty of phase non minimality computational procedures for p r and s p r are discussed an illustrative example is shown

qualitative properties of steady state poisson nernst planck systems mathematical study we examine qualitative properties of solutions of self consistent poisson nernst planck systems including uniqueness in the case of vanishing permanent charge the predominant case studied our results unveil a rich structure inherent in these systems one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes a particularly significant special case that of simple boundary conditions is shown to lead to uniqueness and to a complete characterization this case underlies the more complicated cases studied later a contraction mapping principle is included for completeness and allows for an arbitrary permanent charge distribution

structural properties of the one dimensional drift diffusion models for semiconductors this paper is devoted to the analysis of the one dimensional current and voltage drift diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination we show in the course of this paper that these models satisfy structural properties which are due to the particular form of the coupling of the involved systems these structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current i of the electron and hole current densities and of the electric field at the contacts we also prove analytic dependence of the solutions on i these results allow us to establish several qualitative properties of the current voltage characteristic in particular we give the nature of the possible bifurcation points of this curve we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages as a consequence we show that the currents never saturate as the voltage goes to 00 contrary to what was predicted by numerical simulations by m s mock compel 1 1982 pp 165 174 we also analyze the drift diffusion models under the assumption of quasi neutral approximation we show in particular that the reduced current driven model has at most one solution but that it does not always have a solution then we compare the full and the reduced voltage driven models and we show that in general the quasi neutral approximation is not accurate for large voltages even if no saturation phenomenon occurs finally we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms

order and the index of singular time invariant linar systems various concepts of order have been proposed in the literature it is shown that many of these are directly related to the index of a system

feedback stabilization of single input nonlinear systems abstract nonlinear geometric techniques partial feedback linearization and center manifold theory allow to reduce the design of a feedback stabilizing control for single input nonlinear systems into a lower dimensional stabilization problem the reduced order control system is explicitly constructed

resistant and test based outlier rejection effects on gaussian one and two sample inference resistant and sequential test based procedures for the detection of multiple outliers are compared in gaussian one and two sample problems subsequent to statistical rejection of putative outliers operating characteristics of hypothesis tests applied to samples that are outlier free may differ from their nominal values outlier rejection rules may be calibrated however to control the rate of erroneous outlier labeling in pure gaussian samples the small sample behavior of resistant location and scale estimators used in outlier detection is examined through simulation yielding new formulas for calibration of boxplot based and shorth based outlier rejection rules effects of different outlier criteria and calibration rubrics on postrejection hypothesis tests are compared in a variety of contamination settings and real world examples tests conducted subsequent to calibrated rejection have approximately nominal operating characteristics whether or not outliers are present the selection of an outlier cr

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

multiple steady state solutions in a multijunction semiconductor device multiple steady state solutions are constructed for a multijunction semiconductor device using a combination of asymptotic and numerical techniques the multijunction device is modeled by the drift diffusion equations of semiconductor physics in the drift diffusion model three sign alterations of the doping are assumed and a shockley read hall recombination is allowed for in the parameter range for which the current voltage relation is monotonic the quasi neutral approximation to the drift diffusion model is found to be valid and solutions are constructed asymptotically in the limit of large doping densities in contrast in the parameter range for which the current voltage relation is s shaped the quasi neutral approximation is found to poorly approximate solutions to the full model on the middle and lower branches a suitable modification to the quasi neutral approximation is then introduced to describe the middle and lower branches of the current voltage relation under the assumption of no recombi

subsystems time scales and multimodeling through a couple of naive examples the control theorists are invited to re examine the role of modeling in the study of large scale dynamic systems instead of assuming the existence of n diagonally dominant blocks it is possible to justify one strongly coupled slow core and n weakly coupled fast subsystems this structure is exhibited with a physically meaningful choice of state variables the controls are introduced following the recent concept of multimodeling

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

on strongly reverse biased semiconductor diodes a singular perturbation analysis of the drift diffusion model for stationary flow of charge carriers in a semiconductor device is given an extension of earlier results provides deeper insight into the structure of the solution and the possibility of computing approximations for leakage currents the solvability of the approximating problem is proved

conditioning of the steady state semiconductor device problem when solving numerically the steady state semiconductor device problem using appropriate discretizations extremely large condition numbers are often encountered for the linearized discrete device problem these condition numbers are so large that if they represented a sharp bound on the amplification of input errors or even of roundoff errors then the obtained numerical solution would be meaningless as it turns out one major reason for these large numbers is due to poor row and column scaling which is essentially harmless and or can be fixed but another reason could be an ill conditioned device which yields a true loss of significant digits in the numerical calculation in this paper we carry out a conditioning analysis for the steady state device problem we consider various quasilinearizations as well as gummel type iterations and obtain stability bounds which may indeed allow ill conditioning in general these bounds are exponential in the potential variation and are sharp e g for a thyristor but for devices where each smooth subdomain has an ohmic contact e g a pn diode moderate bounds guaranteeing well conditioning are obtained moreover the analysis suggests how various row and column scalings should be applied in order for the measured condition numbers to correspond more realistically to the true loss of significant digits in the calculations

unmasking outliers and leverage points a confirmation abstract identification of multiple outliers and leverage points is difficult because of the masking effect recently rousseeuw and van zomeren suggested using high breakdown robust estimation methods the least median of squares and minimum volume ellipsoid for unmasking these observations these methods tend to declare too many observations as extreme however a stepwise analysis is proposed here for confirmation of outliers and leverage points detected using the robust methods diagnostic measures are constructed for observations added back to the reduced sample they are shown graphically the complementary use of robust and diagnostic methods gives satisfactory results in analyzing two data sets one data set consists often bad and four good leverage points four or 10 using a different cutoff extreme observations of the other data set of size 28 are identified using the robust methods but the stepwise analysis confirms only one the limitations of atkinson s confirmatory approach are discusse

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

a bifurcation analysis of the one dimensional steady state semiconductor device equations this paper considers the one dimensional steady state semiconductor device equations modeling a thyristor these equations can be considered as a singularly perturbed boundary value problem the reduced problem is considered in order to derive an approximation to the current voltage curve a bifurcation equation is obtained that completely determines the qualitative structure of the current voltage characteristic a numeric example shows that the developed theory applies to data of realistic magnitude

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

a multistage procedure for detecting several outliers in linear regression a new statistic fk is proposed for detecting multiple outliers in linear regression this statistic is incorporated into the following multistage procedure initially a subset of k observations is selected to be tested if fk is found to be significant the most extreme observation in the subset as determined by the largest studentized residual is deleted and the test repeated for the k 1 observations in the subset using the remaining sample the procedure is stopped when a test fails to reject the no outlier hypothesis a monte carlo study is used to evaluate the performance of this procedure

global κ exponential asymptotic stabilization of underactuated surface vessels in this work a time invariant switching control law is proposed to make the desired set point of an underactuated surface vessel globally asymptotically stable with exponential convergence rate exponential stable the construction of the controller relies on discontinuous coordinate input transformations and a lyapunov like switching function the result is the first stabilizing law able to achieve global exponential stability of the underactuated surface vessel the effectiveness of the proposed control law is verified by simulation

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

procedures for the identification of multiple outliers in linear models abstract we consider the problem of identifying and testing multiple outliers in linear models the available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify we introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem both procedures attempt to separate the data into a set of clean data points and a set of points that contain the potential outliers the potential outliers are then tested to see how extreme they are relative to the clean subset using an appropriately scaled version of the prediction error the procedures are illustrated and compared to various existing methods using several data sets known to contain multiple outliers also the performances of both procedures are investigated by a monte carlo study the data sets and the monte carlo indicate that both procedures are effective in the detection of multiple outliers

the identification of influential subsets in regression using a fuzzy clustering strategy a fuzzy clustering strategy is used to identify subsets of influential observations in regression as part of the fuzzy clustering strategy the analyst can explore the uniqueness of selected subsets and the degree of belonging of observations to selected subsets this is accomplished by either varying a fuzzy parameter or the number of clusters once the observations or subsets have been identified the analyst can then compute regression diagnostics to confirm their degree of influence in regression bootstrapping and high breakdown procedures were used to confirm the influence of the previously identified subsets this fuzzy clustering strategy is applied to the modified data on wood specific gravity and an augmented production dataset both datasets have been previously presented in the literature

on the control of complementary slackness juggling mechanical systems studies the feedback control of a class of complementary slackness hybrid mechanical systems roughly the systems we study are composed of an uncontrollable part the object and a controlled one the robot linked by a unilateral constraint and an impact rule a systematic and general control design method for this class of systems is proposed the approach is a nontrivial extension of the one degree of freedom dof juggler control design in addition to the robot control it is also useful to study some intermediate controllability properties of the object s impact poincare mapping which generally takes the form of a nonlinear discrete time system the force input mainly consists of a family of dead beat feedback control laws introduced via a recursive procedure and exploiting the underlying discrete time structure of the system the main goal of the paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases

perturbation analysis of a system of quasi variational inequalities for optimal stochastic scheduling optimal scheduling of continuously evolving dynamical systems involves the analysis of certain partial differential inequalities on solution dependent domains these are the quasi variatlonai inequalities qvi s introduced for such problems by a bensoussan and j l lions they arise naturally in such applications as inventory control and unit commitment scheduling in electric energy systems qvi s are in these contexts the analog of the dynamic programming partial differential equations of r bellman for continuous control problems analytical treatment of qvi s involves not only the solution of partial differential inequalities but also the simultaneous analysis of the free boundaries of the domain of the solution in effect the optimal return function is the solution of the inequalities and the optimal control switching policy is defined by the free boundaries this paper considers a system of two singularly perturbed second order quasi variational inequalities with a turning point in a bounded domain in r1 asymptotic approximations for the free boundaries are derived using standard perturbation analysis for boundary value problems also local regularity properties of the limit solution are obtained the results are illustrated by a parametric study of a simple model of commitment scheduling for a single unit in a power generation system

singular perturbational model reduction in the frequency domain singular perturbational approximations for linear continuous time and discrete time systems are developed in the frequency domain it is shown that the familiar singular perturbational result is an approximation at the origin in the complex plane however if the system has multiple time scale effects other approximations can be obtained at different locations on the negative real axis to emphasize such behavior the relationship between singular perturbational approximations and direct subsystem elimination is also investigated

stabilization of trajectories for systems with nonholonomic constraints a new technique for stabilizing nonholonomic systems to trajectories is presented it is well known that such systems cannot be stabilized to a point using smooth static state feedback in this note we suggest the use of control laws for stabilizing a system about a trajectory instead of a point given a nonlinear system and a desired nominal feasible trajectory the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory the theory is applied to several examples including a car like robot

brief paper singular perturbation analysis of a receding horizon controller a new receding horizon approach to the linear regulator problem is presented at each instant of time the control strategy is based on the minimization of a quadratic performance index extending over an interval of fixed length into the future connections with standard results are discussed and under general assumptions the closed loop system is shown to be asymptotically stable a potential advantage of our method lies in the fact that a singular perturbation analysis is well posed this indicates that for plants containing slow and fast modes the design procedure can be split up into two stages the resulting composite control exhibits attractive engineering properties use and effectiveness of the proposed techniques are demonstrated by investigating a practical example

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

asymptotic stability of nonlinear multiparameter singularly perturbed systems sufficient conditions are derived to guarantee the asymptotic stability of a class of nonlinear singularly perturbed systems with several perturbation parameters of the same order estimates of the region of attraction and bounds on the small parameters are obtained

a generalized extreme studentized residual multiple outlier detection procedure in linear regression this article is concerned with procedures for detecting multiple y outhers in linear regression a generalized extreme studentized residual gesr procedure which controls type i error rate is developed an approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n 25 are tabulated the performance of this procedure is compared with others by monte carlo techniques and found to be superior the procedure however fails in detecting y outliers that are on high leverage cases for this a two phase procedure is suggested in phase 1 a set of suspect observations is identified by gesr and one of the diagnostics applied sequentially in phase 2 a backward testing is conducted using the gesr procedure to see which of the suspect cases are outlicrs several examples are analyzed

universal nonsingular controls abstract in this note we prove that for analytical systems satisfying the strong accessibility rank condition generic inputs produce trajectories along which the linearized system is controllable applications to the steering of systems without drift are briefly mentioned

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

exponentially convergent control laws for nonholonomic systems in power form abstract this paper introduces a method for constructing exponentially convergent control laws for n dimensional nonholonomic systems in power form the methodology is based on the construction of a series of nested invariant manifolds for the closed loop system under a linear control law a recursive algorithm is presented which uses these manifolds to construct a three dimensional system in power form it is shown that the feedback controller for the original system is the one for this three dimensional system with a proper choice of the gains

a reduction process for perturbed markov chains given a perturbed markov chain with generator a varepsilon a 0 varepsilon a 1 varepsilon 2 a 2 cdots it is shown that to each time scale t t varepsilon t varepsilon 2 cdots is associated a reduced markov chain this process of reduction has only finitely many steps it is given in a recursive way and each reduced chain admits as state space the recurrent classes of the reduced chain defined at the previous stage it is shown that if lambda is an eigenvalue different from zero of the generator of the kth reduced chain with multiplicity p then a varepsilon admits p eigenvalues lambda varepsilon such that lambda varepsilon varepsilon k lambda o varepsilon k a basis of ker a 0 resp ker a 0 which is robust to the perturbation is constructed

state decomposition for singular perturbation order reduction a modal approach singular perturbation techniques for order reduction are based on decomposing the high order system into two parts approximation of the high order system dynamics by the low order model is mainly dependent on this partition this paper introduces a measure for the degree of dependence of the state variables on the high order dominant eigenvalues by means of this measure it is not only possible to find an appropriate decomposition yielding a good low order model but also to get an indication of the order of the reduced model two illustrative examples demonstrate the main results

a higher order sufficient condition for local surjectivity soient 7b h et 7b n des espaces de banach reels et f 7b h 7b n une application telle que f 0 0 et f est c 1 frechet differentiable dans un voisinage ouvert de 0 7b h on donne une condition suffisante a la surjectivite locale qui peut s appliquer dans le cas ou df 0 n est pas surjective

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

testing for a single outlier in a linear model the maximum absolute studentized residual may be used for the detection of a single outlier in a general linear model but approximations to its distribution are required ellenberg 1976 biometrics 32 637 645 has proposed the use of the second bonferroni inequality it is now shown that when all the correlations between residuals are smaller in absolute value than a certain tabulated value the approximate test based on the first bonferroni inequality will have size between the nominal value oe and oh 2 e2the results are illustrated by two examples

global stabilizing near optimal control design for nonholonomic chained systems it is well known that a nonlinear optimal control requires the solution to a two point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration in this paper a new and near optimal control design framework is proposed for controlling any nonholonomic system in the chained form the proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system it is shown that no matter whether the first component u1d t of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero uniform complete controllability of the nominal system can be recovered by employing the proposed time folding unfolding technique upon establishing the common property of uniform complete controllability the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner using duality uniform complete observability can also be established a closed form and exponentially convergent observer can be synthesized and the controls designed using the proposed framework can be either state feedback or output feedback the tracking controls are designed using the same three step process that is design of the proposed controls starts with optimal control solutions to two linear nominal subsystems one time invariant and the other time varying the two solutions combined together render a globally stabilizing suboptimal control for the overall system then the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one consequently an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form an example is used to show that regulation control can be designed similarly all the controls designed are in simple closed forms and hence real time implementable they are time varying and smooth globally and exponentially asymptotically stabilizing and they are near optimal since their closeness to the optimal control attainable only offline can be measured monitored on line and has been minimized

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

a general method for local sensitivity analysis with application to regression models and other optimization problems this article introduces a method for sensitivity analysis of general applicability the method is based on the well known duality property of mathematical programming which states that the partial derivatives of the primal objective function with respect to the constraints on the right side parameters are the negative of the optimal values of the dual problem variables for the parameters or data for which sensitivities are sought to appear on the right side they are converted into artificial variables and set to their actual values thus obtaining the desired constraints the method is applicable to linear and nonlinear models to normal and nonnormal models and to least squares and other methods of estimation in addition to its general applicability the method is also computationally inexpensive because the necessary information becomes available without extra calculations the theoretical basis for the method is given and illustrated by its application to least squares least absolute value an

a multimodel approach to stochastic nash games a decentralized filtering and control scheme is presented for obtaining low order nash equilibrium strategies for decision makers using different models of the same large scale system multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables the small parameters are appropriately scaled so that the variables in both time scales are well defined the decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension it is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero

the approximation problem for drift diffusion systems this review surveys a significant set of recent ideas developed in the study of nonlinear galerkin approximation a significant role is played by the krasnosel skii calculus which represents a generalization of the classical inf sup linear saddlepoint theory a description of a proper extension of this calculus and the relation to the ii sup theory are part of this review the general study is motivated by steady state self consistent drift diffusion systems the mixed boundary value problem for nonlinear elliptic systems is studied with respect to defining a sequence of convergent approximations satisfying requirements of i optimal convergence rate ii computability and iii stability it is shown how the fixed point and numerical fixed point maps of the system in conjunction with the newton kantorovich method applied to the numerical fixed point map permit a solution of this approximation problem a critical aspect of the study is the identification of the breakdown of the newton kantorovi

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods