set inversion via interval analysis for nonlinear bounded error estimation abstract in the context of bounded error estimation one is interested in characterizing the set of all the values of the parameters to be estimated that are consistent with the data in the sense that the errors between the data and model outputs fall within prior bounds while the problem can be considered as solved when the model output is linear in the parameters the situation is far less advanced in the general nonlinear case in this paper the problem of nonlinear bounded error estimation is viewed as one of set inversion an original algorithm is proposed based upon interval analysis that makes it possible to characterize the feasible set for the parameters by enclosing it between internal and external unions of boxes the convergence of the algorithm is proved and the algorithm is applied to two test cases the results obtained are compared with those provided by signomial analysis

system identification regime switching unmodeled dynamics and binary sensors abstract this paper is concerned with persistent system identification for plants that are equipped with binary sensors whose unknown parameter is a random process represented by a markov chain we treat two classes of problems in the first class the parameter is a stochastic process modeled by an irreducible and aperiodic markov chain with transition rates sufficiently faster than adaptation rates of identification algorithms in this case an averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and can be estimated with empirical measures upper and lower error bounds are established that explicitly show impact of unmodeled dynamics in the second class of problems the state switches values infrequently a moving window maximum a posterior map algorithm is introduced for tracking the time varying parameters numerical results are presented to illustrate the tracking performance of the map algorithm and compare it with the widely used viterbi algorithm

arma parameter estimation using a novel recursive estimation algorithm with selective updating the authors investigate an extension of a recursive estimation algorithm the so called optimal bounding ellipsoid or obe algorithm which features a discerning update strategy in particular an extension of the algorithm to arma autoregressive moving average parameter estimation is presented along with a convergence analysis the extension is similar to the extended least squares els algorithm however the convergence analysis is complicated due to the discerning update strategy which incorporates an information dependent updating factor the virtues of such an update strategy are more efficient use of the input data in terms of information processing and a modular adaptive filter structure which would facilitate the development of a parallel pipelined signal processing architecture it is shown that if the input noise is bounded and the moving average parameters satisfy a certain magnitude bound then the a posteriori prediction errors are uniformly bounded with an additional persistence of excitation condition the parameter estimates are shown to converge to a neighborhood of the true parameters and the a priori prediction errors are shown to be asymptotically bounded simulation results show that the parameter estimation error for the eobe algorithm is comparable to that for the els algorithm

a minimax chebyshev estimator for bounded error estimation we develop a nonlinear minimax estimator for the classical linear regression model assuming that the true parameter vector lies in an intersection of ellipsoids we seek an estimate that minimizes the worst case estimation error over the given parameter set since this problem is intractable we approximate it using semidefinite relaxation and refer to the resulting estimate as the relaxed chebyshev center rcc we show that the rcc is unique and feasible meaning it is consistent with the prior information we then prove that the constrained least squares cls estimate for this problem can also be obtained as a relaxation of the chebyshev center that is looser than the rcc finally we demonstrate through simulations that the rcc can significantly improve the estimation error over the cls method

maximum likelihood estimators and worst case optimal algorithms for system identification abstract for system identification problems with stochastic noise maximum likelihood estimators are frequently used if noise is deterministic worst case optimal algorithms should be considered in this paper we study the following problem under what circumstances are maximum likelihood estimators optimal in the worst case

parameter estimation algorithms for a set membership description of uncertainty abstract the problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements the model and the error description two different approaches are reviewed and compared in this paper the first one based on a recursive parameter ellipsoidal bounding algorithm the other on an orthotopic bounding set obtained by solving linear programming problems the original ellipsoidal algorithm modified for higher efficiency has been compared with the linear programming method although the orthotopic description may result in a more accurately defined parameter region it is time consuming when a large number of measurements is present conversely the ellipsodal bounding algorithm often provides a loose approximation to the parameter region but allows a fast data preprocessing producing a smaller number of constraints that can be subsequently fed to the linear programming algorithm a combined use of the two procedures is outlined and tested on simulated and real data the latter being relative to the tuning of an a d converter resulting in a remarkable reduction in the computing time

universal role of correlation entropy in critical phenomena in statistical physics if we divide successively an equilibrium system into two parts we will face a situation that to a certain length the physics of a subsystem is no longer the same as the original one the extensive property of the thermal entropy s a boolean or b s a s b is then violated this observation motivates us to introduce a concept of correlation entropy between two points as measured by the mutual information in information theory to study the critical phenomena a rigorous relation is established to display some drastic features of the non vanishing correlation entropy of a subsystem formed by any two distant particles with long range correlation this relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena we also verify these analytical studies in terms of two well studied models for both the thermal and quantum phase transitions the two dimensional ising model and the one dimensional transverse field ising model therefore the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory

optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors the problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed the measurements are assumed to be corrupted by an unknown but bounded additive noise the sampling design assumes that the number of samples is unconstrained and no replication is allowed two main results are shown 1 for particular classes of linear models the optimal number of measurements is equal to the number of parameters as in the statistical context 2 the uncertainty intervals of the parameter estimates are bounded from above by quantities that can be computer a priori knowing only the model and the error structure

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

nonlinear system identification via direct weight optimization a general framework for estimating nonlinear functions and systems is described and analyzed in this paper identification of a system is seen as estimation of a predictor function the considered predictor function estimate at a particular point is defined to be affine in the observed outputs and the estimate is defined by the weights in this expression for each given point the maximal mean square error or an upper bound of the function estimate over a class of possible true functions is minimized with respect to the weights which is a convex optimization problem this gives different types of algorithms depending on the chosen function class it is shown how the classical linear least squares is obtained as a special case and how unknown but bounded disturbances can be handled most of the paper deals with the method applied to locally smooth predictor functions it is shown how this leads to local estimators with a finite bandwidth meaning that only observations in a neighborhood of the target point will be used in the estimate the size of this neighborhood the bandwidth is automatically computed and reflects the noise level in the data and the smoothness priors the approach is applied to a number of dynamical systems to illustrate its potential

blow up of h1 solution for the nonlinear schrodinger equation we consider the blow up of the solution in h1 for the following nonlinear schrodinger equation i tu u u p 1u x rn t 0 u 0 x u0 x x rn t 0 where n 2 and 1 4 n p min n 2 n 2 5 we prove that if the initial data u0 in h1 are radially symmetric and have negative energy then the solution of in h1 blows up in finite time we do not assume that xu0 l2 and therefore our result is the generalization of the results of glassey 4 and m tsutsumi 18 for the radially symmetric case

minimal mass blow up solutions for the l2 critical nls with inverse square potential abstract we study minimal mass blow up solutions of the focusing l 2 critical nonlinear schrodinger equation with inverse square potential i t u u c x 2 u u 4 n u 0 with n 3 and 0 c n 2 2 4 we first prove a sharp global well posedness result all h 1 solutions with a mass i e l 2 norm strictly below that of the ground states are global note that unlike the equation in free space we do not know if the ground state is unique in the presence of the inverse square potential nevertheless all ground states have the same minimal mass we then construct and classify finite time blow up solutions at the minimal mass threshold up to the symmetries of the equation every such solution is a pseudo conformal transformation of a ground state solution

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

orbital stability of standing waves for a system of nonlinear schrodinger equations with three wave interaction abstract we study the existence and stability of standing waves solutions of a three coupled nonlinear schrodinger system related to the raman amplification in a plasma by means of the concentration compactness method we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent l 2 mass constraints as a consequence we establish existence and orbital stability of solitary waves

a comparison of the entanglement measures negativity and concurrence in this paper we investigate two different entanglement measures in the case of mixed states of two qubits we prove that the negativity of a state can never exceed its concurrence and is always larger than 1 c 2 c2 1 c where c is the concurrence of the state furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

identification for systems with bounded noise in this paper we present a set membership identification algorithm for systems with unknown but bounded disturbance the algorithm contains a weighting factor which is selected according to whether the new observed data contains sufficient information the proposed approach ensures that the estimation error is bounded and nonincreasing furthermore it is shown that the parameter estimates provided by the algorithm will converge to a region containing the true parameters and its upper bound is also given

optimal input design for worst case system identification in l 1 l 2 l abstract in this paper we examine optimal sequences that generate worst case parameters estimation errors in the l 1 l 2 and l norm context for algorithms identifying linear time invariant discrete time finite impulse response systems excited by bounded sequences and with l norm measurement error

adaptive control of arma plants using worst case design by semi infinite optimization this paper presents a new approach to on line control system tuning based on worst case design using semi infinite optimlzation together with a plant uncertainty identification scheme which this approach requires

existence stability of standing waves and the characterization of finite time blow up solutions for a system nls with quadratic interaction abstract we study the existence and stability of standing waves for a system of nonlinear schrodinger equations with quadratic interaction in dimensions d 3 we also study the characterization of finite time blow up solutions with minimal mass to the system under mass resonance condition in dimension d 4 finite time blow up solutions with minimal mass are showed to be up to symmetries pseudo conformal transformations of a ground state standing wave

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

entanglement cost under positive partial transpose preserving operations we study the entanglement cost under quantum operations preserving the positivity of the partial transpose ppt operations we demonstrate that this cost is directly related to the logarithmic negativity thereby providing the operational interpretation for this entanglement measure as examples we discuss general werner states and arbitrary bipartite gaussian states then we prove that for the antisymmetric werner state ppt cost and ppt entanglement of distillation coincide this is the first example of a truly mixed state for which entanglement manipulation is asymptotically reversible which points towards a unique entanglement measure under ppt operations

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

consistent parameter bounding identification for linearly parametrized model sets abstract in standard parameter bounding identification a time domain bound on the noise signal is used to construct parameter bounds one of the properties of this standard approach is that there is no consistency if a conservative noise bound has been chosen it is shown that alternative bounds on the noise signal give rise to consistent parameter bounding identification methods i e asymptotically in the number of data samples the feasible parameter set converges to the true parameter vector the first alternative noise bound that is introduced is a bound on the cross covariance between the noise and some instrumental input signal the noise bound is represented by a small number of linear inequalities which can be used in parameter bounding by linear programming it is shown that there is consistency under fairly general conditions even when a conservative bound has been chosen additionally a procedure is presented to estimate the cross covariance bound from data similar consistency results are shown for two other types of noise bounds a bound on the discrete fourier transform of the noise in combination with sinusoidal excitation and a time domain bound on the noise after measurement averaging with periodic excitation

blowup of h1 solutions for a class of the focusing inhomogeneous nonlinear schrodinger equation abstract we consider a class of focusing inhomogeneous nonlinear schrodinger equation i t u u x b u u 0 u 0 u 0 h 1 r d with 0 b min 2 d and where 4 2 b d and 4 2 b d 2 if d 3 and if d 1 2 in the mass critical case we prove that if u 0 has negative energy and satisfies either x u 0 l 2 or u 0 is radial with d 2 then the corresponding solution blows up in finite time moreover when d 1 we prove that if the initial data not necessarily radial has negative energy then the corresponding solution blows up in finite time in the mass and energy intercritical case we prove the finite time blowup for radial negative energy initial data as well as the finite time blowup below ground state for radial initial data in dimensions d 2 this result extends the one of farah in j evol equ 16 193 208 2016 where the blowup below ground state was proved for data in the virial space h 1 l 2 x 2 d x with d 1

parameter estimation in systems with binary valued observations and structural uncertainties this paper studies identification of linear systems with binary valued observations generated via fixed thresholds in addition to stochastic measurement noises the systems are also subject to structural uncertainties including deterministic unmodelled dynamics nonlinear model mismatch and sensor observation bias since binary valued observations can supply only limited information on the signals truncated empirical measures are introduced to extract further information for system identification an effective identification algorithm is constructed based on the proposed empirical measures optimal identification errors time complexity optimal input design and impact of disturbances unmodelled dynamics observation bias and nonlinear model mismatch are thoroughly investigated in a stochastic information framework asymptotic upper and lower bounds are established on identification errors numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results

two new estimation algorithms for linear models with unknown but bounded measurement noise attention is given to linear systems described by y a sub theta e where the measurement error vector e is unknown but bounded two algorithms for sequential parameter identification are introduced their convergence properties are illustrated and compared with those of existing algorithms a simulation study is carried out using simulated data to investigate the possible practical use of the algorithms their performances are compared with those of other offline algorithms as well as with those of the widely used least squares estimates

brief on robustness and precision of mobile robots missions this paper proposes solutions for the robust achievement of displacement missions by a wheeled mobile robot the considered disturbances are generated by the use of inaccurate configuration estimates as feedback information those errors are characterized in a bounded error context we introduce a trajectory tracking controller whose stability is analysed by a lyapunov function the time derivative of which is negative definite inside a large domain around the zero error this property makes it possible to define a bounded attractive domain around the nominal trajectory quantifying thus the guaranteed precision of the mission the method is extended to a parking non stationary controller and illustrated by a real experiment

identification of systems with regime switching and unmodeled dynamics this paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances and whose unknown parameters switch values possibly large jumps that can be represented by a markov chain two classes of problems are considered in the first class the switching parameters are stochastic processes modeled by irreducible and aperiodic markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms in this case tracking real time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and can be estimated with periodic inputs and least squares type algorithms upper and lower error bounds are established that explicitly show impact of unmodeled dynamics in contrast the second class of problems represents systems whose state transitions occur infrequently an adaptive algorithm with variable step sizes is introduced for tracking the time varying parameters convergence and error bounds are derived numerical results are presented to illustrate the performance of the algorithm

identification of objects with unknown bounded disturbances an identification problem for linear objects with unknown bounded disturbances in both input and output channels is solved the experimental information regarding the identified object has an interval character only the lower and upper boundaries for values of the measured signals are known the region of possible values of the model coefficients that do not contradict experimental information is constructed this region is described by a system of linear inequalities which is investigated by linear programming some additional possibilities for the investigation and control of objects in such situations are discussed

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

probabilistic optimal estimation with uniformly distributed noise the classical approach to system identification is based on stochastic assumptions about the measurement error and provides estimates that have random nature worst case identification on the other hand only assumes the knowledge of deterministic error bounds and establishes guaranteed estimates thus being in principle better suited for the use in control design however a main limitation of such deterministic bounds lies in their potential conservatism thus leading to estimates of restricted use in this paper we propose a rapprochement between the stochastic and worst case system identification viewpoints which is based on the probabilistic setting of information based complexity the main idea in this line of research is to discard sets of measure at most where is a probabilistic accuracy from the set of deterministic estimates therefore we are decreasing the so called worst case radius of information at the expense of a given probabilistic risk in the case of uniformly distributed noise we derive new computational results and in particular we compute a trade off curve called violation function which shows how the radius of information decreases as a function of the accuracy to this end we construct randomized and deterministic algorithms which provide approximations of this function we report extensive simulations showing numerical comparisons between the stochastic worst case and probabilistic approaches thus demonstrating the efficacy of the methods proposed in this paper

brief paper an algorithm for bounded error identification of nonlinear systems based on dc functions this paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded error context this method is based on functions which consists of the difference of two convex functions called dc functions the method considers dc representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements the system and the considered bounded error at each iteration the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent this operation is repeated while the obtained solution is improved four examples are provided to clarify the proposed identification algorithm

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

on estimation of errors caused by non linear undermodelling in system identification the problem of quantifying errors due to non linear undermodelling is addressed in particular the wiener system which consists of a linear dynamic block followed by a static non linearity and the hammerstein system in which the order of these two blocks is reversed are studied in either case it is assumed that the objective is to identify the linear part of the system using a purely linear model these scenarios can be interpreted as linear identification applied to systems where non linearity errors may occur and hence need to be quantified the stochastic embedding approach is therefore applied to capture the on average properties of the undermodelling due to inadequate representation of the non linear effects as compared to previous methods the priors on the covariance matrix of the embedding parameters are reduced as a result an expression for the amplitude error bound of the estimated transfer function that does not require knowledge of the true system parameters is obtained the quality of t

technical communique interval constraint propagation with application to bounded error estimation for a large class of bounded error estimation problems the posterior feasible set s for the parameters can be defined by nonlinear inequalities the set inversion approach combines classical interval analysis with branch and bound algorithms to characterize s unfortunately as bisections have to be done in all directions of the parameter space this approach is limited to problems involving a small number of parameters techniques based on interval constraint propagation make it possible to drastically reduce the number of bisections in this paper these techniques are combined with set inversion to bracket s between inner and outer subpavings union of nonoverlapping boxes when only interested in the feasible intervals for the parameters the set inversion approach becomes inefficient and a new algorithm able to compute these intervals is given this algorithm uses a new interval based local research to compute the smallest box that contains s it is then compared with existing methods on an example taken from the literature

projection based bayesian recursive estimation of arx model with uniform innovations abstract autoregressive model with exogenous inputs arx is a widely used black box type model underlying adaptive predictors and controllers its innovations stochastic unobserved stimulus of the model are white zero mean with time invariant variance mostly the innovations are assumed to be normal it induces least squares as the adequate estimation procedure the light tails of the normal distribution allow one to accept the unbounded support as a reasonable approximate description of bounded physical quantities in some cases however this approximation is too crude or does not fit subsequent processing for instance robust control design then techniques that deal with unknown but bounded equation errors are used more often than not these techniques give up a stochastic interpretation of innovations and develop estimation algorithms of a min max type the paper assumes bounded innovations but stays within the standard bayesian estimation framework by assuming uniformly distributed innovations the posterior probability density function pdf is first described and approximated by a pdf with a fixed dimensional statistic consequently the estimation can run in real time moreover its limited memory allows for tracking time varying parameters in this manner an alternative to popular forgetting techniques is also obtained the paper provides a complete algorithmic solution and illustrates its behavior

slide window bounded error time varying systems identification this technical note presents a new identification method for discrete linear systems with time varying parameters based on bounded error approach it is assumed a bounded additive error on measurements and a bound on parameter variation each time instant the identification method uses a slide window along historical data and an explicit expression to provide an outer bound of the set of model parameters that is consistent with measurements model structure and bounds on error and variations considered furthermore the center estimation of the obtained outer solution set is a suitable nominal estimation of the parameters this center is the optimal solution of a least squares problem that penalizes the prediction error of the model and the parameter variations the explicit expression that provides the outer bound of the parameters and the optimal property of the center estimation are the main contributions of the technical note in order to clarify the proposed method an application example and a comparison with a previous recursive bounded error method are included

entropy energy and negativity in fermi resonance coupled states of substituted methanes several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities the dynamics of entropy energy and negativity is studied for fermi resonance coupled vibrations in substituted methanes with three kinds of initial mixed states which are the mixed density matrices of binomial states thermal states and squeezed states on two vibrational modes respectively it is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti correlated in the same oscillatory frequency so do the energies for each kind of state with small magnitudes whereas the entropies exhibit positive correlations with the corresponding energies furthermore for small magnitudes quantum mutual entropy is positively correlated with the interacting energy analytic forms of entropies and energies are provided with initial conditions in which they are stationary and the agreement between analytic and numerical simulations is satisfactory the dynamical entanglement measured by negativity is examined for those states and conditions it is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes and the time averaged negativity has the minimal value under the conditions of stationary entropies and energies moreover negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes those are useful for molecular quantum information processing and dynamical entanglement

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

parameter bounds for armax models from records with bounded errors in variables the errors in variables problem is that of parameter estimation where all observed variables are corrupted by noise so far the computation of parameter bounds for dynamical models has been performed using equation error and output error approaches in this paper parameter bounds for autoregres sive moving average exogenous armax models are derived on the assumption that both input and output are affected by bounded noise parameter bounding by both the bounded equation error and the bounded errors in variables approach is outlined together with the approximation of the feasible parameter region by an orthotope outer bounding set and is tested on simulated data

persistent identification of time varying systems identification of time varying systems especially slowly time varying systems is of importance in the development of a comprehensive theory of adaptation the persistent identification measures employed in this paper capture a main characterization in such identification problems namely one input signal must be used for identification of all possible observation windows this paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation 1 they have computable upper and lower bounds for typical classes of prior uncertainty sets 2 any full rank n periodic signals are optimal and the simple least squares estimates are optimal identification algorithms 3 optimal probing inputs can be approximately generated in a closed loop configuration when the plant and the controller are slowly time varying and 4 n periodic signals are asymptotically optimal for slowly time varying systems the main results of this paper have been successfully combined with a certain slow h sup spl infin design to derive an adaptive stabilization scheme

identification of parameter bounds for armax models from records with bounded noise the computation of bounds on the parameters rather than point estimates and covarianccs is considered for autoregressive moving average exogenous armax models the bounds derive from observations affected by bounded noise the influence of noise structure on the performance of the best known parameter bounding algorithm is examined a problem analogous to the bias in least squares estimates when regressors and noise are mutually correlated is also found to arise in parameter bounding an explanation is offered and the possibility of armax parameter bounds being non convex is pointed out

optimal inner bounds of feasible parameter set in linear estimation with bounded noise some problems arising in parameter estimation theory with unknown but bounded measurement errors are discussed in this theory a key role is played by the feasible parameter set i e the set of all parameter values consistent with the system model and the error bounds if a linear relationship between parameters and measurements is assumed this set is a polytope an exact representation of this polytope may be too complex for practical use and approximate descriptions in terms of simple shaped sets contained in the feasible parameter set inner bounds have shown to be useful in several applications balls in l sub infinity norms boxes l sub 2 norms ellipsoids and l sub 1 norms diamonds are used as bounding sets results are given on the computation of maximal balls when their shape is either known or partially free a numerical example is given in which the results of a computation of inner boxes of fixed shape and fixed orientation are given and compared

a convex analytic approach to system identification this paper introduces a new concept for system identification in order to account for random and nonrandom deterministic set membership uncertainties while random stochastic models are natural for modeling measurement errors nonrandom uncertainties are well suited for modeling parametric and nonparametric components the new concept introduced is distinct from earlier concepts in many respects first inspired by the concept of uniform convergence of empirical means developed in machine learning theory we seek a stronger notion of convergence in that the objective is to obtain probabilistic uniform convergence of model estimates to the minimum possible radius of uncertainty second the formulation lends itself to convex analysis leading to description of optimal algorithms which turn out to be well known instrument variable methods for many of the problems third we characterize conditions on inputs in terms of second order sample path properties required to achieve the minimum radius of uncertainty finally we present fundamental bounds and optimal algorithms for system identification for a wide variety of standard as well as nonstandard problems that include special structures such as unmodeled dynamics positive real conditions bounded sets and linear fractional maps

analysis of finite precision effects on a recursive set membership parameter estimation algorithm analysis of error propagation in an optimal bounding ellipsoid obe algorithm is performed which shows that the errors in the estimates due to an initial perturbation are bounded simulation results demonstrate that the obe algorithm can perform better than the conventional recursive least squares rls in small wordlength environments the analysis presented could also be applied for the finite precision analysis of recursive weighted least squares algorithms

weighted least squares set estimation from l sub spl infin norm bounded noise data the problem of parameter set estimation from pointwise bounded error data is considered the possibilities of employing l sub 2 projection procedures to solve the problem are explored and exact as well as approximate outer bounding solutions are proposed in particular the properties of weighted least squares set estimation in this l sub spl infin norm bounded error context and the implementation of a resulting minimum volume parallelotope bounding algorithm are discussed

identification and prediction propagation of uncertainty in models with bounded noise abstract the identification of measurement parametric and structural model uncertainty is considered for models from observations with bounded noise a min max estimate for the upper bound of the structural model uncertainty is presented the propa gation of the parametric and structural model uncertainty as a result of the obser vation uncertainty bounds to the model prediction error is examined a simple water quality model is used to illustrate the different steps

identification of nonlinear systems in the presence of unknown but bounded disturbances this paper deals with recursive parameter estimation of nonlinear systems in the presence of unknown but bounded disturbances the proposed technique is performed by the use of a modified extended least squares algorithm so that the estimated parameters are consistent with the measurements and the noise constraints while local asymptotic convergence under very general conditions is assured one of the main features is to show from the stability analysis connection between some arbitrary factors and basin of attraction high performances from the design and implementation point of view will be shown through a numerical example under severe conditions

optimality of central and projection algorithms for bounded uncertainty this paper investigates optimality properties of central and projection algorithms for linear problems in the field of system identification in a context in which uncertainty is described in a deterministic rather than statistical way particular attention is devoted to least squares algorithms when the measurement noise is assumed to be unknown but bounded in a hilbert norm a major contribution of this paper consists in proving that least squares algorithms enjoy strong optimality properties on the contrary it is pointed out that these properties do not hold for other frequently used projection algorithms such as least absolute values or minimax algorithms corresponding to a description of the measurement error in h or l norm respectively

model quality evaluation in set membership identification abstract identification from corrupted input output measurements of systems that do not necessarily belong to the model class used is investigated this leads to a nonstandard set membership sm identification problem the goodness of different model classes is measured by the conditional radius of information a generalization of the radius in standard sm identification theory giving a measure of the minimal worst case modeling error upper and lower bounds on the radius are derived for linearly parameterized model classes specific formulas for the upper and lower bounds are given for the case of h 2 identification of exponentially stable systems in the presence of powerbounded noise the bounds are shown to coincide with the conditional radius when the model space dimension is equal to the number of output measurements an almost optimal identification algorithm is derived giving identification error within the range of the derived bounds

estimation theory for nonlinear models and set membership uncertainty this chapter studies the problem of estimating a given function of a vector of unknowns called the problem element by using measurements depending non linearly on the problem element and affected by unknown but bounded noise assuming that both the solution sought and the measurements depend polynomially on the unknown problem element a method is given to compute the axis aligned box of minimal volume containing the feasible solution set i e the set of all unknowns consistent with the actual measurements and the given bound on the noise the center of this box is a point estimate of the solution which enjoys useful optimality properties the sides of the box represent the intervals of possible variation of the estimates important problems like parameter estimation of exponential models time series prediction with arma models and parameter estimates of discrete time state space models can be formalized and solved by using the developed theory

estimation of model quality this paper provides an introduction to recent work on the problem of quantifying errors in the estimation of models for dynamic systems this is a very large field we therefore concentrate on approaches that have been motivated by the need for reliable models for control system design this will involve a discussion of efforts that go under the titles of estimation in th worst case estimation estimation in l1 and stochastic embedding of undermodelling a central theme of this survey is to examine these new methods with reference to the classic bias variance tradeoff in model structure selection

properties of least squares estimates in set membership identification the properties of the least square algorithm in the identification of linear time invariant discrete time systems in the presence of unknown but bounded errors are investigated it is known that the least squares algorithm enjoys strong optimality properties in the case of power bounded l 2 errors while it may be far from optimal in the case of pointwise l bounded errors exact expressions of the local and global worst case errors of the least squares estimates are derived using these results general conditions assuring convergence to zero of the global worst case error are given it is also shown that the least squares algorithm may be optimal in l 1 and l identification of fir systems with pointwise bounded errors

a state set estimation algorithm for linear systems in the presence of bounded disturbances this paper concerns the problem of state set estimation for discrete time linear systems the linear system is given in state space form and the system s uncertainty is described by bounded scalar variations we present a recursive algorithmic procedure of computing guaranteed estimated state sets in particular a polyhedron variation algorithm is presented the new algorithm is based on linear programming and sensitivity analysis techniques for improved computational efficiency and practicability

time complexity and model complexity of fast identification of continuous time lti systems the problem of fast identification of continuous time systems is formulated in the metric complexity theory setting it is shown that the two key steps to achieving fast identification i e optimal input design and optimal model selection can be carried out independently when the true system belongs to a general a priori set these two optimization problems can be reduced to standard gel fand and kolmogorov n width problems in metric complexity theory it is shown that although arbitrarily accurate identification can be achieved on a small time interval by reducing the noise signal ratio and designing the input carefully identification speed is limited by the metric complexity of the a priori uncertainty set when the noise signal ratio is fixed

logarithmic negativity a full entanglement monotone that is not convex it is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation a set of operations that incorporate local operations and classical communication as a subset and in the process a further proof is provided that the negativity does not increase on average under the same set of operations given that the logarithmic negativity is not a convex function this result is surprising as it is generally considered that convexity describes the local physical process of losing information the role of convexity and in particular its relation or lack thereof to physical processes is discussed and importance of continuity in this context is stressed

recursive computation of inner bounds for the parameters of linear models minimum volume ellipsoidal outer bounds on the parameters of linear regression type models with bounded model output error can be computed by an established algorithm a complementary algorithm to compute maximum volume ellipsoidal inner bounds is derived it is little more complicated than the existing outer bounding algorithm in conjunction with that algorithm it allows parameter values to be classified as acceptable dubious or unacceptable it is also found to be effective in determining output error bounds by trial and error during development of parameter bounding models

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

h sub spl infin identification and model quality evaluation set membership h sub spl infin identification is investigated using time domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors the problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error called radius of information is solved for classes of models affine in the parameters the radius of information is obtained as function of the h sub spl infin norm of the unmodeled dynamics a method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics thus allowing the actual evaluation of the radius of information the radius represents a measure of the predictive ability of the considered class of models and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part the effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection

parameter identification for models with bounded errors in all variables in this paper the problem of parameter identification for models with bounded measurement errors both on the input and on the output is addressed and some corrections to previously published results are presented in particular it is shown that only parameter overbounds can in general be computed for systems of the form y y when the bounded measurement errors and y are correlated since armax and bilinear systems can be represented in this form it turns out that tight parameter bounds are in general not available for these systems finally we show that it is possible to check a posteriori whether the obtained bounds are tight or not

entropy correlation and entanglement for mixed states in an algebraic model as an alternative with potential connections to actual experiments other than the systems more usually used in the field of entanglement the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well established algebraic model with parameters extracted from fitting to highly excited spectral experimental results for molecules h2o and so2 is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode for a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti correlation and the linear entropy of each mode is positively correlated with the negativities just for the mixed squeezed states with small parameters in h2o while they do not display any correlation in other cases for the mixed squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy the differences in the linear entropy and the negativities between h2o and so2 are discussed as well those are useful for molecular quantum computing and quantum information processing

feasible parameter set for linear models with bounded errors in all variables abstract when all observed variables of a model are affected by noise parameter estimation is known as the errors in variables problem while parameter bounding methods and algorithms have been extensively developed in the case of exactly known regressor variables little attention has been paid to the bounded errors in variables problem in this paper a formal proof of a previous result on the description of the feasible parameter region for linear models in the presence of bounded errors in all variables is given topological features of the feasible parameter region such as convexity and connectedness are also discussed

a modified ew els algorithm for system with bounded disturbances inclusion abstract this paper presents a new estimation algorithm which is essentially a modification of the exponentially weighted recursive least squares algorithm ew rls for systems with bounded disturbances assuming knowledge of a disturbance upper bound the algorithm s derivation is performed by minimizing a cost function weighted by two factors one is fixed by the user and exponentially weights the arriving information the other is time varying and data dependent the purpose of the latter is to ensure algorithm stability faced with the bounded disturbances from this proposal results a very simple algorithm which completely depends on the significant information and stops when the data are meaningless it is also shown that if the signals are persistently exciting the convergence of the algorithm is exponentially fast an application of the algorithm to the problem of estimating the friction forces in servo mechanisms under structural bounded errors is also presented

critical behaviors of mutual information in the one dimensional spin 1 bilinear biquadratic model the critical behaviors of the mutual information in the one dimensional spin 1 bilinear biquadratic model are studied it is found that all the quantum phase transition points including the order disorder ones and the infinite order ones in the system can be quantified from the singularity analysis of the mutual information of two sites with the longest distance because the mutual information captures the correlation properties about the critical fluctuations more interestingly the special structure of the wavefunction and the special symmetric property of the system can be indicated by the entropy correlation behaviors the finite size scaling laws of the mutual information and its derivative are also studied