restricted ornstein uhlenbeck process and applications in neuronal models with periodic input signals restricted gauss markov processes are used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals the first passage time problem through a time dependent threshold is explicitly developed numerical simulation and asymptotic results for firing densities are provided

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

sequential tests constructed from images a method is described for constructing sequential test boundaries for which the sample size distribution is easily computed assuming a diffusion approximation to be adequate a few suitably placed images with negative weights are added to a basic unit source at the origin to create absorbing boundaries with intuitively desirable properties a simple family of closed boundaries generated in this way is compared with ferebee s 1980 reversed parabolic boundaries and anderson s 1960 trapezoidal boundaries with regard to minimax expected sample size the use of a delayed image to generate two lobed closed boundaries is also briefly described

first passage time statistics of brownian motion with purely time dependent drift and diffusion abstract systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a brownian motion bm driven by time dependent drift and diffusion coefficients modeling such systems requires solving the associated fokker planck equation subject to an absorbing barrier transitional probabilities are derived via the method of images whose applicability to time dependent problems is shown to be limited to state independent drift and diffusion coefficients that only depend on time and are proportional to each other first passage time statistics such as the survival probabilities and first passage time densities are obtained analytically the analysis includes the study of different functional forms of the time dependent drift and diffusion including power law time dependence and different periodic drivers as a case study of these theoretical results a stochastic model of water resources availability in snowmelt dominated regions is presented where both temperature effects and snow precipitation input are incorporated

surmounting oscillating barriers path integral approach for weak noise we consider the thermally activated escape of an overdamped brownian particle over a potential barrier in the presence of periodic driving a time dependent path integral formalism is developed which allows us to derive asymptotically exact weak noise expressions for both the instantaneous and the time averaged escape rate our results comprise a conceptually different systematic treatment of the rate prefactor multiplying the exponentially leading arrhenius factor moreover an estimate for the deviations at finite noise strengths is provided and a supersymmetry type property of the time averaged escape rate is verified for piecewise parabolic potentials the rate expression can be evaluated in closed analytical form while in more general cases as exemplified by a cubic potential an action integral remains to be minimized numerically our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies

first passage time distribution for variable diffusion processes first passage time distribution which presents the likelihood of a stock reaching a pre specified price at a given time is useful in establishing the value of financial instruments and in designing trading strategies first passage time distribution for wiener processes has a single peak while that for stocks exhibits a notable second peak within a trading day this feature has only been discussed sporadically often dismissed as due to insufficient incorrect data or circumvented by conversion to tick time and to the best of our knowledge has not been explained in terms of the underlying stochastic process it was shown previously that intra day variations in the market can be modeled by a stochastic process containing two variable diffusion processes hua et al in physica a 419 221 233 2015 we show here that the first passage time distribution of this two stage variable diffusion model does exhibit a behavior similar to the empirical observation in addition we find that an extended model incorporating overnight price fluctuations exhibits intra and inter day behavior similar to those of empirical first passage time distributions

on the construction of a special class of time inhomogeneous diffusion processes a special class of time inhomogeneous diffusion processes generated starting from gauss markov processes conditioned on the same initial state is considered this class includes many interesting diffusion processes with time dependent infinitesimal drift and variance for which the transition probability density function is explicitly determined moreover closed form results for the first passage time density through suitable time varying boundaries are obtained special cases generated starting from wiener and ornstein uhlenbeck processes are considered and widely discussed

statistics of entrance times abstract the statistical properties of the transitions of a discrete markov process are investigated in terms of entrance times a simple formula for their density is given and used to measure the synchronization of a process with a periodic driving force for the mcnamara wiesenfeld model of stochastic resonance we find parameter regions in which the transition frequency of the process is locked with the frequency of the external driving

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

sobolev norms based state estimation and input recovery for a class of nonlinear systems design and experimental results in this paper we address the problem of state estimation and input recovery for a class of nonlinear systems in the presence of disturbances in both the state and output equations indeed one of the main difficulties that arise when input recovery is considered is how to cope with the problem of disturbance s derivative for the filter design our contribution lies in the use of sobolev norms to develop a simple and useful observer we provide first the state filtering and input recovery equations after based on the lyapunov stability theory and some robustness criteria new sufficient synthesis conditions are given in terms of linear matrix inequalities lmis to show performances of the proposed method we considered the problem of simultaneous synchronization and decryption in chaotic communication systems with some experimental results

assessing the uncertainty associated with intermittent rainfall fields 1 in many practical situations where spatial rainfall estimates are needed rainfall occurs as a spatially intermittent phenomenon an efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas the final rainfall estimates are obtained as the product of the estimates of these two random functions however the published approach does not contain a method for estimation of uncertainties the contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach from the conditional distribution representations of uncertainty such as the estimation variance and confidence intervals can be obtained an approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area the methodology has been validated using simulated and real rainfall data sets the results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data

continuous discrete observer for state affine systems with sampled and delayed measurements the observation of a class of multi input multi output mimo state affine systems with both sampled and delayed output measurements is addressed these two constraints disturb simultaneously the convergence of the observer assuming some persistent excitation conditions to hold and by using lyapunov tools adapted to impulsive systems two classes of global exponential observers are proposed some explicit relations between maximum allowable delay and maximum allowable sampling period are given an extension to some classes of nonlinear systems is also given

h observer design for uncertain one sided lipschitz nonlinear systems with time varying delay abstract the h observer design for uncertain one sided lipschitz nonlinear systems with time varying delay is investigated in this paper by considering the quadratic inner bounded requirement and the one sided lipschitz condition concurrently and employing a class of relaxed integral inequalities the h observer for nominal lipschitz systems is designed firstly then the results are extended to the one sided lipschitz systems with norm bounded uncertainties finally the proposed results are demonstrated via two simulation examples

design of sliding observers for lipschitz nonlinear system using a new time averaged lyapunov function abstractthis paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of gaussian input disturbances and sensor noises the paper first proposes a nov

compatibility of continuous rainfall occurrence models with discrete rainfall observations inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made following the work of i rodriguez iturbe et al 1984 this assertion is tested by examining the compatibility of the neyman scott n s model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day the results suggest that the n s model is inconsistent at different time scales and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought these findings are quite general in that they apply to any model with rainfall deposited instantaneously at times described by a n s process regardless of how the amounts associated with the events are distributed and of the dependence structure of the amounts

series solution to the first passage time problem of a brownian motion with an exponential time dependent drift we derive the first passage time statistics of a brownian motion driven by an exponential time dependent drift up to a threshold this process corresponds to the signal integration in a simple neuronal model supplemented with an adaptation like current and reaching the threshold for the first time represents the condition for declaring a spike based on the backward fokker planck formulation we consider the survival probability of this process in a domain restricted by an absorbent boundary the solution is given as an expansion in terms of the intensity of the time dependent drift which results in an infinite set of recurrence equations we explicitly obtain the complete solution by solving each term in the expansion in a recursive scheme from the survival probability we evaluate the first passage time statistics which itself preserves the series structure we then compare theoretical results with data extracted from numerical simulations of the associated dynamical system and show that the analytical description is appropriate whenever the series is truncated in an adequate order

consensus of nonlinear multi agent systems with observer based protocols abstract this paper is concerned with distributed pinning consensus problem for a class of nonlinear multi agent system with observer based protocols two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents according to the state information observed a distributed pinning observer based protocol is proposed for the leader following consensus of the multi agent system furthermore two multi step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively it is shown that under the condition that the pinning joint communication topology contains a directed spanning tree the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable but also guarantee the consensus of the multi agent system to be solved asymptotically finally two numerical examples are provided to demonstrate the effectiveness of the observer based protocols

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

state and unknown input observers for nonlinear systems with bounded exogenous inputs a systematic design methodology for state observers for a large class of nonlinear systems with bounded exogenous inputs disturbance inputs and sensor noise is proposed the nonlinearities under consideration are characterized by an incremental quadratic constraint parameterized by a set of multiplier matrices linear matrix inequalities are developed to construct observer gains which ensure that a performance output based on the state estimation error satisfies a prescribed degree of accuracy furthermore conditions guaranteeing estimation of the unknown inputs to arbitrary degrees of accuracy are provided the proposed scheme is illustrated with a numerical example which does not satisfy the so called matching conditions

an observer based controller for nonlinear systems a gain scheduling approach abstract this paper presents an observer based controller for discrete time nonlinear systems whose control inputs are subject to a set of equality and or inequality constraints firstly a regularized least square estimator is developed to estimate the states of the nonlinear system then the estimated states are used to generate a feedback control law using the jacobean linearization in conjunction with gain scheduling the stability of the closed loop control system is rigorously investigated applications of the proposed observer based control scheme to two numerical examples are presented then the developed controller is used to control a synchronous machine which is subject to constraints on the control the simulation results show the effectiveness of the proposed observer based control scheme

revisiting multifractality of high resolution temporal rainfall using a wavelet based formalism 1 we reexamine the scaling structure of temporal rainfall using wavelet based methodologies which as we demonstrate offer important advantages compared to the more traditional multifractal approaches such as box counting and structure function techniques in particular we explore two methods based on the continuous wavelet transform cwt and the wavelet transform modulus maxima wtmm the partition function method and the newer and more efficient magnitude cumulant analysis method we also report the results of a two point magnitude correlation analysis which is able to infer the presence or absence of multiplicativity as the underlying mechanism of scaling the diagnostic power of these methodologies for small samples signals with short ranges of scaling and signals for which high frequency fluctuations are superimposed on a low frequency component all common attributes of geophysical signals is carefully documented application of these methodologies to several midwestern convective storms sampled every 5 s over several hours provides new insights they reveal the presence of a very intermittent multifractal structure a wide spectrum of singularities in rainfall fluctuations between the scales of 5 min and the storm pulse duration of the order of 1 2 hours for the analyzed storms the two point magnitude statistical analysis suggests that this structure is consistent with a multiplicative cascading mechanism which however is local in nature that is it applies only within each storm pulse but not over the whole storm duration

generalized scale invariance in the atmosphere and fractal models of rain in recent years there has been considerable interest in stochastic rain models by developing new ideas about scale invariance and intermittency we argue that the scope of such models can be greatly extended the notions of scale invariance intermittency and the associated idea of fractal dimension have lately gained considerable ground particularly in the context of extremely variable phenomena such as those found in the mesoscale and in hydrodynamic turbulence we review some relevant work and argue that the atmosphere respects a symmetry principle that we call generalized scale invariance in which the statistical properties of the small and large scale are related to each other by a magnification coupled with a differential stratification due to gravity and differential rotation due to the coriolis force we further argue that the extremely erratic intermittent nature of the atmosphere is characterized by scale invariant fractal measures leading to hyperbolic fat tailed probability distributions of the fluctuations the standard statistical methods based on exponential fall offs in both correlations and probability distributions are inappropriate when the variability is of this type we show how both the scaling and intermittency may be exploited to develop extremely variable stochastic models of rain although the models examined here are the simplest of a family of extremely variable processes depending on only two radar determined parameters they lead to realizations possessing many realistic features of the rainfield including complexity of form clustering and bands at all scales as well as differential stratification and rotation finally we point to weaknesses in the models in particular their monodimensional nature and suggest possible improvements

revisiting rainfall clustering and intermittency across different climatic regimes 1 one of the vexing questions in rainfall research is the role of intermittency and its nonuniversal signature in anomalous scaling functions whether this lack of universal behavior is due to the bursting patterns in rainfall intensity or the alternation between long dry periods and highly clustered wet phases or both remains an open issue to progress on a narrower scope of this problem the effects of intermittency originating from rainfall occurrence are first separated from rainfall intermittency induced by intensity variability across five climatic regimes considered here it was shown that the rainfall occurrence process op exhibits 1 a near constant spectral slope 2 a near constant clustering exponent and 3 a probability density function of dry phases displaying a power law behavior with an exponent 1 5 consistent with other studies for timescales commensurate with frontal and storm systems also for the op the scaling exponents of the normalized higher order structure functions reveal an extensive monofractal scaling at all five climatic regimes when taken together these intersite results are suggestive that rainfall intensity modulations are the main cause of the nonuniversal anomalous scaling and not the clustering properties associated with the support the nature of these modulations is markedly different when comparing rainfall to a familiar and often interrelated process such as scalar turbulence in the case of turbulence amplitude variability of scalar dissipation rates appear to mitigate the intermittency effects connected with anomalous scaling while for rainfall series intensity fluctuations seem to amplify them

noise induced anomalous diffusion over a periodically modulated saddle we study analytically and numerically the anomalous diffusion across periodically modulated parabolic potential within langevin and fokker planck descriptions we find that the probability of particles passing over the saddle is affected strikingly by the periodical modulation with average zero bias particularly the initial phase plays an important role in the modulation effect the effect of the correlation time of external ornstein uhlenbeck noise on dynamical process is also discussed a reduction in overpassing probability is observed due to finite correlation time

continuous discrete time observer design for lipschitz systems with sampled measurements this technical note concerns observer design for lipschitz nonlinear systems with sampled output using reachability analysis an upper approximation of the attainable set is given when this approximation is formulated in terms of a convex combination of linear mappings a sufficient condition is given in terms of linear matrix inequalities lmis which can be solved employing an lmis solver this novel approach seems to be an efficient tool to solve the problem of observer synthesis for a class of lipschitz systems of small dimensions

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

an entropic stochastic representation of rainfall intermittency the origin of clustering and persistence 1 the well established physical and mathematical principle of maximum entropy interpreted as maximum uncertainty is used to explain the observed dependence properties of the rainfall occurrence process including the clustering behavior and persistence the conditions used for the maximization of entropy are as simple as possible i e that the rainfall processes is intermittent with dependent occurrences intermittency is quantified by the probability that a time interval is dry and dependence is quantified by the probability that two consecutive intervals are dry these two probabilities are used as constraints in a multiple scale entropy maximization framework which determines any conditional or unconditional probability of any sequence of dry and wet intervals at any timescale thus the rainfall occurrence process including its dependence structure is described by only two parameters this dependence structure appears to be non markovian application of this theoretical framework to the rainfall data set of athens indicates good agreement of theoretical predictions and empirical data at the entire range of scales for which probabilities dry and wet can be estimated from one hour to several months

gauss markov processes in the presence of a reflecting boundary and applications in neuronal models abstract gauss markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined furthermore the first passage time density through a time dependent threshold is studied by using analytical numerical and asymptotic methods the restricted gauss markov processes are then used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time varying input signals

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a sandpile model for the distribution of rainfall abstract recently peters et al phys rev lett 88 2002 018701 have found power law behaviour in the distribution of rain events here it is shown that the observed self similar features in both the reservoir level and the distribution of rain events can quantitatively be reproduced from an extension to two dimensions of the oslo model developed to describe the dynamics of a pile of rice furthermore it is argued that the sandpile model may be able to reproduce more detailed features such as the shape of cumulus clouds in addition many other systems which show self similarity in their time variations with the same quantitative characterizations are discussed

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

continuous time versus discrete time point process models for rainfall occurrence series several authors have had apparent success in applying continuous time point process models to rainfall occurrence sequences in this paper it is shown that if rainfall occurrences are interpreted as the events of a point process and not as a censored sample the continuous time point process methodology and estimation procedures are not directly applicable since they fail to account for the time discreteness of the sample process this is demonstrated analytically by studying the effects of discretization on selected statistical properties of a poisson process a neyman scott process and a renewal cox process with markovian intensity in general the study of rainfall occurrences under the continuous time point process framework may result in misleading inferences regarding clustering dispersion and consequently incorrect interpretations of the underlying rainfall generating mechanisms for example daily rainfall occurrence structures underdispersed relative to the poisson process are usually overdispersed relative to the bernoulli process the discrete time analogue of the poisson these findings are confirmed by the statistical analysis of six daily rainfall records representative of a range of u s climates two of which are described in detail

first passage time distributions of anomalous biased diffusion with double absorbing barriers abstract we investigate the first passage time fpt problem of anomalous diffusion governed by the galilei variant fractional diffusion advection equation in the semi infinite and finite domains subject to an absorbing boundary condition we obtain explicit solutions for the fpt distributions and the corresponding laplace transforms for both zero and constant drift cases by using the method of separation of variables as well as the properties of the fox h function an important relation between the fpt distributions corresponding to one and two absorbing barriers is revealed to determine the conditional fpt distributions it shows that the proportion between the conditional fpt distributions only depends on the general peclet number we further discuss the asymptotic behavior of the fpt distributions and confirm our theoretical analysis by numerical results

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

multiscaling properties of rainfall and bounded random cascades the connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed and a new phenomenological model for rainfall time series simulation is proposed the bounded random cascade model presented here is a generalization of the well known model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales this allows one to directly simulate a multiscaling random field with an energy spectrum exponent 1 which is typical for rainfall time series data but which cannot be produced by a standard model a procedure is proposed for estimating the cascade parameters of this new bounded model from observed data parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents the bounded model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts

a nonparametric model for stochastic generation of daily rainfall occurrence 1 this paper presents a nonparametric model for generating single site daily rainfall occurrence the model is formulated to reproduce longer term variability and low frequency features such as drought and sustained wet periods while still reproducing characteristics at daily time scales parsimony is achieved within a markovian framework by using aggregate predictor variables that describe how wet it has been over a period of time the use of a moving window to give a seasonally representative sample at any given time of year ensures an accurate representation of the seasonal variations present in the rainfall time series actual simulation proceeds by resampling from the historical record of rainfall occurrence conditional to the current values of the associated predictors the model is applied using historical daily rainfall occurrence from sydney australia we find that the use of multiple predictors specified at a daily level and at seasonal annual and multiyear aggregation levels leads to sequences that more closely reproduce the longer term variability present in the historic records compared to sequences produced by models incorporating only one or two predictors

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

a unified h adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities abstract this paper investigates the problem of the h adaptive observer design for a class of nonlinear dynamical systems the main contribution consists in providing a unified synthesis method for systems with both lipschitz and monotone nonlinearities not necessarily lipschitz thanks to the innovation terms into the nonlinear functions m arcak p kokotovic observer based control of systems with slope restricted nonlinearities ieee transactions on automatic control 46 7 2001 1146 1150 and to the differential mean value theorem a zemouche m boutayeb g i bara observers for a class of lipschitz systems with extension to h performance analysis systems and control letters 57 1 2008 18 27 the stability analysis leads to the solvability of a linear matrix inequality lmi with several degrees of freedom for simplicity we start by presenting the result in an h adaptive free context furthermore we propose an h adaptive estimator that extends easily the obtained results to systems with unknown parameters in the presence of disturbances we show in particular that the matching condition in terms of an equality constraint required in several works is not necessary and therefore allows reducing the conservatism of the existing conditions performances of the proposed approach are shown through a numerical example with a polynomial nonlinearity

an exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques abstract this paper proposes a comprehensive solution to persistent problems faced by nonlinear observer design via convex optimization techniques namely the construction of an exact error model and the handling of unmeasurable premises instead of using the differential mean value theorem it is shown that the error system is always exactly amenable via algebraic rearrangements to an explicit matrix polynomial form of the gradient where the error signal appears factorized at the rightmost side thus allowing lyapunov based derivation of conditions in the form of linear matrix inequalities or sum of squares an effective exploitation of the nonlinear characteristics of the observer while naturally decoupling available and non available signals is achieved via exact takagi sugeno tensor product models or polynomial rewriting of the error system not the plant generalizations such as h disturbance rejection or decay rate are straightforward in contrast with recent approaches the output is not required to be linear nor the systems involved to be affine in control illustrative examples are provided that overcome recent approaches on the subject

sporadicity between periodic and chaotic dynamical behaviors abstract we define the class of sporadic dynamical systems as the systems where the algorithmic complexity of kolmogorov kolmogorov a n 1983 russ math surv 38 29 40 and chaitin chaitin g j 1987 algorithmic information theory cambridge univ press cambridge u k as well as the logarithm of separation of initially nearby trajectories grow as nv0 log n v1 with 0 v0 1 or v0 1 and v1 0 as time n these systems present a behavior intermediate between the multiperiodic v0 0 v1 1 and the chaotic ones v0 1 v1 0 we show that intermittent systems of manneville manneville p 1980 j phys paris 41 1235 1243 as well as some countable markov chains may be sporadic and furthermore that the dynamical fluctuations of these systems may be of levy s type rather than gaussian

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

nonlinear state observation using h sub spl infin filtering riccati design the authors propose an observer for continuous time nonlinear systems the observer gain is computed by a riccati differential equation similar to the extended kalman filter they prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate lyapunov function furthermore the authors explore some important relations of the proposed observer to robust control theory and h sub spl infin filtering to examine the practical usefulness of the proposed observer they applied it to an induction motor for the estimation of the rotor flux and the angular velocity

analysis of diffusion and trapping efficiency for random walks on non fractal scale free trees abstract in this paper the discrete random walks on the recursive non fractal scale free trees nfsft are studied and a kind of method to calculate the analytic solutions of the mean first passage time mfpt for any pair of nodes the mean trapping time mtt for any target node and mean diffusing time mdt for any starting node are proposed furthermore we compare the trapping efficiency and diffusion efficiency between any two nodes of nfsft by using the mtt and the mdt as the measures of trapping efficiency and diffusion efficiency respectively and find the best or worst trapping sites and the best or worst diffusion sites the results show that the two hubs of nfsft are not only the best trapping site but also the worst diffusion site and that the nodes which are the farthest nodes from the two hubs are not only the worst trapping sites but also the best diffusion sites furthermore we find that the ratio between the maximum and minimum of mtt grows logarithmically with network order but the ratio between the maximum and minimum of mdt is almost equal to 1 the results imply that the trap s position has great effect on the trapping efficiency but the position of starting node has little effect on diffusion efficiency finally the simulation for random walks on nfsft is done and it is consistent with the derived results

multiscaling pulse representation of temporal rainfall 1 we develop a pulse based representation of temporal rainfall with multifractal properties in the small scale limit the representation combines a traditional model for the exterior process at the synoptic scale with a novel hierarchical pulse model for the event interiors for validation we apply the model to a temporal rainfall record from florence italy although the model has only six parameters four for the exterior process and two for the event interiors it accurately reproduces a wide range of empirical statistics including the distribution of dry and wet periods the distribution of rainfall intensity up to extreme fractiles the spectral density the moment scaling function k q and the distribution of the partition coefficients for rainfall disaggregation the model also reproduces observed deviations of physical rainfall from perfect scaling multiscaling behavior

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

trichotomous noise controlled signal amplification in a generalized verhulst model abstract the long time limit of the probability distribution and statistical moments for a population size are studied by means of a stochastic growth model with generalized verhulst self regulation the effect of variable environment on the carrying capacity of a population is modeled by a multiplicative three level markovian noise and by a time periodic deterministic component exact expressions for the moments of the population size have been calculated it is shown that an interplay of a small periodic forcing and colored noise can cause large oscillations of the mean population size the conditions for the appearance of such a phenomenon are found and illustrated by graphs implications of the results on models of symbiotic metapopulations are also discussed particularly it is demonstrated that the effect of noise generated amplification of an input signal gets more pronounced as the intensity of symbiotic interaction increases

observer design for one sided lipschitz discrete time systems abstract this note focuses on state observer design for a general class of nonlinear discrete time systems that satisfies the one sided lipschitz condition it has been shown that this condition may encompass a large class of nonlinearities however challenging problems arise such as relevant choice of the lyapunov function or non convexity of the obtained stability conditions both full order and reduced order observer designs are considered in this work the main contribution is to provide first some mathematical artifacts on the lyapunov function to obtain simple and workable stability conditions furthermore we show how to obtain lmi conditions to ensure asymptotic convergence on the other hand we extend the obtained results to n p reduced order observer design high performances are shown through simulation results

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

high gain observer design for some networked control systems new results on high gain observer design for networked control systems via an emulation like approach are presented by using a general framework and a lyapunov approach we derive some explicit conditions on the maximum allowable transmission interval that ensure an exponential convergence of the observation error for a large class of network protocols

ℋ ℋ fault detection filter for a class of nonlinear descriptor systems this article addresses the problem of designing a robust fault detection filter rfdf for a class of nonlinear descriptor systems whose nonlinear term is globally lipschitz and linear term is described by a linear parameter varying form the effect of perturbations on the residuals is minimised using the norm while the sensitivity performance is guaranteed using the index thanks to a particular lyapunov function which depends on the faults and the filter design problem is formulated as a convex optimisation problem solved via linear matrix inequality techniques performances of the proposed filter are shown through the application of an activated sludge process model

observer synthesis under time varying sampling for lipschitz nonlinear systems in this work the problem of observation of continuous time nonlinear lipschitz systems under time varying discrete measurements is considered this class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation since the network introduces variations in the sampling time the observer must be designed so that it takes them into account here impulsive observers which make instantaneous correction when information is received are investigated moreover we consider time varying observer gains adapting to the varying sampling interval in order to deal with both continuous time and discrete time dynamics a new hybrid model is used to state the problem and establish the convergence of the proposed observer first generic conditions are provided using a hybrid lyapunov function then a restriction of the generic lyapunov function is used to establish tractable conditions that allows the analysis and synthesis of an impulsive gain

observer design for parameter varying differentiable nonlinear systems with application to slip angle estimation this technical note develops observer design techniques in a unified framework for both time invariant and parameter varying lipschitz nonlinear systems that are differentiable w r t state variables first a new sufficient condition for asymptotic convergence is developed for arcak s two dof nonlinear observer for time invariant nonlinear systems in addition to ensuring asymptotic convergence extension of this observer design technique to optimization of a l 2 performance criterion is presented which improves disturbance rejection performance of the observer next augmentation of this technique to parameter varying nonlinear pvnl systems is developed different from methods suggested in the lpv literature a simple but non conservative finite dimensional relaxation method for quadratic parameter dependent lmis is presented these results constitute perhaps the first systematic observer design methodology in literature for pvnl systems finally the performance of the developed observers is evaluated for estimation of slip angle using the commercial vehicle dynamics software carsim unlike previous results which use a lti or a time invariant nonlinear model for observer design this technical note presents a pvnl observer guaranteed to work with continuously varying velocity of the vehicle

design of continuous discrete observers for time varying nonlinear systems we present a new design for continuous discrete observers for a large class of continuous time nonlinear time varying systems with discrete time measurements using the notion of cooperative systems we show that the solutions of the observers converge to the solutions of the original system under conditions on the nonlinear terms and on the largest sampling interval our conditions are given by explicit expressions

filling of a poisson trap by a population of random intermittent searchers we extend the continuum theory of random intermittent search processes to the case of n independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi infinite track each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state we assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process the hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target the particle is removed from the system after delivering its cargo as a further generalization of previous models we assume that up to n successive particles can find the target and deliver its cargo assuming that the rate of target detection scales as 1 n we show that there exists a well defined mean field limit n rightarrow infty in which the stochastic model reduces to a deterministic system of linear reaction hyperbolic equations for the concentrations of particles in each of the internal states these equations decouple from the stochastic process associated with filling the target with cargo the latter can be modeled as a poisson process in which the time dependent rate of filling lambda t depends on the concentration of stationary particles within the target domain hence we refer to the target as a poisson trap we analyze the efficiency of filling the poisson trap with n particles in terms of the waiting time density f n t the latter is determined by the integrated poisson rate mu t int 0 t lambda s ds which in turn depends on the solution to the reaction hyperbolic equations we obtain an approximate solution for the particle concentrations by reducing the system of reaction hyperbolic equations to a scalar advection diffusion equation using a quasi steady state analysis we compare our analytical results for the mean field model with monte carlo simulations for finite n we thus determine how the mean first passage time mfpt for filling the target depends on n and n

two families of semiglobal state observers for analytic discrete time systems two families of observers for discrete time nonlinear systems are presented in this paper whose design is based on the taylor approximation of the inverse of the observation map semiglobal convergence results are provided under the assumption that the system observation map is a globally analytic diffeomorphism the performances of the observers in the two families are compared both from theoretical and practical points of view

analysis of reflected diffusions via an exponential time based transformation let x t be a time homogeneous diffusion process with state space 0 infty where 0 is a reflecting or entrance endpoint and let z denote a random variable that describes the process x t evaluated at an exponentially distributed random time we propose a method to obtain closed form expressions for the conditional density and the mean of a new diffusion process y t with the same state space and with the same infinitesimal variance whose drift depends on the infinitesimal moments of x t and on the hazard rate function of z this method also allows us to obtain the laplace transform of the first passage time density of y t through a lower constant boundary we then discuss the relation between y t and the process x t subject to catastrophes as well as the interpretation of y t as a diffusion in a decreasing potential we study in detail some special cases concerning diffusion processes obtained when x t is the wiener ornstein uhlenbeck bessel and rayleigh process

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

clustering properties in turbulent signals we consider the telegraph approximation ta of turbulent signals by ignoring their amplitude variability and retaining only their zero crossing information we establish a unique relationship between the spectral exponent of a signal and that of its ta whenever the signal possesses a gaussian pdf and a spectral shape in which the high frequency cut off is sufficiently sharp the velocity signals in most turbulent flows away from the wall satisfy these conditions adequately so that the kolmogorov spectral exponent of 5 3 for the turbulent velocity spectrum corresponds to a 4 3 spectral exponent for its ta by introducing a new scaling exponent to characterize the tendency of small scale fluctuations to cluster we show that the velocity and passive scalar signals display a finite tendency to cluster even in the limit of re rightarrow infty we advance the notion on the basis of the properties of the ta that turbulent processes belong to one of two classes either the white noise type or the markov lorentzian type

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

a new approach for time variant probability density function of the maximal value of stochastic dynamical systems abstract the extreme value distribution evd of stochastic processes is an important but still challenging problem for the determination of reliability function and distribution of first excursion time in various science and engineering fields in the present paper a new method to evaluate the time variant probability density function pdf of the maximal value of a markov process or markov vector process is proposed in this method a joint maximum state vector process is constructed by combining the maximal value process mvp and its underlying markov process the markov property of the joint maximum state vector process is rigorously proved incorporated with the ito stochastic differential equation sde governing the underlying markov process a numerical method is developed based on the chapman kolmogorov equation in particular the short time transition probability density function of the joint maximum state process in the path integral solution pis is derived the detailed algorithms for the proposed method in two and three dimensional cases respectively are elaborated several examples are illustrated demonstrating the effectiveness of the proposed method problems to be further studied are also discussed

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

universality and correlations in individuals wandering through an online extremist space the out of the blue nature of recent terror attacks and the diversity of apparent motives highlight the importance of understanding the online trajectories that individuals follow prior to developing high levels of extremist support here we show that the physics of stochastic walks with and without temporal correlation provides a unifying description of these online trajectories our unique data set comprising all users of a global social media site reveals universal characteristics in individuals online lifetimes our accompanying theory generates analytical and numerical solutions that describe the characteristics shown by individuals that go on to develop high levels of extremist support and those that do not going forward it is conceivable that a deeper understanding of these temporal and many body correlations may eventually contribute to the important task of better countering the spread of radical propaganda online

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

first passage and first exit times of a bessel like stochastic process we study a stochastic process x t which is a particular case of the rayleigh process and whose square is the bessel process with various applications in physics chemistry biology economics finance and other fields the stochastic differential equation is dx t nd x t dt 2d dw t where w t is the wiener process the drift term can arise from a logarithmic potential or from taking x t as the norm of a multidimensional random walk due to the singularity of the drift term for x t 0 different natures of boundary at the origin arise depending on the real parameter n entrance exit and regular for each of them we calculate analytically and numerically the probability density functions of first passage times or first exit times nontrivial behavior is observed in the case of a regular boundary

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed