stabilization of nonlinear systems via forwarding mod l sub g v forwarding is a tool for constructing stabilizers for nonlinear systems a key step in this design technique is to find an explicit solution to a partial differential equation pde which may be hard to find actually the pde may even not be solvable at all in this paper we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned pde hence effectively extending the realm of application of the forwarding methodology our contribution is illustrated with the example of an inverted pendulum with a disk inertia

stabilization of uncertain feedforward nonlinear systems with application to underactuated systems this note presents saturated controllers to stabilize uncertain feedforward nonlinear systems whose nominal dynamics contains uncertain gains and is subject to linear perturbations we assign a class of saturated controllers within which multiplicative coefficients appear before both states and saturation functions and the convergence analysis is conducted in the following way to verify the reduction of saturated terms we calculate the time derivative of a boundary surface in a small domain when the states reach the boundary surface to prove the asymptotic stability of the corresponding reduced system we use an m matrix based comparison principle in this way the suggested algorithm does not depend on the small gain theory and is suitable for dealing with strongly nonlinear underactuated systems including the cart pendulum system the overhead crane system and the uncertain vertical takeoff and landing vehicle

slow peaking and low gain designs for global stabilization of nonlinear systems this paper presents an analysis of the slow peaking phenomenon a pitfall of low gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems the phenomenon is best understood on a chain of integrators perturbed by a vector field up x u that satisfies p x 0 0 peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p x u these growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system when this higher order condition is satisfied an explicit control law is derived that achieves global asymptotic stability of x 0 this stabilization result is extended to more general cascade nonlinear systems in which the perturbation p x spl upsi spl upsi spl upsi spl xi u sup t contains the state spl xi and the control u of a stabilizable subsystem spl xi spl dot a spl xi u as an illustration a control law is derived that achieves global stabilization of the frictionless ball and beam model

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

saturated delayed controls for feedforward nonlinear systems the saturated delayed feedback is presented to globally stabilize a class of feedforward nonlinear systems whose nominal dynamics is the cascade of multiple oscillators and multiple integrators key strategies are stated as follows 1 to compensate the arbitrarily large input delay and to carry out the recursive analysis we transform the concerned system into a normal form 2 in the convergence analysis for multiple oscillators that are relatively difficult to treat we combine the saturated delayed terms define the composite lyapunov functions and use the cauchy formula 3 for ease of the analysis on nonlinear terms we employ saturation levels to restrict them as applications the usual feedforward nonlinear systems with multiple integrators as the nominal dynamics and the null controllable linear systems are dealt with in some new manners and a saturated delayed controller is presented for the well known tora system

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

estimation of distributional parameters for censored trace level water quality data 1 estimation techniques a recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations their reliabilities were evaluated by a monte carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels eight methods were used to estimate the mean standard deviation median and interquartile range criteria were developed based on the distribution of uncensored observations for determining the best performing parameter estimation method for any particular data det the most robust method for minimizing error in censored sample estimates of the four distributional parameters over all simulation conditions was the log probability regression method with this method censored observations are assumed to follow the zero to censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores when method performance was separately evaluated for each distributional parameter over all simulation conditions the log probability regression method still had the smallest errors for the mean and standard deviation more but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range when data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions the ranking of estimation methods was similar but the accuracy of error estimates was markedly improved over those without classification less

estimation of descriptive statistics for multiply censored water quality data this paper extends the work of gilliom and helsel 1986 on procedures for estimating descriptive statistics of water quality data that contain less than observations previously procedures were evaluated when only one detection limit was present here we investigate the performance of estimators for data that have multiple detection limits probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use therefore simple substitution procedures e g substitution of the detection limit should be avoided probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown when utilized correctly less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them

log pearson type 3 quantile estimators with regional skew information and low outlier adjustments 1 the recently developed expected moments algorithm ema cohn et al 1997 does as well as maximum likelihood estimations at estimating log pearson type 3 lp3 flood quantiles using systematic and historical flood information needed extensions include use of a regional skewness estimator and its precision to be consistent with bulletin 17b another issue addressed by bulletin 17b is the treatment of low outliers a monte carlo study compares the performance of bulletin 17b using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers including an extended ema estimator the conditional probability adjustment cpa from bulletin 17b and an estimator that uses probability plot regression ppr to compute substitute values for low outliers estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator for lp3 data the low outlier rejection procedure generally results in no loss of overall accuracy and the differences between the mses of the estimators that used an informative regional skew are generally modest in the skewness range of real interest samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment

confidence intervals for expected moments algorithm flood quantile estimates historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied however the federal guidelines for flood frequency analysis set forth in bulletin 17b rely on an inefficient weighting procedure that fails to take advantage of historical and paleoflood information this has led researchers to propose several more efficient alternatives including the expected moments algorithm ema which is attractive because it retains bulletin 17b s statistical structure method of moments with the log pearson type 3 distribution and thus can be easily integrated into flood analyses employing the rest of the bulletin 17b approach the practical utility of ema however has been limited because no closed form method has been available for quantifying the uncertainty of ema based flood quantile estimates this paper addresses that concern by providing analytical expressions for the asymptotic variance of ema flood quantile estimators and confidence intervals for flood quantile estimates monte carlo simulations demonstrate the properties of such confidence intervals for sites where a 25 to 100 year streamgage record is augmented by 50 to 150 years of historical information the experiments show that the confidence intervals though not exact should be acceptable for most purposes

plotting positions for historical floods and their precision plotting positions are needed for situations where in addition to a systematically recorded annual flood series one would have a record of any large floods which occurred during an extended historical period if they occurred many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment plotting positions are derived for such experiments using both classical and bayesian viewpoints in general it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank the number of observed historical floods and the lengths of the historical period and the systematic record for the largest flood the coefficient of variation of exceedance probability estimators is of the order of 1 as it is for complete systematic records examples illustrate the bias and precision of a variety of plotting position formulas the differences among the different plotting positions are generally small in comparison to the sampling variability however plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data three appendices consider the effect of misspecification of the length of the historical period the effect of misspecification of the threshold of perception or observation level and plotting positions for situations with several perception thresholds

saturated stabilization for an uncertain cascaded system subject to an oscillator abstract this paper investigates saturated stabilization of an uncertain cascaded system that consists of an uncertain double integrator and an uncertain oscillator the saturation reduction analysis is carried out by using the time interval based contradiction approach while the exponential stability analysis of the corresponding reduced system is conducted by using the hurwitz lemma in doing the saturation reduction analysis an intractable problem is how to estimate the states of the oscillator fully using the property of saturation functions as well as the technique of lyapunov inequalities we can first estimate the states of the oscillator and then achieve the time derivative bounds that some saturated terms possess in a finite time this has helped to carry out the saturation reduction analysis as the applications of the suggested algorithm the stabilizing controllers have been provided for two benchmark systems the uncertain two mass spring and the translational oscillator with a rotational actuator tora

lh moments for statistical analysis of extreme events statistical analysis of extremes is often conducted for predicting large return period events in this paper lh moments a generalization of l moments that are based on linear combinations of higher order statistics are introduced for characterizing the upper part of distributions and larger events in data using lh moments reduces undesirable influences that small sample events may have on the estimation of large return period events the method of lh moments is formulated for the generalized extreme value gev distribution along with two detailed examples monte carlo simulations are conducted to illustrate the performance of using the method of lh moments to fit the gev distribution to both gev and non gev samples lh moment diagrams are constructed using annual maximum flow data for 107 streams worldwide to examine the ability of the gev distribution to model those series

estimating constituent loads several recent articles have called attention to the problem of retransformation bias which can arise when log linear regression models are used to estimate sediment or other constituent loads in some cases the bias can lead to underestimation of constituent loads by as much as 50 and several procedures have been suggested for reducing or eliminating it however some of the procedures recommended for reducing the bias can actually increase it this paper compares the bias and variance of three procedures that can be used with log linear regression models the traditional rating curve estimator a modified rating curve method and a minimum variance unbiased estimator mvue analytical derivations of the bias and efficiency of all three estimators are presented it is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates however other conditions exist where they have substantial bias and a large mean square error these conditions commonly occur when sample sizes are small or when loads are estimated during high flow conditions the mvue however is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct since an efficient unbiased estimator is available there seems to be no reason to employ biased estimators

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

development of regional regression relationships with censored data when no discharge record is available for a site a regional regression relationship can be used to estimate low flow quantiles problems arise in the derivation of such models when some at site quantile estimates are reported as zero one concern is that quantile estimates reported as zero may be in the range from zero to the measurement threshold a second concern is that a logarithmic transformation cannot be used with zero quantile estimates so traditional log linear least squares estimators cannot be computed this paper uses visual examples and monte carlo simulation to compare the performance of techniques for estimating the parameters of a regional regression model when some at site quantile estimates are zero ordinary least squares ols techniques employed in practice include adding a small constant to all at site quantile estimates denoted olsc or neglecting all observation reported as zero denoted olsd olsc and olsd performed poorly compared to the use of a tobit model which is a maximum likelihood estimator mle procedure that represents the below threshold estimates as a range from zero to the threshold level for a small amount of censoring the olsd method can be acceptable a weighted tobit model that accounts for the heteroscedasticity of the residuals in the regression model provided relatively little gain over the ordinary tobit model

robust global stabilization of a class of uncertain feedforward nonlinear systems abstract the problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered the control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small with respect to previous works on the subject the design procedure is able to deal with uncertain possibly time varying parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system the small gain theorem for nonlinear systems which are input to state stable with restrictions is shown to be a key tool for designing a state feedback saturated control law

generalized extreme value distribution fitted by lh moments for low flow frequency analysis 1 this study introduces a method based on lh moments to use the generalized extreme value gev distribution for low flow frequency analysis and investigates the capability of the gev distribution fitted by lh moments to effectively model the lower tail of the low flow frequency curve without explicitly censoring the data sample the performance of the gev l moment the gev distribution fitted by l moments and gev lh moment the gev distribution fitted by lh moments methods are assessed by evaluating the bias mean square error and relative accuracy of quantile estimates through monte carlo simulations it is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution both gev l2 moment and gev l moment methods make equally accurate quantile estimates however when frequent low flows and extreme low flows do not follow a single trend the bias of the gev l2 moment estimator is negligible while the bias of the gev l moment estimator is significant at large annual recurrence intervals on average the gev l2 moment quantile estimator displays less bias than the gev l moment quantile estimator furthermore as the annual recurrence interval increases the relative accuracy of the gev l2 moment method consistently improves over the gev l moment method the gev lh moment method is thus considered to be the more suitable method to model low flows

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

l moment diagrams for censored observations observed data sets containing values above or below the analytical threshold of measuring equipment are referred to as censored such data are frequently encountered in quality and quantity monitoring applications of water soil and air samples most of the previous literature on the statistical analysis of censored data relates to the problems of moment parameter and quantile estimation methods such estimation methods usually assume an underlying probability distribution few goodness of fit methods exist for censored data we introduce l moment diagrams for the evaluation of the goodness of fit of alternative distributional hypotheses for left censored data experiments with artificial censored data sets document the conditions under which l moment diagrams should be useful our approach like hosking s 1995 approach for right censoring derived l moment diagrams for left censored observations from partial probability weighted moments

estimation of moments and quantiles using censored data censored data sets are often encountered in water quality investigations and streamflow analyses a monte carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets these techniques include a lognormal maximum likelihood estimator mle a log probability plot regression estimator and a new log partial probability weighted moment estimator data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables a robust fill in method which circumvents transformation bias in the real space moments was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation regardless of the underlying distribution the mle generally performed as well as or better than the other estimators though the moment and quantile estimators using all three techniques had comparable log space root mean square errors rmse for censoring at or below the 20th percentile for samples sizes of n 10 the 40th percentile for n 25 and the 60th percentile for n 50 comparison of the log space rmse and real space rmse indicated that a log space rmse was a better overall metric of estimator precision

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

improving search algorithms by using intelligent coordinates we consider algorithms that maximize a global function g in a distributed manner using a different adaptive computational agent to set each variable of the underlying space each agent ensuremath eta is self interested it sets its variable to maximize its own function g ensuremath eta three factors govern such a distributed algorithm s performance related to exploration exploitation game theory and machine learning we demonstrate how to exploit all three factors by modifying a search algorithm s exploration stage rather than random exploration each coordinate of the search space is now controlled by a separate machine learning based player engaged in a noncooperative game experiments demonstrate that this modification improves simulated annealing sa by up to an order of magnitude for bin packing and for a model of an economic process run over an underlying network these experiments also reveal interesting small world phenomena