sliding mode state observation for non linear systems in this paper a class of non linear systems with uncertainty and a lipschitz part is considered the non linear part satisfies the lipschitz condition whilst the uncertain part is a bounded function a sliding mode observer is designed to yield feedforward compensation input to stabilize the error estimation system with and without a lipschitz non linearity sufficient conditions for stability of the thau observer are also proposed these conditions ensure the stability of the non linear observer by selecting a suitable observer gain matrix in general when the system contains unmatched uncertainty ultimate boundedness is obtained the ultimate boundedness radius depends upon the defined distance of the unmatched uncertainty some sufficient conditions may ensure the stability of a non linear observer for systems with uncertainties

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade in observer based fault reconstruction one of the necessary conditions is that the first markov parameter from the fault to the output must be full rank this paper seeks to relax that requirement by using multiple sliding mode observers in cascade signals from an observer are used as the output of a fictitious system whose input is the fault another observer is then designed and implemented for the fictitious system this process is repeated until the first markov parameter of the fictitious system with respect to the fault is full rank the result is that robust fault reconstruction can be carried out for a wider class of systems compared to other works that also seek to relax the requirement of a full rank first markov parameter in addition this paper has also investigated and presented the necessary and sufficient conditions as easily testable conditions and also the precise number of observers required a simulation example verifies the effectiveness of the scheme

stability and observer design for lur e systems with multivalued nonmonotone time varying nonlinearities and state jumps this paper deals with the stability and observer design for lur e systems with multivalued nonlinearities which are not necessarily monotone or time invariant such differential inclusions model the motion of state trajectories which are constrained to evolve inside time varying nonconvex sets using lyapunov based analysis sufficient conditions are proposed for local stability in such systems while specifying the basin of attraction if the sets governing the motion of state trajectories are moving with bounded variation then the resulting state trajectories are also of bounded variation and unlike the convex case the stability conditions depend on the size of jumps allowed in the sets based on the stability analysis a luenberger like observer is proposed which is shown to converge asymptotically to the actual state provided the initial value of the state estimation error is small enough in addition a practically convergent state estimator based on the high gain approach is designed to reduc

observers for lipschitz non linear systems in an interesting paper r rajamani and y m cho have proposed a systematic methodology to design observers they have introduced a new problem relation between distance to unobservability and convergence of luenberger like observers a result for the convergence of the observer has also been given they have presented a quantity denoted by i claimed as the distance to unobservability we show that this number is not actually the distance from the system to the set of unobservable systems moreover the result for the observer is incorrect we provide a counterexample for the result of convergence in this paper results for convergence are obtained with additional strengthened hypothesis to correct rajamani and cho s result the results are used to design an observer for a now classical single link flexible robot joint the behaviour of the observer to noisy output is quite satisfactory

further convergence results on the general iteratively regularized gauss newton methods under the discrepancy principle we consider the general iteratively regularized gauss newton methods xk 1 x0 g k f xk f xk f xk f xk y f xk xk x0 for solving nonlinear inverse problems f x y using the only available noise y of y satisfying y y with a given small noise level 0 in order to produce reasonable approximation to the sought solution we terminate the iteration by the discrepancy principle under much weaker conditions we derive some further convergence results which improve the existing ones and thus expand the applied range

on uniform observation of nonuniformly observable systems abstract in 4 7 9 12 classes of nonlinear systems are considered for which observers can be designed although observability of nonlinear systems is known to be dependent on the input the proposed observers have the property that the estimation error decays to zero irrespective of the input in the first part of this paper it is shown that this phenomenon follows from a common property of these systems for all of them the unobservable states with respect to some input are in some sense stable in the linear case these systems are called detectable and for this reason a reduced order observer can be designed in the second part is given a more general class of nonlinear systems for which such an observer can be designed

on a class of frozen regularized gauss newton methods for nonlinear inverse problems in this paper we consider a class of regularized gauss newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration such methods have the frozen feature that they require only the computation of the frechet derivative at the initial approximation thus the computational work is considerably reduced under certain mild conditions we give the convergence analysis and derive various estimates including the order optimality on these methods

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

on the robust design of sliding observers for linear systems abstract the restrictive character of well known structural constraints related to the matching conditions for the sliding mode feedforward state reconstruction problem in linear time invariant perturbed systems is critically reexamined from a new perspective it is shown that in generalized state space coordinates a matched canonical state space realization exists which always allows discontinuous asymptotic stabilization of the observation error dynamics the well known structural conditions thus become largely irrelevant and robust asymptotic state estimation is shown to be feasible for any perturbed observable system by means of sliding mode observers

between controllable and uncontrollable the distance between a system a b and the set of uncontrollable systems is the minimum of the smallest singular value of i a b with respect to

towards a general convergence theory for inexact newton regularizations we develop a general convergence analysis for a class of inexact newton type regularizations for stably solving nonlinear ill posed problems each of the methods under consideration consists of two components the outer newton iteration and an inner regularization scheme which applied to the linearized system provides the update in this paper we give a novel and unified convergence analysis which is not confined to a specific inner regularization scheme but applies to a multitude of schemes including landweber and steepest decent iterations iterated tikhonov method and method of conjugate gradients

observer based perturbation extremum seeking control with input constraints for direct contact membrane distillation process abstractan observer based perturbation extremum seeking control is proposed for a direct contact membrane distillation dcmd process the process is described with a dynamic model that is based on a 2d advection diffusion equation model which has pump flow rates as process inputs the objective of the controller is to optimise the trade off between the permeate mass flux and the energy consumption by the pumps inside the process cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates a nonlinear lyapunov based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the dcmd process moreover control inputs are constrained with an anti windup technique to be within feasible and physical ranges performance of the proposed structure is analysed and simulations based on real dcmd process parameters for each control input are provided

on almost compactness in the fuzzy setting net theoretic and filter theoretic characterizations of almost n compactness are provided corrected version of a result of meng han and meng guangwu fuzzy sets and systems 91 1997 115 is provided almost fuzzy compactness is introduced and its characterization is provided by using fuzzy nets and fuzzy filters

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

on the development of discontinuous observers abstract a framework is proposed for the development and analysis of robust observers for uncertain dynamical systems a variable structure systems approach is used emphasis is placed upon the numerical tractability of the associated synthesis procedure a selected numerical example is used to illustrate the proposed algorithm

on the discrepancy principle for some newton type methods for solving nonlinear inverse problems we consider the computation of stable approximations to the exact solution x dagger of nonlinear ill posed inverse problems f x y with nonlinear operators f x y between two hilbert spaces x and y by the newton type methods x k 1 delta x 0 g alpha k left f x k delta f x k delta right f x k delta left f x k delta y delta f x k delta x k delta x 0 right of y satisfying y delta y le delta with a given small noise level delta 0 we terminate the iteration by the discrepancy principle in which the stopping index k delta is determined as the first integer such that f x k delta delta y delta le tau delta f x k delta y delta quad 0 le k k delta converges to x dagger as delta rightarrow 0 and establish various order optimal convergence rate results it is remarkable that we even can show the order optimality under merely the lipschitz condition on the frechet derivative f of f if x 0 x dagger is smooth enough

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on the stabilization and observation of nonlinear uncertain dynamic systems the problem of stabilization and observation of uncertain and or nonlinear dynamic systems for which matching conditions are not satisfied is investigated no statistical description of uncertain elements is assumed the uncertain and or nonlinear quantities are described only in terms of bounds on their possible sizes stabilizing feedback controllers and observers are proposed whose design is based on the constructive use of lyapunov functions and the bellman gronwall lemma

a pseudo heuristic parameter selection rule for l1 regularized minimization problems abstract this paper considers the regularization parameter determination of l 1 regularized minimization problem we solve the l 1 regularized problem using iterative reweighted least squares irls which involves solving a linear system whose coefficient matrix has the form m 1 n 0 1 the aim of this paper is to find an efficient and computationally inexpensive algorithm to both choose the regularization parameter and solve the l 1 regularized problem in order to achieve this we propose an irls algorithm with adaptive regularization parameter selection based on a heuristic parameter determination rule de boor s parameter selection criterion compared with some of the state of the art algorithms and parameter selection rules the numerical experiments show the efficiency and robustness of the proposed method

a general convergence analysis of some newton type methods for nonlinear inverse problems we consider the methods x n 1 delta x n delta g alpha n f x n delta f x n delta f x n delta f x n delta y delta for solving nonlinear ill posed inverse problems f x y using the only available noise data y delta satisfying y delta y leq delta with a given small noise level delta 0 we terminate the iteration by the discrepancy principle f x n delta delta y delta leq tau delta 1 under certain conditions on alpha n and f we prove for a large class of spectral filter functions g alpha the convergence of x n delta delta to a true solution as delta rightarrow0 moreover we derive the order optimal rates of convergence when certain holder source conditions hold numerical examples are given to test the theoretical results

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

one approach to the control of uncertain dynamical systems we present a controller design methodology for uncertain systems which is based on the constructive use of lyapunov stability theory the uncertainties which are deterministic are characterized by certain structural conditions and known as well as unknown bounds as a consequence of the lyapunov approach the methodology is not restricted to linear or time invariant systems the robustness of these controllers in the presence of singular perturbations is considered the situation in which the full state of the system is not available for measurement is also considered as are other generalizations

theorem of l fuzzy h sets abstract the concept of h set was introduced by n v velicko in this paper we generalize it and introduce the concept of l fuzzy h set we prove that the concept is hereditary for regular closed subsets is an l good extension and topologically invariant

state estimation for non linear uncertain systems a design based on properties related to the uncertainty bound observers for non linear uncertain dynamical systems are proposed the non linearity and uncertainty in the systems are assumed to be bounded the bound is however unknown the observer contains an adaptive scheme designed to accommodate the uncertainty the design of the observer is only based on certain functional properties of the bound no statistical information about the uncertainty needs to be assumed or utilized

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

variable structure observer with a boundary layer for correlated noise disturbance models and disturbance minimization we present a design methodology for state estimation of nonlinear stochastic systems and measurement models with coloured noise processes the method is based on the extension of variable structure observer schemes the deterministic versions of these results are also included a new approach for obtaining the required parameters in the observer design is provided together with the design of a dynamic feedback controller to minimize the effect of known waveform type disturbances with unknown magnitudes and arrival times two simulation examples illustrate the design procedures

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

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

almost n compact sets in l fuzzy topological spaces abstract in this paper the concept of almost n compactness in l fuzzy topological spaces is introduced the characterizations of almost n compact sets are systematically discussed it is showed that the fuzzy almost continuous image of an almost n compact set is an almost n compact set it is proved that the almost n compactness is a good extension

input output linearization approach to state observer design for nonlinear system presents a state observer for a class of nonlinear systems based on the input output linearization while the previous result presented state observers for nonlinear systems of full relative degree we proposed a procedure fur the design of nonlinear state observers which do not require the hypothesis of full relative degree assuming that there exists a global state observer for internal dynamics and that some functions are globally lipschitz we can design a globally convergent state observer it is also shown that if the zero dynamics are locally exponentially stable then there exists a local state observer an example is given to illustrate the proposed design of nonlinear state observers

high order sliding mode observer for linear systems with unbounded unknown inputs a global observer is designed for strongly detectable systems with unbounded unknown inputs the design of the observer is based on three steps first the system is extended taking the unknown inputs and possibly some of their derivatives as a new state then using a global high order sliding mode differentiator a new output of the system is generated in order to fulfil what we will call the hautus condition which finally allows decomposing the system in new coordinates into two subsystems the first one being unaffected directly by the unknown inputs and the state vector of the second subsystem is obtained directly from the original system output such decomposition permits designing of a luenberger observer for the first subsystem which satisfies the hautus condition i e all the outputs have relative degree one w r t the unknown inputs this procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible simulations are given in order to show the effectiveness of the proposed observer

on the convergence of a regularizing levenberg marquardt scheme for nonlinear ill posed problems in this note we study the convergence of the levenberg marquardt regularization scheme for nonlinear ill posed problems we consider the case that the initial error satisfies a source condition our main result shows that if the regularization parameter does not grow too fast not faster than a geometric sequence then the scheme converges with optimal convergence rates our analysis is based on our recent work on the convergence of the exponential euler regularization scheme hochbruck et al in inverse probl 25 7 075009 2009

a posteriori parameter choice strategies for some newton type methods for the regularization of nonlinearill posed problems this paper treats a class of newton type methods for the approximate solution of nonlinear ill posed operator equations that use so called filter functions for regularizing the linearized equation in each newton step for noisy data we derive an aposteriori stopping rule that yields convergence of the iterates to asolution as the noise level goes to zero under certain smoothness conditions on the nonlinear operator appropriate closeness and smoothness assumptions on the starting value and the solution are shown to lead to optimal convergence rates moreover we present an application of the newton type methods under consideration to a parameter identification problem together with some numerical results

output feedback stabilization of uncertain dynamical systems given an uncertain dynamical system with a linear nominal part matched uncertainties and a measured output a sufficient condition is given for the existence of an output feedback stabilizing controller for the general multiinput multioutput case checking the sufficient condition involves the selection of a matrix f for the special class of single input single output systems f is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real then an output feedback stabilizing controller does indeed exist

optimal a posteriori parameter choice for tikhonov regularization for solving nonlinear ill posed problems the authors propose an a posteriors strategy for choosing the regularization parameter in tikhonov regularization for solving nonlinear ill posed problems and show that under certain conditions the convergence rate obtained with this strategy is optimal as a by product a new stability estimate for the regularized solutions is given which applies to a class of parameter identification problems the authors compare the parameter choice strategy with morozov s discrepancy principle finally numerical results are presented

existence and design of observers for nonlinear systems relation to distance to unobservability this paper presents a systematic design methodology and some fundamental insights into observer design for the class of lipschitz nonlinear systems the existence of an asymptotically stable observer is shown to be guaranteed when the distance to unobservability is larger than the lipschitz constant of the nonlinear system an analytical solution for the observer is provided in this case a methodology for the use of a coordinate transformation is then developed so as to reduce the lipschitz constant and increase the distance to unobservability in the new coordinates the methodology is directly applicable to the important class of feedback linearizable systems the developed theory is used successfully in the design of an observer for a flexible joint robotic system

on an a posteriori parameter choice strategy for tikhonov regularization of nonlinear ill posed problems in the study of the choice of the regularization parameter for tikhonov regularization of nonlinear ill posed problems scherzer engl and kunisch proposed an a posteriori strategy in 1993 to prove the optimality of the strategy they imposed many very restrictive conditions on the problem under consideration their results are difficult to apply to concrete problems since one can not make sure whether their assumptions are valid in this paper we give a further study on this strategy and show that tikhonov regularization is order optimal for each 0 nu le 2 with the regularization parameter chosen according to this strategy under some simple and easy checking assumptions this paper weakens the conditions needed in the existing results and provides a theoretical guidance to numerical experiments

state observation of nonlinear uncertain dynamical systems this note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties the design of these observers utilizes techniques related to variable structure systems theory a measure for the rate at which the estimates converge to the actual states is derived

on a regularized levenberg marquardt method for solving nonlinear inverse problems we consider a regularized levenberg marquardt method for solving nonlinear ill posed inverse problems we use the discrepancy principle to terminate the iteration under certain conditions we prove the convergence of the method and obtain the order optimal convergence rates when the exact solution satisfies suitable source wise representations

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

on the iteratively regularized gauss newton method in banach spaces with applications to parameter identification problems in this paper we propose an extension of the iteratively regularized gauss newton method to the banach space setting by defining the iterates via convex optimization problems we consider some a posteriori stopping rules to terminate the iteration and present the detailed convergence analysis the remarkable point is that in each convex optimization problem we allow non smooth penalty terms including l 1 and total variation like penalty functionals this enables us to reconstruct special features of solutions such as sparsity and discontinuities in practical applications some numerical experiments on parameter identification in partial differential equations are reported to test the performance of our method

on state observers for nonlinear systems abstract for linear systems it is known that there exists a state observer if and only if the system is detectable or in other words asymptotically stabilizable by output injection in this paper it is shown that asymptotic stabilizability by output injections is neither necessary nor sufficient for the construction of a nonlinear observer which may not have an exponential error decay rate the concept of uniform observers is introduced and necessary conditions and sufficient conditions are given for the construction of uniform observers

state observers and state feedback controllers for a class of non linear systems a design methodology for observers and controllers for a class of single input single output non linear systems is developed a non linear observer form is defined and a corresponding observer using non linear observer gains is specified the resulting error dynamics which are non linear are asymptotically stable for a proper choice of those gains and bounded inputs and outputs a non linear controller form is defined and a corresponding controller which results in linear closed loop dynamics with arbitrary eigenvalue placement is devised transformations from the class of interest to the defined forms are derived in the observer case the transformation to the observer form and the non linear entries in the state matrix of that form can be determined separately leading to a system of linear partial differential equations a major simplification in the controller case a simple well known system of linear partial differential equations is obtained the efficacy of the developed methodology is sho

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

an adaptive fuzzy hybrid state observer for bioprocesses in order to monitor and control bioprocesses online measurements of certain biological variables like biomass concentration are normally required unfortunately there is a lack of highly reliable and low cost instruments for online measuring these important variables these limitations have motivated the use of observers this paper describes a state observer for bioprocesses based on a hybrid fuzzy model the model combines the mass balances and a fuzzy inference system for approximating the uncertain dynamic of the kinetic reactions the convergence stability and robustness of the observer are analyzed the main features of this observer are illustrated by considering a lactic fermentation

a novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions abstract in this paper a novel sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation in particular the so called matching condition and minimum phase condition other works attempt to circumvent the matching condition by using multiple observers in cascade or higher order sliding modes whilst the minimum phase condition can be relaxed at the cost of some faults and the states being not estimated or the fault estimation being corrupted by the fault time derivative or other dynamics for the proposed scheme in this paper only one observer is required the minimum phase condition is relaxed to detectability and the matching condition is greatly simplified to a condition related to the system dimensions which makes the scheme also applicable to the case where there are less outputs than faults finally a simulation example is conducted to verify the effectiveness of the proposed observer

stabilizing compensator design for uncertain nonlinear systems abstract an observer based control scheme is proposed for exponentially stabilizing a class of uncertain nonlinear systems the control and observer gain expressions given in this paper resemble those used in variable structure designs but they are continuous in nature resulting in a simple analysis of stability

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

almost compactness in fuzzy topological spaces abstract we introduce and study almost compactness for fuzzy topological spaces we show that the almost continuous image of an almost compact fuzzy topological space is almost compact moreover we show that generally almost compactness for fuzzy topological spaces is not product invariant but if x and y are almost fuzzy topological spaces and x is product related to y then their fuzzy topological product is almost compact

on convergence rates of inexact newton regularizations reginn is an algorithm of inexact newton type for the regularization of nonlinear ill posed problems inverse problems 15 1999 pp 309 327 in the present article convergence is shown under weak smoothness assumptions source conditions moreover convergence rates are established some computational illustrations support the theoretical results

an lmi approach for designing sliding mode observers this paper presents a method to design sliding mode observers for a class of uncertain systems using linear matrix inequalities the objective is to exploit the degrees of freedom available in the design which have hitherto been ignored because of the lack of a tractable solution framework the relationship between the linear component of the sliding mode observer and a particular sub optimal observer arising from classical linear quadratic gaussian lqg theory is demonstrated this helps motivate how the design weighting matrices inherent in the method may be chosen in practice it will also be shown how the weighting matrices affect the dynamics of the sliding motion furthermore using pole placement and pole clustering methods the poles of the sliding motion can be forced to lie in a specified region in the complex plane so that the performance of the sliding motion can be tuned this paper will also present a more general solution where the eigenvalues of the linear part of the observer are forced

design of asymptotic estimators an approach based on neural networks and nonlinear programming a methodology to design state estimators for a class of nonlinear continuous time dynamic systems that is based on neural networks and nonlinear programming is proposed the estimator has the structure of a luenberger observer with a linear gain and a parameterized in general nonlinear function whose argument is an innovation term representing the difference between the current measurement and its prediction the problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error toward this end if a neural network is used to take on this function the parameters i e the neural weights are chosen together with the gain by constraining the derivative of a quadratic lyapunov function for the estimation error to be negative definite on a given compact set it is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points the gain is determined by solving a lyapunov equation the neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid point constraints that are not satisfied techniques based on low discrepancy sequences are applied to deal with a small number of sampling points and hence to reduce the computational burden required to optimize the parameters numerical results are reported and comparisons with those obtained by the extended kalman filter are made

levenberg marquardt method in banach spaces with general convex regularization terms we propose a levenberg marquardt method with general uniformly convex regularization terms to solve nonlinear inverse problems in banach spaces which is an extension of the scheme proposed by hanke in inverse probl 13 79 95 1997 in hilbert space setting the method is so designed that it can be used to detect the features of the sought solutions such as sparsity or piecewise constancy it can also be used to deal with the situation that the data is contaminated by noise containing outliers by using tools from convex analysis in banach spaces we establish the convergence of the method numerical simulations are reported to test the performance of the method

continuously implemented sliding mode adaptive unknown input observers under noisy measurements we propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise the estimator design is based on the combination of observer design for descriptor systems sliding modes theory and adaptive control the estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state two adaptive parameters are updated online one to compensate for the unknown bounds on the states the unknown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities to join robust state estimation and unknown inputs reconstruction our approach borrows inspiration from sliding mode theory however all signals are continuously implemented we demonstrate that both state and unknown inputs estimation are achieved up to arbitrarily small tolerance the utility of our theoretical results is illustrated through simulation case studies

a discontinuous output feedback controller and velocity observer for nonlinear mechanical systems in this paper we develop a new discontinuous output feedback tracking controller for a class of uncertain nonlinear multi input multi output mechanical systems whose dynamics are first order differentiable a novel filter design and lyapunov type stability analysis are used to prove semi global asymptotic tracking as a by product of the proposed framework we also present the design of a new simple discontinuous velocity observer that ensures global asymptotic velocity observation

brief an observer for systems with nonlinear output map a nonlinear observer with the feedback gain weighted by the sensitivity of the output with respect to the state is developed for systems with nonlinear output map the observer can be obtained from the extended kalman filter by a special choice of time varying weighting matrices it is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived the observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal using plant data from the converter at ssab oxelosund ab the observer is shown to provide accurate estimates of the carbon content

on the state observation and output feedback problems for nonlinear uncertain dynamic systems abstract in this paper we examine the problems of state observation and state trajectory control by output feedback for the class of non linear systems in 3 11 we begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is globally exponentially stable ges we then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the ges sense specific time varying bounds on the observation error and the state trajectory are also developed revealing how the corresponding observer or control parameters can be adjusted to improve the system performance

on exponential observers for nonlinear systems abstract the aim of the paper is to identify the class of nonlinear systems that have exponential observers a concept introduced by previous authors it is shown that a necessary condition for the existence of an exponential observer for a nonlinear system is that the corresponding linearized system is detectable and for local exponential stabilization problems the condition is also sufficient this paper gives also a theorem on the separation property for the exponential design problem and it enables us to tell exactly to what extent the classical local linearization approach is applicable

dynamical systems method dsm for solving equations with monotone operators without smoothness assumptions on f u abstract a version of the dynamical systems method dsm for solving ill posed nonlinear equations f u f with monotone operators f in a hilbert space is studied in this paper under less restrictive assumptions on the nonlinear operators f than the assumptions used earlier a new method of proof of the basic results is used an a posteriori stopping rule based on a discrepancy type principle is proposed and justified mathematically under weaker assumptions on the nonlinear operator f than the assumptions used earlier

adaptive sliding mode control of multi input nonlinear systems with perturbations to achieve asymptotical stability a design of adaptive sliding surfaces for a class of multi input mi nonlinear systems with matched and mismatched perturbations is proposed in this note to solve regulation problems based on the lyapunov stability theorem and backstepping technique by using some adaptive gains designed in the sliding surface function the virtual input and the controllers not only the mismatched perturbations are automatically overcome during the sliding mode but also the property of asymptotical stability of controlled systems is achieved at the same time furthermore the knowledge of the upper bound of partial perturbations is not required controlling a two link robot manipulator is given to demonstrate the feasibility of the proposed control scheme

robust nonlinear observer for lipschitz nonlinear systems subject to disturbances this note proposes a robust nonlinear observer for systems with lipschitz nonlinearity the proposed nonlinear observer whose linear part adopts the linear ltr observer design technique has two important advantages over previous designs first the new observer does not impose the small lipschitz constant condition on the system nonlinearity nor other structural conditions on the system dynamics as in the existing observer designs second it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances

on the iteratively regularized gauss newton method for solving nonlinear ill posed problems the iteratively regularized gauss newton method is applied to compute the stable solutions to nonlinear ill posed problems f x y when the data y is given approximately by y with y y in this method the iterative sequence x k is defined successively by x k 1 x k k i f x k f x k 1 f x k f x k y k x k x 0 where x 0 x 0 is an initial guess of the exact solution x and k is a given decreasing sequence of positive numbers admitting suitable properties when x k is used to approximate x the stopping index should be designated properly in this paper an a posteriori stopping rule is suggested to choose the stopping index of iteration and with the integer k determined by this rule it is proved that x k x c inf x k x k k 0 1 with a constant c independent of where x k denotes the iterative solution corresponding to the noise free case as a consequence of this result the convergence of x k is obtained and moreover the rate of convergence is derived when x 0 x satisfies a suitable source wise representation the results of this paper suggest that the iteratively regularized gauss newton method combined with our stopping rule defines a regularization method of optimal order for each 0 v 1 numerical examples for parameter estimation of a differential equation are given to test the theoretical results

amplitude variation with angle inversion using the exact zoeppritz equations theory and methodology to overcome the weaknesses of conventional prestack amplitude variation with angle inversion based on various linear or quasi linear approximations we have conducted a nonlinear inversion method using the exact zoeppritz matrix ezai however the inversion using the exact zoeppritz matrix was highly nonlinear and often unstable if not properly treated to tackle these issues we have used an iteratively regularizing levenberg marquardt scheme irlm which regularizes the inversion problem within an algorithm that minimizes the misfit between the observed and the modeled data at the same time by incorporating the tikhonov regularization method as a result the new ezai method solved using the irlm scheme is feasible for seismic data sets with large incidence angles even up to or beyond the critical angle as well as strong parameter contrasts single and multilayered synthetic examples were used to test these features these tests also showed that ezai is robust on noisy gathers for parameter extraction and has weak dependence on the initial model for the influence of inaccurate amplitudes dominant frequencies and phase angles we found that ezai is less sensitive to the variation in amplitude and phase shifts than to the dominant frequencies specifically the inversion results of ezai for p and s wave velocities and density were reliable if the inaccurate range for the amplitude was within 20 or the angle of the phase shift was no more than 20 the superiority of ezai makes it a very promising method for the estimation of subsurface elastic parameters