a new approach to design interval observers for linear systems interval observers are dynamic systems that provide upper and lower bounds of the true state trajectories of systems in this work we introduce a technique to design interval observers for linear systems affected by state and measurement disturbances based on the internal positive representations iprs of systems that exploits the order preserving property of positive systems the method can be applied to both continuous and discrete time systems

robust state estimation for singularly perturbed systems abstractthis paper deals with the design of interval observers for singularly perturbed linear systems the full order system is first decoupled into slow and fast subsystems then using the cooperativity theory an interval observer is designed for the slow and fast subsystems assuming that the measurement noise and the disturbances are bounded and the singular perturbed parameter is uncertain this decoupling leads to two observers that estimate the lower and upper bounds for the feasible state domain a numerical example shows the efficiency of the proposed technique

interval and linear matrix inequality techniques for reliable control of linear continuous time cooperative systems with applications to heat transfer lower and upper state bounds can be computed independently for cooperative ordinary differential equations odes with interval valued initial conditions then all reachable states are enclosed by

generating positive and stable solutions through delayed state feedback for time varying forward complete nonlinear systems with delay in the input a new reduction model approach is proposed it presents three advantages first the corresponding control laws do not include distributed terms second it yields closed loop systems with positive solutions that can be easily derived finally the stabilized systems possess some robustness properties that can be estimated

a brezis browder principle on partially ordered spaces and related ordering theorems abstract through a simple extension of brezis browder principle to partially ordered spaces a very general strong minimal point existence theorem on quasi ordered spaces is proved this theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems and three general ekeland variational principles in optimization problems where the objective space is quasi ordered then they are applied to prove strong minimal point existence results generalizations of bishop phelps lemma in linear spaces and ekeland variational principles in set valued optimization problems through a set solution criterion

pointwise well posedness in set optimization with cone proper sets abstract this paper deals with the well posedness property in the setting of set optimization problems by using a notion of well posed set optimization problem due to zhang et al 2009 18 and a scalarization process we characterize this property through the well posedness in the tykhonov sense of a family of scalar optimization problems and we show that certain quasiconvex set optimization problems are well posed our approach is based just on a weak boundedness assumption called cone properness that is unavoidable to obtain a meaningful set optimization problem

existence theorems for set optimization problems abstract in this paper we consider set optimization problems by using a partial ordering based on a set relation we establish several existence results of minimal elements more general than those existing in the literature as an application we present sufficient conditions for the existence of solutions of a set valued optimization problem under some semi continuity assumption

design of interval observer for a class of uncertain unobservable nonlinear systems this paper investigates the interval observer design for a class of nonlinear continuous systems which can be represented as a superposition of a uniformly observable nominal subsystem with a lipschitz nonlinear perturbation it is shown in this case there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements an illustrative example of the observer application is given with simulation results

interval observers for time varying discrete time systems this techical note deals with interval state observer design for time varying discrete time systems the problem of a similarity transformation computation which connects a time varying matrix and its nonnegative representation is studied three solutions are proposed for a generic time varying system a system with positive state and for a particular class of periodical systems numerical simulations are provided to demonstrate advantages of the developed techniques

interval estimation methods for discrete time linear time invariant systems this paper investigates interval estimation methods for discrete time linear time invariant systems we propose a novel interval estimation method by integrating robust observer design with reachability analysis by introducing h infty design into interval estimation the proposed method is effective in improving the accuracy of interval estimation moreover the comparisons and relationships between the existing methods and the proposed method are discussed in detail finally simulation results are presented to demonstrate the effectiveness of the proposed method

well posedness for set optimization problems abstract in this paper three kinds of well posedness for set optimization are first introduced by virtue of a generalized gerstewitz s function the equivalent relations between the three kinds of well posedness and the well posedness of three kinds of scalar optimization problems are established respectively then sufficient and necessary conditions of well posedness for set optimization problems are obtained by using a generalized forcing function respectively finally various criteria and characterizations of well posedness are given for set optimization problems

asymptotically stable interval observers for planar systems with complex poles in some parametric domains the problem of designing an exponentially stable interval observer for an exponentially stable two dimensional time invariant linear system is open we show that in some cases no linear time invariant change of coordinates can help to determine an exponentially stable interval observer next we solve the problem by constructing interval observers of a new type which have as key feature the property of being time varying this new design is applied to the chaotic chua s system

interval state estimation for uncertain polytopic systems the aim of this article is the state estimation of uncertain polytopic dynamic systems the parametric uncertainties affecting the system are time varying unknown and bounded with known bounds the objective is to determine the state estimates consisting in the smallest interval containing the real state value caused by the parametric uncertainties this set will be characterized by the lower and upper bounds of the state trajectory given the uncertainty bounds the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a luenberger type observer fed with the system measurements the proposed observer is designed to minimize the interval width of the estimates the observer gains are obtained by solving an optimization problem under lmi constraints the efficiency of the proposed approach is illustrated by numerical examples

h 2 and h_ infty robust filtering for discrete time linear systems this paper investigates robust filtering design problems in h2 and h infty spaces for discrete time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain it is shown that by a suitable change of variables both design problems can be converted into convex programming problems written in terms of linear matrix inequalities lmi the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h2 and h infty filters are proven to be of the same order as the order of the system comparisons with robust filters for systems subjected to norm bounded uncertainty are provided in both theoretical and practical settings in particular it is shown that under the same assumptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of h2 or h infty norms is considered some numerical examples illustrate the theoretical results

robust interval observers and stabilization design for discrete time systems with input and output for a family of nonlinear discrete time systems with input output and uncertain terms a new interval observer is designed its main feature is that it is composed of two copies of classical observers this interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback an illustrative example completes the presentation

generalized e quasi solutions in multiobjective optimization problems existence results and optimality conditions abstract this paper is concerned with approximate solutions of multiobjective optimization problems whose order cone is not necessarily the nonnegative orthant we introduce the concept of generalized e quasi solution that extends other well known approximate efficiency notions of the literature and we study the limit behavior of these solutions as approximations to the efficient and weak efficient sets moreover we prove several existence results and a bound for the generalized e quasi solution set under convexity assumptions and by using asymptotic analysis tools finally we develop optimality conditions for a particular case of these kinds of e quasi solutions in nonsmooth convex and nonconvex problems

combined mollification future temperatures procedure for solution of inverse heat conduction problem abstract the inverse heat conduction problem involves the calculation of surface heat flux and or temperature histories from transient measured temperatures inside solids this paper proposes and investigates a new combined procedure that is based on two different methods a data filtering interpretation of the mollification method and beck s future temperature method a test case is investigated of a semi infinite body exposed to a heat flux that is initially zero has a unit increase an then drops to zero the combined procedure is shown to be accurate and stable with respect to perturbations in the data even for small dimensionless time steps the future temperatures method can be significantly improved upon by the combined procedure

optimal interval observers for discrete time linear switched systems the main goal of this paper is to present a methodology to design interval observers for discrete time linear switched systems affected by bounded but unknown disturbances two design techniques a

nonconvex scalarization in set optimization with set valued maps abstract the aim of this work is to obtain scalar representations of set valued optimization problems without any convexity assumption using a criterion of solution introduced by kuroiwa d kuroiwa some duality theorems of set valued optimization with natural criteria in proceedings of the international conference on nonlinear analysis and convex analysis world scientific river edge nj 1999 pp 221 228 which is based on ordered relations between sets we characterize this type of solutions by means of nonlinear scalarization the scalarizing function is a generalization of the gerstewitz s nonconvex separation function as applications of our results we give two existence theorems for set valued optimization problems

brief paper near optimal interval observers bundle for uncertain bioreactors in this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors the observer is based on a bounded error observer as proposed in lemesle v gouze j l 2005 hybrid bounded error observers for uncertain bioreactor models bioprocess and biosystems engineering 27 311 318 that makes use of a loose approximation of the bacterial kinetics we first show how to generate guaranteed upper and lower bounds on the state provided that known intervals for the initial condition and the uncertainties are available these so called framers depend on a tuning gain they can be run in parallel and the envelope provides the best estimate an optimality criterion is introduced leading to the definition of an optimal observer we show that this criterion provides directly a gain set containing the best framers the method is applied to the estimation of the total biomass of an industrial wastewater treatment plant demonstrating its efficiency

combined function specification regularization procedure for solution of inverse heat conduction problem methode combinee basee sur 2 methodes differentes la methode de specification sequentielle proposee par beck et la methode de regularisation utilisee par tikhonov

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

delayed output feedback control for nonlinear systems with two layer interval fuzzy observers in this paper the design problem of a delayed output feedback control scheme using two layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated the takagi sugeno type fuzzy linear model with an online update law is used to approximate the nonlinear system based on the fuzzy model a two layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices subsequently a delayed output feedback adaptive fuzzy controller is developed to overcome the nonlinearities time delays and external disturbances such that h infty tracking performance is achieved the linguistic information is developed by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly using linear analytical results instead of estimating nonlinear system functions the tracking error dynamics are designed to enable our adaptive controller to avoid the filtering of the basis vectors whose dimension is much larger than that of the state vector of the controlled system this is achieved by not imposing the strictly positive real condition based on the lyapunov stability criterion and linear matrix inequalities some sufficient conditions are derived so that all the states of the system are uniformly ultimately bounded therefore the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and h infty tracking control is achieved building on our previous work in this area the proposed control scheme is extended to handle a class of uncertain nonlinear systems with state and output delays and external disturbances this is achieved through the use of a robust variable structure scheme and h infty control techniques finally a numerical example of a two link robot manipulator is studied to illustrate the effectiveness of the proposed control scheme

parameter selection by discrete mollification and the numerical solution of the inverse heat conduction problems abstract a procedure for the numerical solution of the one dimensional inverse heat conduction problem based on the computaion of the solution associated with a suitable filtered version of the noisy data by discrete mollification is presented and a parameter choice criterion which automatically determines the radius of mollification as a function of the amount of noise in the data is introduced several numerical examples of interest are also analyzed showing the accuracy and stability properties of the method

interval methods and contractor based branch and bound procedures for verified parameter identification of quasi linear cooperative system models abstract a large number of dynamic system models in engineering as well as computational physics chemistry or biology are described after first principle modeling approaches by sets of either discrete time difference equations or by sets of ordinary differential equations in both cases the structure of those system models results from fundamental physical system properties such as conservation laws of mass momentum and energy newton s or kirchhoff s laws as well as a structural subdivision into subsystems or individual compartments regardless of the area of application all of these system models involve parameters which are not perfectly known due to uncertainty resulting from tolerances in the construction of the respective real life systems or which are described by an inherent uncertainty coming from model simplifications or even from a lack of knowledge about detailed microscopic dynamic effects this is especially true for applications in engineering where a trade off between the model accuracy and the resulting computational complexity has to be made in order to obtain mathematical representations which can be evaluated numerically in real time this real time applicability is inevitable if tasks such as feedback control or model based state estimation on the basis of incomplete state measurements are of interest hence all aforementioned tasks depend on the reliable estimation of those parameters of the structurally predefined sets of state equations which are feasible with respect to the knowledge about selected measurable state variables under consideration of the associated measurement tolerances this paper presents computational techniques for a model based identification of system parameters under the a priori knowledge of stability of the underlying open loop dynamics and the structural constraint of cooperativity

stable interval observers in bbc for linear systems with time varying input bounds this technical note deals with the design of stable interval observers and estimators for continuous time linear dynamic systems under uncertain initial states and uncertain inputs enclosed within time varying zonotopic bounds no monotony assumption such as cooperativity is required in the vector field the interval observer stability directly derives from the stability of the observer state matrix where any poles real or complex single or multiple are handled in the same way

interval observers for linear time invariant systems with disturbances it is shown that for any time invariant exponentially stable linear system with additive disturbances time varying exponentially stable interval observers can be constructed the technique of construction relies on the jordan canonical form that any real matrix admits and on time varying changes of coordinates for elementary jordan blocks which lead to cooperative linear systems the approach is applied to detectable linear systems

strict efficiency in set valued optimization in this paper we develop the notion of a phi minimizer or strict efficiency for a set valued map its properties and relations with other similar notions are studied in special circumstances under suitable conditions we prove that a point is a phi minimizer of a vector function if and only if it is a phi minimizer of a certain family of linear scalarizations we also establish a characterization of strict efficiency through a nonlinear scalarization which is a generalization of the gerstewitz function defined on the power set of the image space the final part is focused on minimizers of order one and we provide several necessary or sufficient conditions without convexity assumptions through different kinds of derivatives as contingent radial among others various illustrative examples showing the applicability of our results are also presented

strict approximate solutions in set valued optimization with applications to the approximate ekeland variational principle this work deals with strict solutions of set valued optimization problems under the set optimality criterion in this context we introduce a new approximate solution concept and we obtain several properties of these solutions when the error is fixed and also for their limit behavior when the error tends to zero then we prove a general existence result which is applied to obtain approximate ekeland variational principles

stability analysis for time varying systems with delay using linear lyapunov functionals and a positive systems approach we prove stability of time varying systems with delays using linear lyapunov functionals and positive systems and we provide robustness of the stability with respect to multiplicative uncertainty in the vector fields we allow cases where the delay may be unknown and where the vector fields defining the systems are not necessarily bounded we illustrate our work using a chain of integrators and other examples

nonlinear observers for a class of biological systems application to validation of a phytoplanktonic growth model the authors construct nonlinear observers in order to discuss the validity of biological models they consider a class of systems including many classical models used in biological modeling they formulate the nonlinear observers corresponding to these systems and prove the conditions necessary for their exponential convergence they apply these observers on the well known droop model which describes the growth of a population of phytoplanktonic cells the validity of this model is discussed based on the performance of the observers working on experimental data

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

guaranteed nonlinear parameter estimation in knowledge based models knowledge based models are ubiquitous in pure and applied sciences they often involve unknown parameters to be estimated from experimental data this is usually much more difficult than for black box models only intended to mimic a given input output behavior the output of knowledge based models is almost always nonlinear in their parameters so that linear least squares cannot be used and analytical solutions for the model equations are seldom available moreover since the parameters have some physical meaning it is not enough to find some numerical values of these quantities that are such that the model fits the data reasonably well one would like for instance to make sure that the parameters to be estimated are identifiable if this is not the case all equivalent solutions should be provided the uncertainty in the parameters resulting from the measurement noise and approximate nature of the model should also be characterized this paper describes how guaranteed methods based on interval analysis may contribute to these tasks examples in linear and nonlinear compartmental modeling widely used in biology are provided

an efficient adaptive boundary algorithm to reconstruct neumann boundary data in the mfs for the inverse stefan problem abstract in this exposition a simple practical adaptive algorithm is developed for efficient and accurate reconstruction of neumann boundary data in the inverse stefan problem which is a highly nontrivial task primarily this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the inverse stefan problem efficiently to deal with the ill conditioning of the matrix generated by the mfs we use tikhonov regularization and the algorithm is designed in such a way that the optimal regularization parameter is detected automatically without any use of traditional methods like the discrepancy principle the l curve criterion or the generalized cross validation gcv technique furthermore this algorithm can be thought of as an alternative to the concept of beck s future temperatures for obtaining stable and accurate fluxes but without it being necessary to specify data on any future time interval a matlab code for the algorithm is discussed in more than usual detail we have studied the effects of accuracy and measurement error random noise on both optimal location and number of source points the effectiveness of the proposed algorithm is shown through several test problems and numerical experiments indicate promising results

an easy design for interval observers this paper deals with the problem of interval estimation the proposed approach is based on the use of successive derivatives in continuous time or forward measurements in discrete time in an alg

parallelotopic and practical observers for non linear uncertain systems for a class of dynamical systems with uncertain non linear terms considered as unknown inputs we give suffcient conditions for observability we show also that there does not exist any exact observer independent of the unknown inputs under the additional assumption that the uncertainty is bounded we build practical observers whose error converges exponentially towards an arbitrarily small neighbourhood of the origin under the hypothesis that bounds are available for the uncertain terms we build parallelotopic observers providing time varying bounds for the state variables even when the system is not observable for unknown inputs these results are illustrated with a biological model of a structured population

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

a set valued ekeland s variational principle in vector optimization this paper deals with ekeland s variational principle for vector optimization problems by using a set valued metric a set valued perturbed map and a cone boundedness concept based on scalarization we introduce an original approach to extending the well known scalar ekeland s principle to vector valued maps as a consequence of this approach we obtain an ekeland s variational principle that does not depend on any approximate efficiency notion this result is related to other ekeland s principles proved in the literature and the finite dimensional case is developed via an varepsilon efficiency notion that we introduced in math methods oper res 64 2006 pp 165 185 siam j optim 17 2006 pp 688 710

an effective method to interval observer design for time varying systems an interval observer for linear time varying ltv systems is proposed in this paper usually the design of such observers is based on monotone systems theory monotone properties are hard to satisfy in many situations to overcome this issue in a recent work it has been shown that under some restrictive conditions the cooperativity of an ltv system can be ensured by a static linear transformation of coordinates however a constructive method for the construction of the transformation matrix and the observer gain making the observation error dynamics positive and stable is still missing and remains an open problem in this paper a constructive approach to obtain a time varying change of coordinates ensuring the cooperativity of the observer error in the new coordinates is provided the efficiency of the proposed approach is shown through computer simulations

robust interval observers for global lipschitz uncertain chaotic systems abstract in this paper we develop and apply a robust interval observer to estimate the unknown variables of uncertain chaotic systems we consider that bounds of the uncertainties are known and propose an observer that computes guaranteed upper and lower bounds for the unknown variables we show that the proposed observer converges asymptotically toward a bounded error leading to an original scheme of observer based synchronization the method is applied to the estimation of the variables of chua s chaotic system