non linear observer based on the euler discretization in this paper we present an estimator based on the euler discretization first we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated euler discretized system can be neglected otherwise we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time finally numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator

a robust observer for discrete time nonlinear systems abstract this paper extends the results developed in ciccarella et al 1993 and presents a robust observer for discrete time nonlinear systems a simple robust and easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems combined parameter and state estimation is made for a numerical example which compares the robust observer to the observer given in ciccarella et al 1993

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

a hybrid redesign of newton observers in the absence of an exact discrete time model abstract we study the newton observer design developed by moraal and grizzle when the exact discrete time model of the sampled data plant is not known analytically we eliminate the dependence on this exact model with a hybrid reconstruction that makes use of continuous time filters to produce the numerical value of the exact model we then implement the newton method with finite difference and secant approximations for the jacobian despite the continuous time filters the proposed hybrid redesign preserves the sampled data characteristic of the newton observer because it only employs discrete time measurements of the output it also offers flexibility to be implemented with nonuniform or event driven sampling we finally study how a line search scheme can be incorporated in this hybrid newton observer to enlarge the region of convergence

on construction of sampling patterns for preserving observability controllability of linear sampled data systems in this paper we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of

deadbeat observer construction via sets a geometric generalization of discrete time linear deadbeat observer is presented the proposed method to generate a deadbeat observer for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of observer dynamics are provided for two example systems based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar output is given

observer design for autonomous discrete time nonlinear systems abstract we obtain a necessary and sufficient condition for a discrete time nonlinear system to be locally state equivalent to the nonlinear observer form the result looks similar to the continuous counterpart except for the fact that ad operation is utilized instead of ad operation

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

hammerstein systems identification in presence of hard nonlinearities of preload and dead zone type hammerstein system identification is considered in presence of preload and dead zone nonlinearities the discontinuous feature of these nonlinearities makes it difficult to get a single system parameterization involving linearly all unknown parameters those of the linear subsystem and those of the nonlinearity therefore system identification has generally been dealt with using multiple stage schemes including different parametrizations and several data acquisition experiences however the consistency issue has only been solved under restrictive assumptions regarding the identified system in this paper a new identification scheme is designed and shown to be consistent under mild assumptions

non coercive lyapunov functions for infinite dimensional systems abstract we show that the existence of a non coercive lyapunov function is sufficient for uniform global asymptotic stability ugas of infinite dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied for evolution equations in banach spaces with lipschitz continuous nonlinearities these additional assumptions become especially simple the results encompass some recent results on linear switched systems on banach spaces finally we derive new non coercive converse lyapunov theorems and give some examples showing the necessity of our assumptions

distribution of lattice points visible from the origin let be a region in the plane which contains the origin is star shaped with respect to the origin and has a piecewise c 1 boundary for each integer q 1 we consider the integer lattice points from which are visible from the origin and prove that the 1 st consecutive spacing distribution of the angles formed with the origin exists this is a probability measure supported on an interval m with m 0 its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

the distribution of the free path lengths in the periodic two dimensional lorentz gas in the small scatterer limit we study the free path length and the geometric free path length in the model of the periodic two dimensional lorentz gas sinai billiard we give a complete and rigorous proof for the existence of their distributions in the small scatterer limit and explicitly compute them as a corollary one gets a complete proof for the existence of the constant term c 2 3 ln 2 frac 27 zeta 3 2 pi 2 in the asymptotic formula h t 2 ln epsilon c o 1 of the ks entropy of the billiard map in this model as conjectured by p dahlqvist

power law distributions for the free path length in lorentz gases it is well known that in the boltzmann grad limit the distribution of the free path length in the lorentz gas with disordered scatterer configuration has an exponential density if on the other hand the scatterers are located at the vertices of a euclidean lattice the density has a power law tail proportional to xi 3 in the present paper we construct scatterer configurations whose free path lengths have a distribution with tail xi n 2 for any positive integer n we also discuss the properties of the random flight process that describes the lorentz gas in the boltzmann grad limit the convergence of the distribution of the free path length follows from equidistribution of large spheres in products of certain homogeneous spaces which in turn is a consequence of ratner s measure classification theorem

sampled data observers for 1 d parabolic pdes with non local outputs abstract the present work provides a systematic approach for the design of sampled data observers to a wide class of 1 d parabolic pdes with non local outputs the studied class of parabolic pdes allows the presence of globally lipschitz nonlinear and non local terms in the pde two different sampled data observers are presented one with an inter sample predictor for the unavailable continuous measurement signal and one without an inter sample predictor explicit conditions on the upper diameter of the uncertain sampling schedule for both designs are derived for exponential convergence of the observer error to zero in the absence of measurement noise and modeling errors moreover explicit estimates of the convergence rate can be deduced based on the knowledge of the upper diameter of the sampling schedule when measurement noise and or modeling errors are present input to output stability ios estimates of the observer error hold for both designs with respect to noise and modeling errors the main results are illustrated by two examples which show how the proposed methodology can be extended to other cases e g boundary point measurements

free path lengths in quasicrystals previous studies of kinetic transport in the lorentz gas have been limited to cases where the scatterers are distributed at random e g at the points of a spatial poisson process or at the vertices of a euclidean lattice in the present paper we investigate quasicrystalline scatterer configurations which are non periodic yet strongly correlated a famous example is the vertex set of a penrose tiling our main result proves the existence of a limit distribution for the free path length which answers a question of wennberg the limit distribution is characterised by a certain random variable on the space of higher dimensional lattices and is distinctly different from the exponential distribution observed for random scatterer configurations the key ingredients in the proofs are equidistribution theorems on homogeneous spaces which follow from ratner s measure classification

global exponential observers for two classes of nonlinear systems abstract this paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems i the class of systems with a globally asymptotically stable compact set and ii the class of systems that evolve on an open set in the first class the derived continuous time observer also leads to the construction of a robust global sampled data exponential observer under additional conditions two illustrative examples of applications of the general results are presented one is a system with monotone nonlinearities and the other is a chemostat system

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

robust exponential input to state stability of impulsive systems with an application in micro grids abstract this paper studies the robust exponential input to state stability robust e iss for impulsive systems new notions of input to state exponent is e and e property are proposed based on the established relation between is e and e property and the method of variation of constants formula the equivalent conditions for robust e iss have been derived then the notion of robust event e iss is defined the sufficient conditions and the robust regions for robust e iss and robust event e iss are also derived by using the is e of every subsystem it shows the whole system may have robust event e iss while every subsystem may have no iss it also shows the external disturbances may lead to relatively small robust regions the results are then specialized to derive the equivalent conditions of interval e iss for interval impulsive systems as an application the result is used to test the iss for a controlled micro grid

a cascade observer for a class of mimo non uniformly observable systems with delayed sampled outputs abstract this paper investigates the observation problem for a class of mimo non uniformly observable systems in the presence of sampled and delayed outputs a high gain observer is first designed for the delay free and continuous output measurement case the observer gain involves the resolution of an appropriate lyapunov differential equation allowing to show that the underlying observation error converges exponentially to zero under a well defined persistent excitation condition this observer is then redesigned to cope with the output sampling process as well as the output delay thanks to an appropriate cascade structure composed of a set of dynamical subsystems the first subsystem in the cascade is an impulsive continuous discrete time observer which provides the estimation of the delayed state and each remaining subsystem in the cascade is a predictor which estimates the state over a small horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state the exponential convergence to zero of the observation error related to the cascade observer is established for arbitrarily long delays provided that the maximum value of the sampling partition diameter is lower than a certain given bound simulations results are given to highlight the performance and the main properties of the proposed cascade observer

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

algebraic conditions for state equivalence to a discrete time nonlinear observer canonical form abstract algebraic necessary and sufficient conditions for a single output discrete time system to be state equivalent to a generalized nonlinear observer canonical form with or without output transformation are derived our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry in addition our proofs are constructive and contain the state and output transformations for generalized nonlinear observer canonical forms

state estimation for invariant systems on lie groups with delayed output measurements this paper proposes a state estimation methodology for invariant systems on lie groups where outputs of the system are measured with delay the proposed method is based on cascading an observer and a predictor the observer uses delayed measurements and provides estimates of delayed states the predictor uses those estimates together with the current inputs of the system to compensate for the delay and to provide a prediction of the current state of the system we consider three classes of left invariant right invariant and mixed invariant systems and propose predictors tailored to each class the key contribution of the paper is to exploit the underlying symmetries of systems to design novel predictors that are computationally simple and generic in the sense that they can be combined with any stable observer or filter we provide a rigorous stability analysis demonstrating that the prediction of the current state converges to the current system trajectory if the observer state converges to the delayed system trajectory the good performance of the proposed approach is demonstrated using a sophisticated software in the loop simulator indicating the robustness of the observer predictor methodology even when large measurement delays are present

global existence of solutions of differential inclusions abstract in this paper we consider sufficient conditions for global existence of solutions to a differential inclusion dx dt f t x assuming existence of local solutions to it by means of lyapunov s second method our theorem includes as special cases s w seah s theorems 1982 j math anal appl 89 648 663

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

a framework for nonlinear sampled data observer design via approximate discrete time models and emulation we study observer design for sampled data nonlinear systems using two approaches i the observer is designed via an approximate discrete time model of the plant ii the observer is designed based on the continuous time plant model and then discretized for sampled data implementation emulation we investigate under what conditions and in what sense these designs achieve convergence for the unknown exact discrete time model we present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model

canonical observer forms for multi output systems up to coordinate and output transformations in discrete time in the present paper the problem of equivalence under coordinate changes and output transformations to observer canonical forms is addressed in discrete time for multi output systems necessary and sufficient conditions are given for local equivalence to this form which yields a straightforward observer design with linear error dynamics

state equivalence of discrete time nonlinear control systems to state affine form up to input output injection in this paper the problem of transformation of a discrete time nonlinear control system into a state affine form up to input output injection is addressed a set of coordinate free necessary and sufficient conditions for such a transformation to be possible is first proposed and a more constructive procedure is then presented no restriction of invertibility of the state transition map is required

a characterization of quadratic forms of type e6 e7 and e8 the goal of this article is to show that quadratic forms of type e6 e7 a nde8 are completely characterized by their even clifford algebras or equivalently by their discriminant and witt invariant 2002 elsevier science usa all rights reserved

necessary and sufficient conditions for state equivalence to a nonlinear discrete time observer canonical form in this technical note we obtain necessary and sufficient conditions for a multi input multi output discrete time nonlinear system to be state equivalent to a nonlinear observer form and for an uncontrolled multi output system to be state equivalent to a linear observer form we adopt a geometric approach and the proofs are constructive with respect to the required coordinate change

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

adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs in this paper we propose an adaptive observer for a class of uniformly observable nonlinear systems with nonlinear parametrization and sampled outputs a high gain adaptive observer is first designed under the assumption that the output is continuously measured and its exponential convergence is investigated thanks to a well defined persistent excitation condition then we address the case where the output is available only at non uniformly spaced sampling instants to this end the continuous time output observer is redesigned leading to an impulsive observer with a corrective term involving instantaneous state impulses corresponding to the measured samples and their estimates moreover it is shown that the proposed impulsive observer can be put under the form of a hybrid system composed of a continuous time observer coupled with an inter sample output predictor two design features are worth to be emphasized firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation and parameter estimation errors is established under a well defined condition on the maximum value of the sampling partition diameter more specifically the observer design is firstly carried out in the case of linear parametrization before being extended to the nonlinear one the theoretical results are corroborated through simulation results involving a typical bioreactor

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

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

statistical properties of lorentz gas with periodic configuration of scatterers in our previous paper markov partitions for some classes of dispersed billiards were constructed using these partitions we estimate the decay of velocity auto correlation function and prove the central limit theorem of probability theory and donsker s invariance principle for lorentz gas with periodic configuration of scatterers

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

global exponential sampled data observers for nonlinear systems with delayed measurements abstract this paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements by using a small gain approach we provide sufficient conditions which involve both the delay and the sampling period ensuring exponential convergence of the observer system error the proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule moreover new results on the robust global exponential state predictor design problem are provided for wide classes of nonlinear systems

symbolic models for nonlinear control systems affected by disturbances in the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an aggregate of continuous states in this article we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances the main contribution of this article is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation

high gain observer design with sampled measurements application to inverted pendulum new results on high gain observer design for sampled data systems are presented for a large class of nonlinear uniformly observable systems it is shown that by using an appropriate lyapunov function it is possible to design a continuous high gain observer coupled with a large class of output predictors an explicit bound on the maximum allowable sampling interval guaranteeing stability of the observation error is given this result is illustrated on an experimental setup

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

high gain estimation for nonlinear systems abstract this work is a continuation of 4 where the third author exhibits a high gain exponential observer for miso nonlinear systems affine in the input and observable for any input with continuous dynamics and measurements in this paper we establish stability results for continuous continuous and continuous discrete extended kalman filters derived from the observer of 4

descent of affine buildings i large minimal angles in this two part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups combined with earlier results on classical groups this gives a complete and positive answer to the conjecture concerning the existence of affine buildings arising from such groups defined over a skew field with a complete valuation as proposed by jacques tits this first part lays the foundations for our approach and deals with the large minimal angle case

observers for discrete time nonlinear systems abstract the problem of observers for discrete time nonlinear systems has been considered and a simple easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems some numerical examples show the effectiveness of the proposed observer

a note on the stability of single frequency laser diode models a formal proof of the stability of a widely applicable form of the laser diode rate equations is presented the conditions under which this proof holds provide guidance to designers and modellers of laser diodes in the identification of ranges of parameter values that preserve stability the proof requires that there is some non zero threshold for gain in order to guarantee stability laser models incorporating purcell enhancement factors are found to be stable for all physically allowed values of the factor

observer design in convergent series for a class of nonlinear systems this paper deals with convergence analysis for power series solutions to a partial differential equation for nonlinear observer design with linear observer error dynamics this power series solution is used to design the gain matrix for a luenberger like observer for nonlinear systems an explicit domain of convergence around the origin is identified which is related to the relative sizes of high order terms in the original nonlinear system with respect to the linearized model the convergent conditions can provide a guideline for nonlinear observer design with a truncated series for the observer gain

exponential stability analysis of sampled data ode pde systems and application to observer design a small gain approach is presented for analyzing exponential stability of a class of dynamical hybrid systems the systems considered in the paper are composed of finite dimensional dynamics represented by a linear ordinary differential equation ode and infinite dimensional dynamics described by a parabolic partial differential equation pde exponential stability is established under conditions involving the maximum allowable sampling period masp this new stability result is shown to be useful in the design of sampled output exponentially convergent observers for linear systems that are described by an ode pde cascade the new stability result also proves to be useful in designing practical approximate observers involving no pdes

observer design for uniformly observable systems with sampled measurements this work considers the problem of observer design for continuous time systems with sampled output measurements continuous discrete time systems in classical literature and in many applications the continuous discrete time extended kalman filter ekf is used in order to tackle this problem in this work using a normal form characterizing the class of nonlinear uniformly observable single output nonlinear systems it is shown that a particular stationary solution of a continuous discrete time lyapunov equation can be used in order to design a constant high gain observer explicit conditions are given to ensure global convergence of the observer finally an illustration of this result is given using an example of a biological process

the distribution of free path lengths in the periodic lorentz gas and related lattice point problems the periodic lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers and is one of the fundamental models for chaotic diffusion in the present paper we investigate the boltzmann grad limit where the radius of each scatterer tends to zero and prove the existence of a limiting distribution for the free path length we also discuss related problems such as the statistical distribution of directions of lattice points that are visible from a fixed position

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

sampled data adaptive observer for a class of state affine output injection nonlinear systems the problem of observer design is addressed for output injection nonlinear systems a major difficulty with this class of systems is that the state equation involves an output dependent term that is explicitly dependent on unknown parameters as the output is only accessible to measurement at sampling times the output dependent term turns out to be almost all time subject to a double uncertainty making previous adaptive observers inappropriate presently a new hybrid adaptive observer is designed and shown to be exponentially convergent under ad hoc conditions

sampled data chain observer design for a class of delayed nonlinear systems the problem of observer design is addressed for a class of triangular nonlinear systems with not necessarily small delay and sampled output measurements one more difficulty is that the system stat

parameter and state estimation of experimental chaotic systems using synchronization we examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems we focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic colpitts oscillator as an example system we explore the impact of model imperfection on the ability to extract valid information from an experimental system we compare two optimization methods an initial value method and a constrained method each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold we explore both time dependent and time independent coupling and discuss the use of periodic impulse coupling we also examine both optimized and fixed or manually adjusted coupling for the case of an optimized time dependent coupling function u t we find a robust structure which includes sharp peaks and intervals where it is zero this structure shows a strong correlation with the location in phase space and appears to depend on noise imperfections of the model and the lyapunov direction vectors for time independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength comparison of this result with that obtained using simulated data may provide one measure of model imperfection the constrained method with time dependent coupling appears to have benefits in synchronizing long data sets with minimal impact while the initial value method with time independent coupling tends to be substantially faster more flexible and easier to use we also describe a method of coupling which is useful for sparse experimental data sets our use of the colpitts oscillator allows us to explore in detail the case of a system with one positive lyapunov exponent the methods we explored are easily extended to driven systems such as neurons with time dependent injected current they are expected to be of value in nonchaotic systems as well software is available on request

discrete time nonlinear observer design using functional equations abstract the present research work proposes a new approach to the discrete time nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer the proposed approach develops a nonlinear analogue the formulation of the discrete time nonlinear observer design problem is realized via a system of first order linear nonhomogeneous functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

a heuristic kalman filter for a class of nonlinear systems one of the basic assumptions involved in the optimality of the kalman filter theory is that the system under consideration must be linear if the model is nonlinear a linearization procedure is usually performed in deriving the filtering equations this approach requires the nonlinear system dynamics to be differentiable this note is an attempt to develop a heuristic kalman filter for a class of nonlinear systems with bounded first order growth that does not require the system dynamics to be differentiable the proposed filter approximates the nonlinear state function by its state argument multiplied by a particular gain matrix only in the recursion of the estimation error covariance matrix under certain conditions the error covariance remains bounded by bounds which can be precomputed from noise and system models and the upper bound tends to zero when the state noise covariance tends to zero a numerical example with backlash nonlinearity is also added

on the observer problem for discrete time control systems this paper studies the construction of observers for nonlinear time varying discrete time systems in a general context where a certain function of the states must be estimated appropriate notions of robust complete observability are proposed under which a constructive proof of existence of an observer is developed moreover a transitive observer property is proven according to which a state observer can be generated as the series connection of two observers the analysis and the results are developed in general normed linear spaces to cover both finite dimensional and infinite dimensional systems

on the observer design in discrete time abstract the paper deals with the equivalence under coordinates change and output transformation of a discrete time nonlinear system to observer canonical forms necessary and sufficient conditions for local equivalence to these forms are given

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

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

the statistics of the trajectory of a certain billiard in a flat two torus we consider a billiard in the punctured torus obtained by removing a small disk of radius 0 from the flat torus 2 with trajectory starting from the center of the puncture in this case the phase space is given by the range of the velocity only let and respectively r denote the first exit time length of the trajectory and respectively the number of collisions with the side cushions when 2 is being identified with 0 1 2 we prove that the probability measures on 0 associated with the random variables and r are weakly convergent as varepsilon rightarrow 0 and explicitly compute the densities of the limits

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

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

a reduced order observer for non linear discrete time systems abstract in this note a simple and useful reduced order observer for a large class of non linear discrete time systems is presented neither detectability of the linear part nor resolution of the sylvester constraint is required from the stability analysis we show that the proposed state observer has strong tracking properties under very general conditions and generalizes results in m boutayeb et al ieee trans automat control 42 4 1997 581 586 high performances from the design and implementation point of view will be shown through three numerical examples of physical processes largely used in industrial applications

non uniform in time robust global asymptotic output stability abstract the notions of non uniform in time robust global asymptotic output stability and robust forward completeness for time varying systems are introduced necessary and sufficient conditions and lyapunov like characterizations are given for these notions

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

on the distribution of free path lengths for the periodic lorentz gas consider the domain and let the free path length be defined as the distribution of values of is studied in the limit as for all it is shown that the value is critical for this problem in other words the limiting behavior of depends only on whether is larger or smaller than

a neural state estimator with bounded errors for nonlinear systems a neural state estimator is described acting on discrete time nonlinear systems with noisy measurement channels a sliding window quadratic estimation cost function is considered and the measurement noise is assumed to be additive no probabilistic assumptions are made on the measurement noise nor on the initial state novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators to ensure the convergence properties of the neural estimator a minimax tuning technique is used the approximate estimator can be designed offline in such a way as to enable it to process on line any possible measure pattern almost instantly

a dual pair of optimization based formulations for estimation and control a finite horizon optimal estimation problem for discrete time linear systems is formulated and solved the formulation is a natural extension of that which yields a deadbeat observer the resultant observer is the dual of the controller produced by the finite horizon minimum energy control problem with terminal equality constraint nonlinear extensions of this dual pair are also considered and sufficient conditions are provided for stability and convergence

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

from continuous time design to sampled data design of observers in this work a sampled data nonlinear observer is designed using a continuous time design coupled with an inter sample output predictor the proposed sampled data observer is a hybrid system it is shown that under certain conditions the robustness properties of the continuous time design are inherited by the sampled data design as long as the sampling period is not too large the approach is applied to linear systems and to triangular globally lipschitz systems

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

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