linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

multiple augmentations of nonlinear systems and generalized minimum rank perturbations for damage detection a generalized minimum rank perturbation theory for identifying damage location and extent in nonlinear systems using a model based approach is presented this model updating method is able to handle changes in the mass damping and stiffness parameters arising from the damage the method uses a nonlinear discrete model of the system and the functional form of the nonlinearities to create an augmented linear model of the system a modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage the methodology has been demonstrated for cubic spring nonlinearities in this work the class of nonlinearities is expanded to include coulomb friction several new algorithms are presented including an iterative generalized minimum rank perturbation theory and a technique based on multiple augmentations to determine damages in linear and nonlinear parameters when there is an incomplete set of eigenvectors finally two eigenvector filtering algorithms which reduce the effects of measurement noise are presented

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

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

the false discovery rate for multiple testing in factorial experiments identifying the important factors and effects is an important goal in the analysis of two level fractional factorial experiments in moderate and large experiments the large number of potential effects presents problems of multiple statistical inference in this work we apply the false discovery rate fdr idea in multiple inference to effect identification in factorial experiments the fdr is the expected proportion of inert effects among those declared active which we believe is a more relevant quantity to control than the probability of a single erroneous declaration the criterion that has been adopted in previous studies we show how to combine the control of fdr with popular methods for estimating contrast standard error in unreplicated experiments we present simulations of unreplicated 16 and 32 run experiments that illustrate the improvements in power that can be obtained by controlling the fdr we also analyze data from an actual 128 run experiment with replication in which the fdr identifie

moving horizon state estimation for nonlinear systems using neural networks moving horizon mh state estimation is addressed for nonlinear discrete time systems affected by bounded noises acting on system and measurement equations by minimizing a sliding window least squares cost function such a problem is solved by searching for suboptimal solutions for which a certain error is allowed in the minimization of the cost function nonlinear parameterized approximating functions such as feedforward neural networks are employed for the purpose of design thanks to the offline optimization of the parameters the resulting mh estimation scheme requires a reduced online computational effort simulation results are presented to show the effectiveness of the proposed approach in comparison with other estimation techniques

a direct method for the construction of nonlinear discrete time observer with linearizable error dynamics we provide a direct method for the design of nonlinear discrete time observers by a construction of a change of variables an explicit expression of the change of variables is given some simulations for chaotic systems such as lozi system and he spl acute non system are provided to illustrate the proposed method

nonlinear discrete time observer design with linearizable error dynamics a necessary and sufficient condition for the existence of a discrete time nonlinear observer with linearizable error dynamics is provided the result can be applied to any real analytic nonlinear system whose linear part is observable the necessary and sufficient condition is the solvability of a nonlinear functional equation furthermore the well known siegel s theorem on the linearizability of a mapping is naturally reproduced in a corollary the proposed observer design method is constructive and can be applied approximately to any sufficiently smooth linearly observable system yielding a local observer with approximately linear error dynamics

a new methodology for observer design and implementation observers are usually formulated as explicit systems of differential equations and implemented using standard ode solvers in this paper we show that there can be advantages in formulating the observer as a differential algebraic equation dae we propose a canonical dae observer and show that it can be implemented using standard dae solvers the dae implementation of the observer can be considered regardless of the design philosophy used we present a simple design strategy for this canonical dae observer based on the extended linearization method

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

an approach to parametric nonlinear least square optimization and application to task level learning control this paper considers a parametric nonlinear least square nls optimization problem unlike a classical nls problem statement we assume that a nonlinear optimized system depends on two arguments an input vector and a parameter vector the input vector can be modified to optimize the system while the parameter vector changes from one optimization iteration to another and is not controlled the optimization process goal is to find a dependence of the optimal input vector on the parameter vector where the optimal input vector minimizes a quadratic performance index the paper proposes an extension of the levenberg marquardt algorithm for a numerical solution of the formulated problem the proposed algorithm approximates the nonlinear system in a vicinity of the optimum by expanding it into a series of parameter vector functions affine in the input vector in particular a radial basis function network expansion is considered the convergence proof for the algorithm is presented the proposed approach is applied to task level learning control of a two link flexible arm each evaluation of the system in the optimization process means completing a controlled motion of the arm

moving horizon numerical observers of nonlinear control systems in this note we develop moving horizon numerical observers and analyze the error in the error estimation we take into consideration both the integration error and the optimization error the design facilitates the use of a variety of numerical algorithms to form different observers as a special case an euler newton observer is introduced the numerical observer is independent of any optimization software or toolbox furthermore the observer is formulated in a way that is especially efficient for systems with sampled measurement

nonlinear small gain theorems for discrete time feedback systems and applications we derive in this work a local nonlinear small gain theorem in the framework of input to state stability for discrete time systems our primary objective is to show that as in the continuous time context these discrete time nonlinear small gain theorems are very effective in stability analysis and synthesis for various classes of discrete time control systems two converse lyapunov theorems for discrete exponential stability are developed to assist these applications new results in stability and stabilization presented in this paper are significant extensions of previous work by other authors ieee trans automat control 38 1993 1398 39 1994 2340 33 1988 1082

observation for markov jump piecewise affine systems with admissible region switching paths the technical note investigates the problem of state observation for discrete time markov jump piecewise affine pwa systems which cover both markov jump systems and traditional pwa systems as two special classes a new method for determining the admissible region switching paths between adjacent time instants is proposed for both the plant state and the estimator state so that both the computation cost and the conservatism of the theoretical results are reduced to analyze the mean square stability of the observation error system a novel piecewise lyapunov function is constructed which depends on the current mode and the region indices of both the system and observer states as the partitions of the state space are different for different modes the region indices are dependent on the system mode then mode dependent pwa observers are designed by means of s procedure and ellipsoidal outer approximation such that the observation error system is mean square stable the proposed observation strategy is demonstrated via an illustrative example

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

input to error stable observer for nonlinear sampled data systems with application to one sided lipschitz systems in this paper the design of sampled data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals we establish general design principles using the standard approaches of i direct discrete time design via approximation and ii discretization of a continuous time observer emulation by interpreting the disturbances as exogenous inputs affecting the error dynamics sufficient conditions are derived which ensure the input to state stability iss of the observer error system in a semiglobal practical sense for the unknown exact discrete time model next we focus on systems whose vector fields are one sided lipschitz to develop constructive design techniques via linear matrix inequalities lmis numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled data estimators

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

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

nonlinear offset free model predictive control this paper addresses offset free reference tracking of asymptotically constant reference signals using model predictive control existing results for linear models are extended to general nonlinear models the core of the proposed method employs a disturbance model and an observer to estimate its state typical disturbance models are shown and the implications of using them are discussed conditions are given for which this setup eliminates the tracking error asymptotically basically we prove that error free output estimation and error free nominal tracking imply offset free model predictive control

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

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

use of observers for the inversion of nonlinear maps abstract in this paper we deal with the problem of the inversion of nonlinear maps the first contribution of the paper is the definition in a formal framework of some problems related to map inversion which are already present in the literature for instance in the robotics area and in observer theory the second and the main contribution consists in the solution of such problems by means of observers for which some structures are proposed for the state estimation of a time varying nonlinear system associated with the given map and reference trajectory

a class of nonlinear filtering problems arising from drifting sensor gains this paper considers a state estimation problem where the nominal system is linear but the sensor has a time varying gain component giving rise to a bilinear output equation this is a general sensor self calibration problem and is of particular interest in the problem of estimating wafer thickness and etch rate during semiconductor manufacturing using reflectometry we explore the use of a least squares estimate for this nonlinear estimation problem and give several approximate recursive algorithms for practical realization stability results for these algorithms are also given simulation results for comparing the new algorithms with the extended kalman filter and iterated kalman filter are given

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

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

on an application of dynamical systems theory to determine all the zeros of a vector function abstract a continuous time dynamical system is constructed and analyzed in this paper to help locate all the zeros of nonlinear vector functions lyapunov stability technique is used to show that the zeros of the vector function become asymptotically stable equilibria for this dynamical system a strict lyapunov function is constructed to indicate local stability and to estimate the domains of attraction of all equilibria manifolds on which the jacobian of the vector field is singular play a significant role in characterizing the global behavior of the system examples are provided to illustrate the extent of the theory new computational techniques to determine all the zeros of a vector function can be developed based on the dynamical aspects of the theory given in this paper

noise covariance identification for time varying and nonlinear systems abstractkalman based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise however in most practical situations noise statistics and initial conditions are often unknown and need to be estimated from measurement data this paper presents an auto covariance least squares based algorithm for noise and initial state error covariance estimation of large scale linear time varying ltv and nonlinear systems compared to existing auto covariance least squares based algorithms our method does not involve any approximations for ltv systems has fewer parameters to determine and is more memory computationally efficient for large scale systems for nonlinear systems our algorithm uses full information estimation moving horizon estimation instead of the extended kalman filter so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved respectively

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

on the uniform observability of discrete time nonlinear systems in constructing an observer for a discrete time nonlinear system the system is commonly required to satisfy a certain kind of uniform observability condition that is the state should always be reconstructible from observation windows of a specific length irrespective of the values of the state and inputs in this technical note it is proved that this uniform requirement is unnecessary in the sense that if the initial state and inputs are on a compact set then the uniform observability is derived from its non uniform counterpart

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

brief paper circle criterion approach to discrete time nonlinear observer design this paper addresses the design of discrete time nonlinear observers through the circle criterion the new design method is mainly devoted to either globally lipschitz systems or bounded state systems whose nonlinearities can be decomposed into a linear combination of positive slope nonlinearities the observer design is not restricted to systems with positive slope nonlinearities but it encompasses systems with non positive slope nonlinearities too stability conditions of the observation error are given in terms of numerically tractable linear matrix inequalities illustrative examples are presented in order to highlight the main features and advantages of the new proposed technique over some classical designs

on line optimization of switched mode dynamical systems this paper considers an optimization problem in the setting of switched mode hybrid dynamical systems where the control variable independent variable consists of the mode switching times and the performance criterion is a cost functional defined on the system s state trajectory the system is deterministic nonlinear and autonomous and its state variable cannot be measured and hence it has to be estimated we propose an on line newton like optimization algorithm that recomputes the control variable by attempting to optimize the cost to go at equally spaced epochs the main result concerns the algorithm s convergence rate which can vary from sublinear to quadratic depending on its computing rate and the state estimation error

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

analysis of artificial boundary conditions for exterior boundary value problems in three dimensions simple boundary conditions on an artificial boundary are discussed then an exact boundary condition on the artificial boundary is obtained approximation to this boundary condition with high accuracy is given and the error estimates are obtained a numerical example is presented and the numerical results are compared with the exact solution

brief paper an ekf based nonlinear observer with a prescribed degree of stability the topic of this article is a nonlinear observer based on a slight modification of the extended kalman filter the purpose of this modification is twofold first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities using the second method of lyapunov it is proved that the proposed observer is an exponential observer to examine the practical usefulness the proposed observer is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines

adaptive nn control for a class of discrete time non linear systems in this paper adaptive neural network nn control is investigated for a class of single input single output siso discrete time unknown non linear systems with general relative degree in the presence of bounded disturbances firstly the systems are transformed into a causal state space description adaptive state feedback nn control is presented based on lyapunov s stability theory then by converting the systems into a causal input output representation adaptive output feedback nn control is given finally adaptive nn observer design and observer based adaptive control are presented under the assumption of persistent excitation pe all the control schemes avoid the so called controller singularity problem in adaptive control by suitably choosing the design parameters the closed loop systems are proven to be semi globally uniformly ultimately bounded sguub simulation studies show the effectiveness of the newly proposed schemes

observability criteria for impulsive control systems with applications to biomedical engineering processes one of the fundamental properties of the impulsive systems is analyzed observability algebraic criteria for testing this property are obtained for the nonlinear case considering continuous and discrete outputs for this class of systems observability is explored not only through time derivatives of the output but also considering few discrete measurements at different time instants in this context it is shown that nonlinear impulsive control systems can be strongly observable or observable over a finite time interval a new rank condition based on the structure of the impulses is found to characterize observability of linear impulsive systems it generalizes the celebrated kalman criterion for both kind of outputs discrete and continuous finally these results are tested and illustrated both on academic examples and on two impulsive dynamical models from biomedical engineering science

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

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

receding horizon recursive state estimation describes a receding horizon discrete time state observer using the deterministic least squares framework the state estimation horizon which determines the number of past measurement samples used to reconstruct the state vector is introduced as a tuning parameter for the proposed state observer a stability result concerning the choice of the state estimation horizon is established it is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function

discrete time observers for singularly perturbed continuous time systems the use of discrete time observers for nonlinear singularly perturbed continuous time systems is explored the observer design approach is based on inversion of state to measurement maps the two time scale nature of the system is exploited by constructing separate reduced order observers for the approximate slow and fast subsystems using multirate measurements and computation the reduced order observers are compared to a full order observer designed for the same system the comparison shows that although the reduced order observers exhibit some approximation error they also result in reduced computational requirements if the inversion is performed on line reduced memory requirements if the inversion is implemented by look up table and reduced stiffness the trade off between accuracy and implementation requirements always favors the reduced order approach for systems with significant separation of time scales numerical examples are provided including a case study of an observer based control system for permanent magnet synchronous motors

on the number of samples necessary to achieve observability in 1 we have shown that almost all dynamical systems are observable with respect to an almost arbitrary sample program consisting of 2 n 1 samples n is the dimension of the differentiable manifold supporting the dynamical system in this paper we construct a dynamical system which is unobservable with respect to any sample program consisting of 1 n samples small perturbations of the dynamics do not destroy the non observability this shows that the results obtained in 1 are the best ones possible in general

moving horizon observers and observer based control in this paper two topics are explored a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed the moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing or approximately minimizing a cost function over the preceding interval horizon t t t as t advances so does the horizon convergence of the estimator is established under the assumption that the corresponding global optimization problem can be approximately solved and a uniform reconstructability condition is satisfied the latter condition is automatically satisfied for linear observable systems the utility of the estimator for receding horizon control is explored in particular stability of a composite moving horizon system comprising a moving horizon regulator and a moving horizon observer is established

noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation in order to estimate states from a noise driven state space system the state estimator requires a priori knowledge of both process and output noise covariances unfortunately noise statistics are usually unknown and have to be determined from output measurements current expectation maximization em based algorithms for estimating noise covariances for nonlinear systems assume the number of additive process and output noise signals are the same as the number of states and outputs respectively however in some applications the number of additive process noises could be less than the number of states in this paper a more general nonlinear system is considered by allowing the number of process and output noises to be smaller or equal to the number of states and outputs respectively in order to estimate noise covariances a semi definite programming solver is applied since an analytical solution is no longer easy to obtain the expectation step in current em algorithms rely on state estimates from the extended kalman filter ekf or smoother however the instability and divergence problems of the ekf could cause the em algorithm to converge to a local optimum that is far away from true values we use moving horizon estimation instead of the ekf smoother so that the accuracy of the covariance estimation in nonlinear systems can be significantly improved

nonlinear approximate observers for feedback control a class of approximate nonlinear observers is presented and when used to implement stabilizing state feedback control laws shown to yield asymptotically stable output feedback regulation

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

optimal control of nonlinear systems to given orbits abstract using optimal control techniques we derive and demonstrate the use of an explicit single step control method for directing a nonlinear system to a target orbit and keeping it there we require that control values remain near the uncontrolled settings the full nonlinearity of the problem in state space variables is retained the one step of the control is typically a composition of known or learned maps over a the time required to learn the state b the time to compute the control and c the time to apply the control no special targeting is required yet the time to control is quite rapid working with the dynamics of a well studied nonlinear electrical circuit we show how this method works efficiently and accurately in two situations when the known circuit equations are used and when control is performed only on a poincare section of the reconstructed phase space in each case because the control rule is known analytically the control strategy is computationally efficient while retaining high accuracy the target locations on the selected target trajectory at each control stage are determined dynamically by the initial conditions and the system dynamics and the target trajectory is an approximation to an unstable periodic orbit of the uncontrolled system a linear stability analysis shows that dissipation in the dynamical system is essential for reaching a controllable state

brief paper a discrete time observer design for spacecraft attitude determination using an orthogonality preserving algorithm this paper studies a nonlinear discrete time partial state observer design problem for rigid spacecraft systems particularly for spacecraft attitude estimation the construction is inspired by an orthogonality preserving numerical algorithm and it yields a semiglobal practical asymptotic observer we show that the separation principle holds and hence stabilization using output feedback is possible an example is provided to illustrate the usefulness of our results in a sampled data implementation of an attitude control for a rigid spacecraft using output feedback and to illustrate the advantages of the proposed observer design especially compared to a sample and hold version of a similar type observer designed in continuous time

a direct algebraic approach to observer design under switching measurement equations based on the algebraic transformation of a switched linear measurement equation into a nonlinear yet deterministic equation an asymptotic state observer is constructed for discrete time linear systems whose observations are generated according to randomly switching measurement modes the observer which combines the algebraic transformation with a newton observer applied to the resulting nonlinear measurement equation is shown to be locally exponentially convergent under arbitrary mode sequences

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 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

a concept of local observability abstract a notion of local observability which is natural in the context of nonlinear input output regulation is introduced a simple characterization is provided a comparison is made with other local nonlinear observability definitions and its behavior under constant rate sampling is analyzed

robust receding horizon state estimation for uncertain discrete time linear systems an approach to robust receding horizon state estimation for discrete time linear systems is presented estimates of the state variables can be obtained by minimizing a worst case quadratic cost function according to a sliding window strategy this leads to state the estimation problem in the form of a regularized least squares one with uncertain data the optimal solution involving on line scalar minimization together with a suitable closed form approximation are given the stability properties of the estimation error for both the optimal filter and the approximate one have been studied and conditions to select the design parameters are proposed simulation results are reported to show the effectiveness of the proposed approach

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

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

approximate set valued observers for nonlinear systems a set valued observer svo produces a set of possible states based on output measurements and a priori models of exogenous disturbances and noises previous work considered linear time varying systems and unknown but bounded exogenous signals in this case the sets of possible state vectors take the form of polytopes whose centers are optimal state estimates these polytopic sets can be computed by solving several small linear programs an svo can be constructed conceptually for nonlinear systems however the set of possible state vectors no longer takes the form of polytopes which in turn inhibits their explicit computation this paper considers an extended svo as in the extended kalman filter the state equations are linearized about the state estimate and a linear svo is designed along the linearization trajectory under appropriate observability assumptions it is shown that the extended svo provides an exponentially convergent state estimate in the case of sufficiently small initial condition uncertainty and provides a nondivergent state estimate in the case of sufficiently small exogenous signals

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

moving horizon observer with regularisation for detectable systems without persistence of excitation a constrained moving horizon observer is developed for nonlinear discrete time systems the algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times however in many practical estimation problems such as combined state and parameter estimation the data may not be exciting for every period of time the algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting this includes the use of a priori estimates in the moving horizon cost function and the use of thresholded singular value decomposition to avoid ill conditioned or ill posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function the latter regularisation relies on monitoring of the rank of an estimate of a hessian like matrix and conditions for uniform exponential convergence are given the method is in particular useful with augmented state sp

comparative study of non linear state observation techniques abstract this paper contains a comparative study of four techniques for observing the slates of non linear systems the first technique examined is inspired by bestle and zeitz and icrener and respondek in this method a non linear transformation is found that brings the system into a canonical form from where observer design is facilitated the second technique is attributable to thau in this method the error between the system s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid the third technique is due to baumann and rugh in this method extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant finally techniques from variable structure systems are utilized to design an observer that yields an exponentially decaying error like thau s observer but unl

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

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

on nonlinear observers in this note we make some remarks about the general observer problem for nonlinear systems we show how the existence of a partial observer without stability requirements is locally equivalent to the existence of a conditioned invariant distribution we argue that by considering not only identity observers we can put the stability issue in a broader perspective

further results on the uniform observability of discrete time nonlinear systems in this technical note the relation between notions of uniform observability of discrete time nonlinear systems based on injectivity of an observation map window the full rankness of its jacobian and a k function is investigated it is proven that a system is uniformly observable in the sense of injectivity of the observation map together with the full rankness of its jacobian if and only if it is so in some k function senses

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

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

nonlinear observers for autonomous lipschitz continuous systems this paper considers the state observation problem for autonomous nonlinear systems an observation mapping is introduced which is defined by applying a linear integral operator rather than a differential operator to the output of the system it is shown that this observation mapping is well suited to capture the observability nature of smooth as well as nonsmooth systems and to construct observers of a remarkably simple structure a linear state variable filter followed by a nonlinearity the observer is established by showing that observability and finite complexity of the system are sufficient conditions for the observer to exist and by giving an explicit expression for its nonlinearity it is demonstrated that the existence conditions are satisfied and hence our results include a new observer which is not high gain for the wide class of smooth systems it is shown that the observer can as well be designed to realize an arbitrary finite accuracy rather than ultimate exactness on a compact region of the state space this requires only observability of the system a corresponding numerical design procedure is described which is easy to implement and computationally feasible for low order systems

generic observability of differentiable systems a dynamical system consists of a smooth vectorfield defined on a differentiable manifold and a smooth mapping from the manifold to the real numbers the vectorfield represents the dynamics of a physical system the mapping stands for a measuring device by which experimental information on the dynamics is made available the information itself is modeled as a sampled version of the image of the state trajectory under the smooth mapping in this paper the observability of this set up is discussed from the viewpoint of genericity first the observability property is expressed in terms of transversality conditions then the theory of transversal intersection is called upon to yield the desired results it is shown that almost any measuring device will combine with a given physical system to form an observable dynamical system if 2n 1 samples are taken and not fewer where n is the dimension of the manifold dually it is shown that almost any physical system will combine with a given measuring device

observer based control of discrete time lipschitzian non linear systems application to one link flexible joint robot the problem of designing asymptotic observers along with observer based feedbacks for a class of discrete time non linear systems is considered we assume that the system non linearity is globally lipschitz and the system is supposed to be stabilizable by a linear controller sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states a numerical example of a single link flexible joint robot is presented to illustrate the efficacy of the theoretical developments

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

technical communique continuous discrete adaptive observers for state affine systems the observation of a class of multi input multi output mimo state affine systems with constant unknown parameters and discrete time output measurements is addressed assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses system observability is ensured and a class of global exponential observers is synthesized

linear moving horizon estimation with pre estimating observer in this note a moving horizon estimation mhe strategy for detectable linear systems is proposed like the idea of pre stabilizing model predictive control the states are estimated by a forward simulation with a pre estimating observer in the mhe formulation compared with standard linear mhe approaches it has more degrees of freedom to optimize the noise filtering tuning parameters are chosen to minimize the effects of measurement noise and model errors which is implemented by finding tightest estimation error bounds the performance of the proposed observer is demonstrated on one linear discrete time example