the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

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

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

circle criterion based ℋ observer design for lipschitz and monotonic nonlinear systems enhanced lmi conditions and constructive discussions a new lmi design technique is developed to address the problem of circle criterion based mathcal h infty observer design for nonlinear systems the developed technique applies to both locally lipschitz as well as monotonic nonlinear systems and allows for nonlinear functions in both the process dynamics and output equations the lmi design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems by judicious use of a modified young s relation additional degrees of freedom are included in the observer design these additional decision variables enable improvements in the feasibility of the obtained lmi several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper illustrative examples are given to show the effectiveness of the proposed methodology the application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented

estimation of adjusted rate differences using additive negative binomial regression rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios when the data are event counts observed during an exposure period adjusted rate differences may be estimated using an identity link poisson generalised linear model also known as additive poisson regression a problem with this approach is that the assumption of equality of mean and variance rarely holds in real data which often show overdispersion an additive negative binomial model is the natural alternative to account for this however standard model fitting methods are often unable to cope with the constrained parameter space arising from the non negativity restrictions of the additive model in this paper we propose a novel solution to this problem using a variant of the expectation conditional maximisation either algorithm our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi parametric regression functions we illustrate the method using a placebo controlled clinical trial of fenofibrate treatment in patients with type ii diabetes where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy an r package is available that implements the proposed method copyright 2016 john wiley sons ltd

on undecidability bounds for matrix decision problems in this paper we consider several reachability problems such as vector reachability membership in matrix semigroups and reachability problems in piecewise linear maps since all of these questions are undecidable in general we work on lowering the bounds for undecidability in particular we show an elementary proof of undecidability of the reachability problem for a set of 5 two dimensional affine transformations then using a modified version of a standard technique we also prove that the vector reachability problem is undecidable for two rational matrices in dimension 11 the above result can be used to show that the system of piecewise linear functions of dimension 12 with only two intervals has an undecidable set to point reachability problem we also show that the zero in the upper right corner problem is undecidable for two integral matrices of dimension 18 lowering the bound from 23

example of undecidable problems for 2 generator matrix semigroups abstract we show that the following two problems are undecidable given two square matrices decide whether the semigroup that they generate contains the zero matrix and whether it contains a matrix having a zero in the right upper corner

observer based control of systems with slope restricted nonlinearities an observer design is presented which makes use of bounds on the slope of system nonlinearities necessary and sufficient conditions are derived for the feasibility of the design a class of state feedback control laws are characterized which when implemented with the observer states ensure global asymptotic stability one such certainty equivalence design is illustrated on an active magnetic bearing example

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

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

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

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

reachability problems in quaternion matrix and rotation semigroups we examine computational problems on quaternion matrix and rotation semigroups it is shown that in the ultimate case of quaternion matrices in which multiplication is still associative most of the decision problems for matrix semigroups are undecidable in dimension two the geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2 and 3 sphere in particular we show that the reachability of the rotation problem is undecidable on the 3 sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers

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

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

termination and derivational complexity of confluent one rule string rewriting systems it is not known whether the termination problem is decidable for one rule string rewriting systems though the confluence of such systems is decidable by wrathall in word equations and related topics lecture notes in computer science vol 572 1992 pp 237 246 in this paper we develop techniques to attack the termination and complexity problems of confluent one rule string rewriting systems with given such a system we associate another rewriting system over another alphabet the behaviour of the two systems is closely related and the termination problem for the new system is sometimes easier than for the original system we apply our method to systems of the special type apbq t where t is an arbitrary word over a b and give a complete characterization for termination we also give a complete analysis of the derivational complexity for the system apbq bnam

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

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

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

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

extension of the decidability of the marked pcp to instances with unique blocks in the post correspondence problem pcp an instance h g consists of two morphisms h and g and the problem is to determine whether or not there exists a nonempty word w such that h w g w here we prove that the pcp is decidable for instances with unique blocks using the decidability of the marked pcp also we show that it is decidable whether an instance satisfying the uniqueness condition for continuations has an infinite solution these results establish a new and larger class of decidable instances of the pcp including the class of marked instances

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

robust adaptive observers for nonlinear systems with bounded disturbances since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances robust adaptive observers are presented which prevent parameter estimate drift in addition the input to state stability of the error dynamics with respect to disturbances and parameter time derivatives is guaranteed by generalizing a persistency of excitation result asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present by a suitable extension of barbalat s lemma

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

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

new lmi condition for observer based mathcal h _ infty stabilization of a class of nonlinear discrete time systems in this paper a new lmi linear matrix inequality condition is provided for the observer based mathcal h infty stabilization of a class of nonlinear discrete time systems with the proposed design methodology the observer and controller gains are computed simultaneously by solving only one inequality based on the lyapunov theory and the use of mathematical artifacts such as matrix decomposition and the young relation the novel sufficient synthesis condition is expressed in terms of lmi which can be easily solved by numerical tools an application to a flexible link robot manipulator is provided to show the consistency of the proposed approach a second numerical example is devoted to demonstrating the superiority and the lower conservatism of the proposed lmi compared to those available in the literature

krein space based h adaptive smoother design for a class of lipschitz nonlinear discrete time systems in this paper the problem of h adaptive smoother design is addressed for a class of lipschitz nonlinear discrete time systems with l2 bounded disturbance input by comprehensively analyzing the h performance lipschitz conditions and unknown parameter s bounded condition a positive minimum problem for an indefinite quadratic form is introduced such that the h adaptive smoothing problem is achieved a krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form the minimum of indefinite quadratic form is derived in the form of innovations through utilizing krein space orthogonal projection and innovation analysis approach via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard riccati difference equations the quality of the estimator is checked on an example

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

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

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

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

the ecme algorithm a simple extension of em and ecm with faster monotone convergence a generalisation of the ecm algorithm meng rubin 1993 which is itselfan extension of the em algorithm dempster laird rubin 1977 can be obtained by replacing some cm steps of ecm which maximise the constrained expected complete data loglikelihood function with steps that maximise the correspondingly constrained actual likelihood function this algorithm which we call ecme algorithm for expectation conditional maximisation either shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods moreover ecme can have a substantially faster convergence rate than either em or ecm measured using either the number of iterations or actual computer time

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

a note on non linear observers a general non linear exponential observer is presented for non linearly perturbed nonlinear systems this is done by using the non linear variation of constants formula

nonlinear observer design for state and disturbance estimation a new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed the nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in n kazantzis c kravaris nonlinear observer design using lyapunov s auxiliary theorem systems control lett 34 1998 241 a j krener m xiao nonlinear observer design in the siegel domain siam j control optim 41 2002 932 for state estimation purposes only from a mathematical standpoint the problem under consideration is addressed through a system of first order singular pdes for which a rather general set of solvability conditions is derived a nonlinear observer is then designed with a state dependent gain that is computed from the solution of the system of singular pdes under the aforementioned conditions both state and disturbance estimation errors converge to zero with assignable rates the convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor

smoothing parameter selection in nonparametric regression using an improved akaike information criterion summary many different methods have been proposed to construct nonparametric estimates of a smooth regression function including local polynomial convolution kernel and smoothing spline estimators each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set in this paper an improved version of a criterion based on the akaike information criterion aic termed aicc is derived and examined as a way to choose the smoothing parameter unlike plug in methods aicc can be used to choose smoothing parameters for any linear smoother including local quadratic and smoothing spline estimators the use of aicc avoids the large variability and tendency to undersmooth compared with the actual minimizer of average squared error seen when other classical approaches such as generalized cross validation or the aic are used to choose the smoothing parameter monte carlo simulations demonstrate that the aicc based smoothing parameter is competitive with a plug in method assuming that one exists when the plug in method works well but also performs well when the plug in approach fails or is unavailable

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

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

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

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

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

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

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

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

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

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

relative undecidability in term rewriting i the termination hierarchy for a hierarchy of properties of term rewriting systems related to termination we prove relative undecidability for implications x y in the hierarchy the property x is undecidable for term rewriting systems satisfying y for most implications we obtain this result for term rewriting systems consisting of a single rewrite rule

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

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

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

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

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

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

decidability of termination of grid string rewriting rules termination of string rewriting is known undecidable termination of string rewriting with only one rule is neither known decidable nor known undecidable this paper presents a decision procedure for rules u rightarrow v such that some letter b from u occurs as often or less often in v we call such rules grid rules by far most rules are grid rules grid rules cover all rules which terminate by a total division order thus total division orders are shown to be irrelevant for the termination problem of one rule string rewriting

decidable and undecidable problems about quantum automata we study the following decision problem is the language recognized by a quantum finite automaton empty or nonempty we prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or nonstrict thresholds this result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and nonstrict thresholds both lead to undecidable problems

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

parameter and state estimation of nonlinear systems using a multi observer under the supervisory framework we present a hybrid scheme for the parameter and state estimation of nonlinear continuous time systems which is inspired by the supervisory setup used for control state observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant which provides state and parameter estimates assuming that a persistency of excitation condition holds the convergence of the parameter and state estimation errors to zero is ensured up to a margin which can be made as small as desired by increasing the number of observers to reduce the potential computational complexity of the scheme we explain how the sampling of the parameter set can be dynamically updated using a zoom in procedure this strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy the results are shown to be applicable to linear systems and to a class of nonlinear systems we illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model

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

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

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

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

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

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

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

decision problems for semi thue systems with a few rules we show that the accessibility problem the common descendant problem the termination problem and the uniform termination problem are undecidable for 3 rules semi thue systems as a corollary we obtain the undecidability of the post correspondence problem for 7 rules

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

a robust circle criterion observer with application to neural mass models a robust circle criterion observer is designed and applied to neural mass models at present no existing circle criterion observers apply to the considered models i e the required linear matrix inequality is infeasible therefore we generalise available results to derive a suitable estimation algorithm additionally the design also takes into account input uncertainty and measurement noise we show how to apply the observer to estimate the mean membrane potential of neuronal populations of a popular single cortical column model from the literature

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

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

a systematic approach to adaptive observer synthesis for nonlinear systems geometric techniques of controller design for nonlinear systems have enjoyed great success a serious shortcoming however has been the need for access to full state feedback this paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty an adaptive nonlinear observer is suggested for lipschitz nonlinear systems and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables a coordinate transformation is used to reformulate this inequality as a linear matrix inequality a systematic algorithm is presented which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible the state estimation errors then are guaranteed to converge to zero asymptotically the convergence of the parameters however is determined by a persistence of excitation type constraint

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