continuous discrete time observers for a class of mimo nonlinear systems this technical note addresses the observer design problem for a class of continuous time dynamical systems with non uniformly sampled measurements more specifically we propose an observer that runs in continuous time with an output error correction term that is updated in a mixed continuous discrete fashion the proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates nevertheless we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous time high gain observer coupled with an inter sample output predictor two design features of the proposed observer are worth emphasizing firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer

robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

finite time trajectory tracking control in a task space of robotic manipulators this work addresses the problem of the accurate task space control subject to finite time convergence dynamic equations of a rigid robotic manipulator are assumed to be uncertain moreover globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end effector based on suitably defined task space non singular terminal sliding vector variable and the lyapunov stability theory we derive a class of absolutely continuous jacobian transpose robust controllers which seem to be effective in counteracting uncertain dynamics unbounded disturbances and possible kinematic and or algorithmic singularities met on the end effector trajectory the numerical simulations carried out for a robotic manipulator of a scara type consisting of two revolute kinematic pairs and operating in a two dimensional task space illustrate performance of the proposed controllers

global output feedback stabilisation of a class of stochastic systems with unknown growth rate this paper is concerned with the global output feedback stabilisation problem for a class of stochastic systems with unknown growth rate the output of the system under consideration contains unkno

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

non uniform hyperbolicity and universal bounds for s unimodal maps an s unimodal map f is said to satisfy the collet eckmann condition if the lower lyapunov exponent at the critical value is positive if the infimum of the lyapunov exponent over all periodic points is positive then f is said to have a uniform hyperbolic structure we prove that an s unimodal map satisfies the collet eckmann condition if and only if it has a uniform hyperbolic structure the equivalence of several non uniform hyperbolicity conditions follows one consequence is that some renormalization of an s unimodal map has an absolutely continuous invariant probability measure with exponential decay of correlations if and only if the collet eckmann condition is satisfied the proof uses new universal bounds that hold for any s unimodal map without periodic attractors

finite time and fixed time observer design implicit lyapunov function approach abstract this work deals with the problem of finite time and fixed time observation of linear multiple input multiple output mimo control systems the proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed defined a priori time algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out the theoretical results are illustrated by numerical examples that consider both noisy and noise free measurements and a comparison with a high gain observer is included

a monte carlo analysis of terminally attached self avoiding polymer sequences in the vicinity of a rigid boundary a monte carlo analysis of terminally attached hard sphere sequences of n or 24 segments in the vicinity of a rigid plane is presented the principal configurational properties of the system are determined in particular the segment density distribution rho z mod n normal to the boundary the mean square end to end length r1n2 the mean square radius of gyration sn2 and the mean thickness of the adsorbed layer z1n comparisons with a previously presented iterative convolution analysis are made and the existence of a density discontinuity in rho z mod n is confirmed exponent representation of the data suggest r1n2 approximately n 1 gamma with gamma approximately 1 2 consistent with lattice based analyses the boundary configurations are resolved into loop train and tail components and their dependence upon chain length determined good agreement with the convolution analysis is found the results being consistent with earlier analyses by roe 1965 and chan et al 1975 and the experimental investigations of cosgrove et al 1983

robust design of nonlinear internal models without adaptation we propose a solution to the problem of semiglobal output regulation for nonlinear minimum phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals rather the proposed approach relies upon regression like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude phase and frequency the design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input if this is not the case a bounded steady state regulation error is ensured whose amplitude though can be arbitrarily decreased by acting on a design parameter of the regulator

ekf like observer with stability for a class of nonlinear systems an extended kalman filter ekf like observer is derived from a former observer result for a class of nonlinear systems which can be written as a linear part in the unmeasured states on the one hand and some additive nonlinearity with a triangular jacobian on the other hand it is shown how the previously presented excitation condition for exponential stability of the observer extends to this ekf version the observer is illustrated in simulation with two challenging examples the first one in leak detection and the second one in chaos synchronization

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

the observer follower filter a new approach to nonlinear suboptimal filtering this paper investigates the state estimation problem for a class of stochastic nonlinear differential systems a novel algorithm is proposed denoted as observer follower filter off based on a two steps mixed approach the first step makes use of a high gain observer based estimator for nonlinear systems applied to the system equations in order to provide the trajectory around which a n degree carleman approximation of the stochastic differential system is achieved second step in principle any other high gain estimator can be used but in this note we prove that the one here proposed provides a bounded mean square error numerical simulations show the effectiveness of the proposed methodology and the improvements of the off with respect to the standard extended kalman bucy filter ekbf obtained by increasing the order of the carleman approximation

brief paper an adaptive high gain observer for nonlinear systems in this paper the authors provide a solution to the noise sensitivity of high gain observers the resulting nonlinear observer possesses simultaneously 1 extended kalman filter s good noise filtering properties and 2 the reactivity of the high gain extended kalman filter with respect to large perturbations the authors introduce innovation as the quantity that drives the gain adaptation they prove a general convergence result propose guidelines to practical implementation and show simulation results for an example

time varying increasing gain observers for nonlinear systems a full order state observer for a class of nonlinear continuous time systems is presented as generalization of the high gain observer for having a time varying gain that is let to be small in the first time instants increases over time up to its maximum and then is kept constant the global stability of the resulting estimation error is proved by means of a lyapunov functional via a change of coordinate the design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time varying gain

optimal differentiation based on stochastic signal models the problem of estimating the time derivative of a signal from sampled measurements is addressed the measurements may be corrupted by colored noise a key idea is to use stochastic models of the signal to be differentiated and of the measurement noise two approaches are suggested the first is based on a continuous time stochastic process as a model of the signal the second uses a discrete time arma model of the signal and a discrete time approximation of the derivative operator digital differentiators are presented in a shift operator polynomial form they minimize the mean square estimation error and are calculated from a linear polynomial equation and a polynomial spectral factorization the three obstacles to perfect differentiation namely a finite smoothing lag measurement noise and aliasing effects due to sampling are discussed

on thermodynamics of rational mapsi negative spectrum we study the pressure spectrum p t of the maximal measure for arbitrary rational maps we also consider its modified version which is defined by means of the variational principle with respect to non atomic invariant measures it is shown that for negative values of t the modified spectrum has all major features of the hyperbolic case analyticity the existence of a spectral gap for the corresponding transfer operator rigidity properties etc the spectrum p t can be computed in terms of their legendre transforms are the hausdorff and the box counting dimension spectra of the maximal measure respectively this work is closely related to a paper 32 by d ruelle

increasing gain observers for nonlinear systems for the purpose to estimate the state of nonlinear continuous time systems we focus on the increasing gain observer regarded as generalization of the well known high gain observer as compared with the previous results on increasing gain observers the assumptions under which the global asymptotic stability of the estimation error is proved are relaxed the stability analysis is drawn by using a more general type of lyapunov functional where design parameters can be tuned to set the time varying gain a new design method based on such a lyapunov functional is proposed to construct the observer simulation results affirm the effectiveness of the increasing gain approach as compared with the high gain observer

the active disturbance rejection control to stabilization for multi dimensional wave equation with boundary control matched disturbance in this paper we consider boundary stabilization for a multi dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables the active disturbance rejection control adrc approach is adopted in investigation an extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi dimensional system by infinitely many test functions the disturbance is canceled in the feedback loop together with a collocated stabilizing controller all subsystems in the closed loop are shown to be asymptotically stable in particular the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature the overall picture of the adrc in dealing with the disturbance for multi dimensional partial differential equation is presented through this system the numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction

nice inducing schemes and the thermodynamics of rational maps we study the thermodynamic formalism of a complex rational map f of degree at least two viewed as a dynamical system acting on the riemann sphere more precisely for a real parameter t we study the existence of equilibrium states of f for the potential t rm ln left f prime right and the analytic dependence on t of the corresponding pressure function we give a fairly complete description of the thermodynamic formalism for a large class of rational maps including well known classes of non uniformly hyperbolic rational maps such as topological collet eckmann maps and much beyond in fact our results apply to all non renormalizable polynomials without indifferent periodic points to infinitely renormalizable quadratic polynomials with a priori bounds and all quadratic polynomials with real coefficients as an application for these maps we describe the dimension spectrum for lyapunov exponents and for pointwise dimensions of the measure of maximal entropy and obtain some level 1 large deviations results for polynomials as above we conclude that the integral means spectrum of the basin of attraction of infinity is real analytic at each parameter in mathbb r with at most two exceptions

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

equivalence and topological invariance of conditions for non uniform hyperbolicity in the iteration of rational maps we show equivalence of several standard conditions for non uniform hyperbolicity of complex rational functions including the topological collet eckmann condition tce uniform hyperbolicity on periodic orbits exponential shrinking of components of pre images of small discs backward collet eckmann condition at one point positivity of the infimum of lyapunov exponents of finite invariant measures on the julia set the condition tce is stated in purely topological terms so we conclude that all these conditions are invariant under topological conjugacy for rational maps with one critical point in julia set all the conditions above are equivalent to the usual collet eckmann and backward collet eckmann conditions thus the latter ones are invariant by topological conjugacy in the unicritical setting we also prove that neither part of this stronger statement is valid in the multicritical case

measures with positive lyapunov exponent and conformal measures in rational dynamics ergodic properties of rational maps are studied generalising the work of f ledrappier a new construction allows for simpler proofs of stronger results very general conformal measures are considered equivalent conditions are given for an ergodic invariant probability measure with positive lyapunov exponent to be absolutely continuous with respect to a general conformal measure if they hold we can construct an induced expanding markov map with integrable return time which generates the invariant measure

spectral theory zeta functions and the distribution of periodic points for collet eckmann maps we study unimodal interval mapst with negative schwarzian derivative satisfying the collet eckmann condition dtn tc k cn for some constantsk 0 and c 1 c is the critical point oft we prove exponential mixing properties of the unique invariant probability density oft describe the long term behaviour of typical in the sense of lebesgue measure trajectories by central limit and large deviations theorems for partial sum processes of the form s n sigma i 0 n 1 f t i x and study the distribution of typical periodic orbits also in the sense of a central limit theorem and a large deviations theorem

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

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

on iterations of 1 ax 2 on 1 1 on etudie des iterations de f x a 1 ax u 2 1 x 1 ou a est un parametre dans l intervalle 0 2 on etablit la non existence de cycles attractifs on definit une partition on donne une estimation uniforme de la a derivee

a remark on the problem of semiglobal nonlinear output regulation this paper shows how the method for semiglobal stabilization by output feedback based on high gain observer and saturation and the method for structurally stable regulation based on system immersion can be effectively coupled in order to solve problems of robust output regulation in the presence of parameter uncertainties ranging over compact sets

high gain observers in the presence of measurement noise a switched gain approach this paper considers output feedback control using high gain observers in the presence of measurement noise for a class of nonlinear systems we study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other based on this tradeoff we propose a high gain observer that switches between two gain values this scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error we argue boundedness and ultimate boundedness of the closed loop system under switched gain output feedback

multirate sampled data output feedback control with application to smart material actuated systems we consider multirate sampled data output feedback control of a class of nonlinear systems using high gain observers where the measurement sampling rate is made faster than the control update rate we show that in the presence of bounded disturbances given a sampled data state feedback controller that achieves stabilization with respect to a closed set the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast as an application we consider the control of smart material actuated systems this scheme combines a discrete time high gain observer with a hysteresis inversion controller where the hysteresis is modeled using a preisach operator experimental results for the control of a shape memory alloy actuated rotary joint are provided

a nonlinear high gain observer for systems with measurement noise in a feedback control framework we address the problem of state estimation for a class of nonlinear systems with measurement noise in the context of feedback control it is well known that high gain observers are robust against model uncertainty and disturbances but sensitive to measurement noise when implemented in a feedback loop this work presents the benefits of a nonlinear gain structure in the innovation process of the high gain observer in order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation the goal is to generate a larger observer gain during the transient response than in the steady state response thus by reducing the observer gain after achieving satisfactory state estimates the effect of noise on the steady state performance is reduced moreover the nonlinear gain observer presented in this paper is shown to surpass the system performance achieved when using comparable linear gain observers the proof argues boundedness and ultimate boundedness of the closed loop system under the proposed output feedback

an iterative convolution approach to the statistics of polymer conformation an iterative convolution description of polymer conformation for short to intermediate length self avoiding sequences is reported the intrachain spatial distribution functions and the mean square end to end separation for such systems are in the closest reported agreement with monte carlo estimates with which they are compared the simplicity versatility and quantitative accuracy of the model is emphasised and applications to problems of physical and biophysical interest are indicated the radius of gyration and the expansion of internal subsequences with respect to their end to end counterparts are also determined

a high gain observer with updated gain for a class of mimo non triangular systems a high gain like observer with updated gain is proposed for a class of cascade nonlinear and non triangular systems that are observable for any input the objective of the gain adaptation is to perform an admissible tradeoff between state reconstruction dynamics on the one hand versus noise amplification on the other hand to this end the gain of the proposed observer is tuned through a single scalar time varying parameter governed by an adequate differential riccati equation the involved adaptation process is mainly driven by the power of the output observation error norm computed on a moving horizon window simulation results are given to show the effectiveness of the proposed observer namely its exponential convergence and its insensitivity with respect to noise measurements

convergent fault estimation for linear systems with faults and disturbances the problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note a differential equation based convergence theorem of mean sequence of estimates is proposed which provides an iterative mean estimation technique that has not been fully reported yet in the literature based on the technique a convergent fault estimation strategy for the linear system in consideration is designed and the convergence of mean sequence of fault estimates is proved theoretically an iterative algorithm is given subsequently to compute the fault estimates numerical simulation results demonstrate the effectiveness and merits of the proposed method

observer design based on immersion technics and canonical form abstract a crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system and the analytical expression of the inverse of the immersion is unknown in this paper we have proposed a method for constructing observers for such autonomous nonlinear systems

a new varying gain exponent based differentiator observer an efficient balance between linear and sliding mode algorithms it is well known that the supertwisting algorithm is robust to matched perturbation but is sensitive to measurement noise contrary to this the classical linear algorithm is less sensitive to measurement noise but less robust to perturbation to combine both the good accuracy of the supertwisting algorithm with respect to perturbation and the good performance of the linear algorithm with respect to measurement noise this article proposes a new differentiator observer with a varying exponent gain alpha whose variation depends on the magnitude of measurement noise high frequency signal when the magnitude of measurement noise increases respectively decreases alpha tends to 1 respectively tends to 0 5 and the proposed differentiator observer behaves as a linear algorithm respectively as a supertwisting algorithm thus by one parameter alpha the differentiator observer can take care of high frequency noise and matched perturbations a complete stability analysis of the proposed differentiator observer is provided to highlight the applicability of the proposed methodology the dedicated differentiator observer is respectively validated on the electropneumatic actuator and electric machine test benches these experimental results are compared to those of linear and supertwisting algorithms

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

distributed moving horizon state estimation of two time scale nonlinear systems abstract in this paper we focus on distributed moving horizon estimation dmhe for a class of two time scale nonlinear systems described in the framework of singularly perturbed systems by taking advantage of the time scale separation property a two time scale system is first decomposed into a reduced order fast system and a reduced order slow system the slow system is further decomposed into several interconnected slow subsystems in the proposed distributed state estimation scheme a local estimator is designed for each slow subsystem and for the reduced order fast system the slow subsystem estimators communicate with each other to exchange information and they are only required to send information to the fast system one directionally the fast system estimator does not send out any information the local estimators are designed as observer enhanced moving horizon estimators sufficient conditions on the convergence of the estimation error of the dmhe are derived the application of the proposed dmhe to a chemical process example demonstrates its applicability and effectiveness

error bounds in differentiation of noisy signals by high gain observers the error in estimating the derivative s of a noisy signal by using a high gain observer is studied and quantified the error is bounded in terms of the infinity norms of the noise and a derivative of the signal the error bound is independent of the frequency or derivatives of the noise guidelines are presented for the observer gain design when it is used for on line differentiation analytical and simulation results are presented

statistical properties of unimodal maps the quadratic family we prove that almost every nonregular real quadratic map is colleteckmann and has polynomial recurrence of the critical orbit proving a conjecture by sinai it follows that typical quadratic maps have excellent ergodic properties as exponential decay of correlations keller and nowicki young and stochastic stability in the strong sense baladi and viana this is an important step in achieving the same results for more general families of unimodal maps

dynamic observers as asymptotic limits of recursive filters special cases a method for constructing observers for dynamical systems as asymptotic limits of filters is described the program is carried out in detail for linear systems and in addition an observer is obtai

low temperature phase transitions in the quadratic family abstract we give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function this implies that several dimension spectra and large deviation rate functions associated to this map are not expected to be real analytic in contrast to the uniformly hyperbolic case the quadratic map we study has a non recurrent critical point so it is non uniformly hyperbolic in a strong sense

renormalisation induced phase transitions for unimodal maps the thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential t log df multiple and indeed infinitely many phase transitions at positive t can occur for some quadratic maps all unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum

convergence acceleration for observers by gain commutation increasing convergence rates of observers and differentiators for a class of nonli near systems in the output canonical form under presence of bounded matched disturbances lipschitz uncertainties and measurement noises is investigated a supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation in the noise free case the presented switched gain observer ensures global uniform time of convergence of the estimation error to the origin in the presence of noise the goals of overshoot reducing for the initial phase acceleration of convergence and improvement of asymptotic precision of estimation are achieved efficiency of the proposed switching gain observer is demonstrated by numerical comparison with a sliding mode and linear high gain observers

on the lyapunov spectrum for rational maps we study the dimension spectrum for lyapunov exponents for rational maps on the riemann sphere

the development of loops trains and tails in a self avoiding terminally attached molecule the configuration of self avoiding polymer molecules terminally attached to a rigid boundary is resolved into loop train and tail components on the basis of a convolution integral analysis the expectation lengths lloop ltrain and ltail and the component fractions are determined as functions of chain length and chain plane interaction in the case of zero chain plane attraction thre is good quantitative agreement with monte carlo estimates although the predicted dependence of lloop upon chain length appears too strong results are also presented for hard sphere sequences as a function of chain plane attraction when it is found that there is a progressive redistribution amongst loop and tail states the train exponent remaining essentially unmodified over the range of interactions investigated exponent representations are proposed and compared with earlier analyses the various component structures are discussed in terms of the interplay of entropic and energetic processes at the boundary

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

on the stability of a differential riccati equation for continuous discrete observers abstractthis article deals with the stability properties of a continuous discrete riccati differential equation the main motivation comes from the theory of kalman filters for continuous time nonlinear systems with sampled measurements where this type of equation often arises stability is to be understood in the following sense under appropriate hypotheses the solution matrix is always symmetric positive definite and bounded from above and below no uniformity is expected from the sampling procedure only an upper bound on the elapsed time between consecutive samples is needed the exposition consists of two parts first the stability properties are proven and second by means of three examples it is shown how the article s main result applies

harmonic measure and polynomial julia sets there is a natural conjecture that the universal bounds for the dimension spectrum of harmonic measure are the same for simply connected and for non simply connected domains in the plane because of the close relation to conformal mapping theory the simply connected case is much better understood and proving the above statement would give new results concerning the properties of harmonic measure in the general case we establish the conjecture in the category of domains bounded by polynomial julia sets the idea is to consider the coefficients of the dynamical zeta function as subharmonic functions on a slice of teichmuller s space of the polynomial and then to apply the maximum principle 1 dimension spectrum of harmonic measure in this paper we discuss some properties of harmonic measure in the complex plane for a domain and a point a let a denote the harmonic measure of evaluated at a the measure a can be defined for instance as the hitting distribution of a brownian motion started at a if e then a e is the probability that a random brownian path first hits the boundary at a point of e much work has been devoted to describing dimensional properties of when the domain is as general as possible in particular jones and wolff 7 proved that no matter what the domain is harmonic measure is concentrated on a borel set of hausdorff dimension at most one in other words dim 1 for all plane domains 1 1 we are interested in finding similar but stronger universal estimates involving the dimension spectrum of 1 1 universal spectrum for every positive we denote f dim z where z is the lower pointwise dimension of z lim inf 0 log b z log b z is a general notation for the disc with center z and radius the universal dimension spectrum is the function sup f 1 2 where the supremum is taken over harmonic measures of all planar domains the first author is supported by n s f grant dms 9970283 the second author is supported by n s f grant dms 9800714

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

discrete time implementation of high gain observers for numerical differentiation high gain observers have been used in non linear control to estimate derivatives of the output in this paper we study discrete time implementation of high gain observers and their use as numerical differentiators in noise free as well as noisy measurements we show that discretization using the bilinear transformation method gives better results than other discretization methods we also show that many of the available numerical differentiators are special cases of the bilinear discrete time equivalents of full order or reduced order high gain observers

observer design for a class of uncertain nonlinear systems with sampled outputs application to the estimation of kinetic rates in bioreactors a continuous discrete time observer is proposed for a class of uncertain nonlinear systems where the output is available only at non uniformly spaced sampling instants the underlying correction term depends on the output observation error and is updated in a mixed continuous discrete fashion the proposed observer is first introduced under a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates two features of the proposed observer are worth to be pointed out the first one consists in the simplicity of its calibration while the second one lies in its comprehensive convergence analysis more specifically it is shown that in the case of noise free sampled outputs the observation error lies in a ball centered at the origin and its radius is proportional to the bounds of the uncertainties and the sampling partition diameter moreover in the free uncertainties case the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter the ability of the proposed observer to perform a suitable estimation of the reactions rates in biochemical reactors is highlighted through a simulation study dealing with an ethanolic fermentation

observer design for uncertain nonlinear systems with unmodeled dynamics this paper is concerned with the observer design problem for a class of multi input multi output nonlinear systems with the unmodeled dynamics unknown parameters and external disturbance a dynamic signal which can dominate the unmodeled dynamics is firstly constructed then two types of observer schemes that is adaptive observer and robust observer are respectively proposed the observation error in the two schemes can be made arbitrarily small by choosing the appropriate design parameters an illustrative example is provided to demonstrate the validity of the proposed design methods

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

chaos butterflies also generate phase transitions we exhibit examples of mixing subshifts of finite type and of continuous potentials such that there are phase transitions but the pressure is always strictly convex more surprisingly we show that the pressure can be analytic on some interval although there exist several equilibrium states

efficiency of the extended kalman filter for nonlinear systems with small noise the problem of nonlinear filtering is studied asymptotically as the noise tends to zero detectability conditions ensuring that the filtering error tends to zero are derived and under these conditions it is proved that the extended kalman filter provides a good suboptimal filter the smoothing problem is also studied the proofs use some estimates for the linearization of stochastic systems some changes of probability and stochastic differentiation techniques