the dual ghr zeros and residues abstract the dual generalized hessenberg representation dual ghr is a canonic form for single input single output systems which identifies the input output properties of the system here it is shown how the dual ghr can be used to identify almost pole zero cancellations and small residues of the corresponding poles this connection between the state space representation and transfer function is established using geometrical arguments near unobservability and near uncontrollability measures relying on angles between subspaces play a key role

an adaptive tracking problem with a control input constraint abstract in this paper we consider the problem of controlling an uncertain linear time invariant lti continuous time plant when there is a control input constraint a switching controller is presented which will carry out asymptotic error regulation for constant reference and constant disturbance signals which are compatible with the control input constraint assuming that i the plant is asymptotically stable ii the plant has no transmission zeros at zero and iii the plant has as many inputs as outputs this controller is quite easy to implement especially in the single input single output siso case and is noise tolerant some examples including a model of a three input three output distillation column are included to illustrate the controller behaviour

a multivalued generalization of hick s c contraction in this paper a coincidence point theorem for multivalued mappings in probabilistic metric spaces is proved

model reference adaptive control of time varying and stochastic systems the adaptive control of general delay linear time varying systems is addressed a simple model reference adaptive control law is devised it does not require a priori knowledge of the sign of the high frequency gain this control law coupled with the parameter estimation equations allows a simple representation of the closed loop system this greatly eases the stability and performance analysis and has potential for generalization to adaptive pole placement and other control laws suitable for nonminimum phase systems for the kalman filter parameter estimator coupled with this control law stability is obtained without persistence of excitation or knowledge of the sign of the high frequency gain performance results for the extended least squares algorithm are described

brief low gain integral control of continuous time linear systems subject to input and output nonlinearities continuous time low gain integral control strategies are presented for tracking of constant reference signals for finite dimensional continuous time asymptotically stable single input single output linear systems subject to a globally lipschitz and non decreasing input nonlinearity and a locally lipschitz non decreasing and affinely sector bounded output nonlinearity both non adaptive but possibly time varying and adaptive integrator gains are considered in particular it is shown that applying error feedback using an integral controller ensures asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is ultimately sufficiently small and c the reference value is feasible in a very natural sense the classes of actuator and sensor nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone

deinterleaving pulse trains using discrete time stochastic dynamic linear models pulse trains from a number of different sources are often received on the one communication channel it is then of interest to identify which pulses are from which source based on different source characteristics this sorting task is termed deinterleaving the authors propose time domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival toa and pulse energy if available of the pulses received on the one communication channel they formulate the pulse train deinterleaving problem as a stochastic discrete time dynamic linear model dlm the discrete time variable k being associated with the kth received pulse the time varying parameters of the dlm depend on the sequence of active sources the deinterleaving detection estimation task can then be done optimally via linear signal processing using the kalman filter or recursive least squares when the source periods are constant and tree searching the optimal solution however is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length the authors propose and study two of a number of possible suboptimal solutions 1 forward dynamic programming with fixed look ahead rather than total look ahead as required for the optimal scheme 2 a probabilistic teacher kalman filtering for the detection estimation task

convergence of the generalized dual control algorithm in this paper the convergence properties of the generalized dual controller proposed by chan and zarrop 1985 are analysed using the martingale convergence theory we present solutions for global stability of the algorithm strong consistency of the estimates and their convergence rate it is demonstrated that the passivity of two time varying operators and strict passivity of at least one of them is sufficient for global stability of the algorithm in the context of the attenuating excitation technique we show that under certain conditions related to the properties of the optimal regulator and order of the adaptive regulator the regression vector satisfies the persistency exciting condition bearing this in mind we derive a relation describing the convergence rate of the parameter estimates

recursive algorithm for the computation of the h sup infinity norm of polynomials a recursive algorithm for computing the h sup infinity norm of polynomials is developed the algorithm is shown to converge monotonically and the convergence rate is also established some examples are presented to illustrate the algorithm

robustness of adaptive control for stochastic systems robustness of the stochastic adaptive systems with unmodelled dynamics and external disturbances is discussed in this paper an adaptive controller is designed using the els algorithm except for the finite switches it is shown that the closed loop system is globally stable both the estimation error and the tracking error approach their minima when the unmodelled dynamics diminish that is the asymptotically adaptive system operating with the els algorithm has a good robustness with respect to unmodelled dynamics and external disturbances

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

local stabilization of linear systems under amplitude and rate saturating actuators this note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation considering the actuator represented by a first order system subject to input and state saturation a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stability results from this condition an algorithm based on the iterative solution of linear matrix inequalities based problems is proposed in order to compute the control law

floating point arithmetic and digital filters the roundoff noise properties of floating point digital filters are examined to make the analysis tractable a high level model to deal with the errors in the inner product operation is developed this model establishes a broad connection between coefficient sensitivity and roundoff noise along with the model an efficient procedure to keep track of the addition scheme used in the inner product and to compute the statistics of the errors is introduced a systematic procedure based on the model is then developed to derive general expressions for the roundoff noise of fir direct form iir and state space filters the expressions in the context of state space filters are explored in some detail optimality issues are considered and it is shown that when double precision accumulation is used the optimal filters are similar in nature to those derived in the context of fixed point arithmetic with the essential difference that they also do depend on the spectrum of the input signal optimality with respect to addition schemes and second order filters are also examined in some detail

low roundoff noise and normal realizations of fixed point iir digital filters explicit design and performance equations are given in terms of the parameters of the desired transfer function h z for two classes of realizations these realizations offer the digital circuit designer an alternative to the usual designs based on direct forms in addition to low roundoff noise these new realizations offer other desirable properties such as low coefficient sensitivities and freedom from overflow oscillations numerical results are presented which detail the design process and verify the theory

robustness analysis of identification and adaptive control for stochastic systems abstract this paper gives a preliminary robustness analysis for stochastic systems with unmodelled dynamics the extended least squares algorithm and stochastic adaptive control for tracking are defined on the basis of the modelled part of the system and it is shown that the parameter estimate is closed to the true one and the tracking error is small if the unmodelled dynamics is small

a robust stochastic adaptive controller the adaptive tracking problem is considered for discrete time stochastic systems consisting of a modeled part being a stable armax process and unmodeled dynamics dominated by a small constant epsilon multiplied by a quantity independent of epsilon but tending to infinity as the past input output and noise grow the adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant sigma it is shown that the closed loop system is globally stable the estimation errors for parameters contained in the modeled part of the order epsilon and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of o epsilon sup 2 o sigma sup 2

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

on robust aml identification algorithms abstract strong consistency results for a class of nonlinear approximate maximum likelihood algorithms for robust system identification are developed where the system is assumed to be of the armax form the analysis uses the martingale results and strong consistency is shown to hold under a new assumption representing a generalization of the strictly positive real condition arguments are also given for using huber s nonlinearity in order to reduce the influence of outliers in practice

adaptive stabilization of unstable and nonminimum phase stochastic systems abstract the system under consideration is the discrete time stochastic system a z yn zb z un wn driven by a martingale difference sequence wn where a z are polynomilas in backward shift operator z with unknown coefficients and both a z and b z may be unstable with the purpose of demonstrating theoretical possibility rather than designing a practically applicable control law this paper constructs an adaptive control that stabilizes the system and simultaneously guarantees strong consistency of the least squares estimates for unknown coefficients

adaptive one step ahead control subject to an input amplitude constraint this paper investigates the adaptive control of a single input single output process when there exists a constraint on the amplitude of the applied control signal in particular an adaptive control scheme is proposed and is shown to be globally convergent in the sense that the control asymptotically matches the amplitude constrained one step ahead optimal control some simulation results are presented to demonstrate the performance of the scheme

principal components algorithms for arma spectrum estimation principal components algorithms are presented for the problem of fitting an arma model to a given segment of a sample sequence of a discrete time stochastic process and the model is used to estimate the process power spectrum to reduce the effects of finite wordlength errors balanced state pace parameterization of the arma model is used instead of the more popular difference equation parameterization model identification is formulated as a problem of selecting a partial state to span approximately an apparently large dimensional information interface between the past and the future of the process different criteria are used to measure the quality of the approximation which leads to principal components algorithms for the problem that are based on singular value decomposition

consistent order estimation for linear stochastic feedback control systems carma model abstract a new criterion cic is introduced to estimate orders p0 q0 r0 of the linear stochastic feedback control system with correlated noise described by a carma model it is proved that the estimate is strongly consistent when the upper bounds for p0 q0 and r0 are available but neither the stability condition nor the ergodicity of the input and output are imposed on the system

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

analysis of coefficient quantization errors in state space digital filters in this paper we examine the sensitivity of state space digital filters to coefficient quantization errors a cost function using an l p norm criteria is used to measure the deviation in frequency response of the filter the cost function is used to indicate the connection between roundoff noise and filter sensitivity to coefficient quantization errors then based on this cost function it is shown that low roundoff noise state space digital filters filters in balanced coordinates and filters based on polynomials orthogonal on the unit circle have low sensitivity to coefficient quantization errors furthermore the sensitivity of the filters is shown to depend on the second order modes thereby exhibiting certain robustness and immunity to filter bandwidth

robust estimation without positive real condition the strictly positive real spr condition on the noise model is necessary for a discrete time linear stochastic control system with unmodeled dynamics even so for a time invariant armax system in the past robust analysis of parameter estimation however this condition is hardly satisfied for a high order and or multidimensional system with correlated noise the main work in this paper is to show that for robust parameter estimation and adaptive tracking as well as closed loop system stabilization the spr condition is replaced by a stable matrix polynomial the main method is to design a two step recursive least squares algorithm with or without a weighted factor and with a fixed lag regressive vector and to define an adaptive control with bounded external excitation and with randomly varying truncation

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

direct adaptive decoupling control for general stochastic multivariable systems this paper presents a novel adaptive decoupling controller for general stochastic multivariable systems with arbitrary time delay structure the decoupling controller is constructed using a diagonal dynamic precompensator to diagonalize the system interactor matrix and then combining the feedforward control strategy and the generalized minimum variance approach it cannot only control unstable and or non minimum phase processes but also decouple the closed loop systems both dynamically and in the static state it is adaptively implemented in direct form the global convergence properties and parameter estimate consistency for this adaptive decoupling algorithm are also discussed it is shown that this adaptive controller not only has globally convergent properties but also generates strongly consistent parameter estimates the results of simulations and an application are proposed to demonstrate the effectiveness of the algorithm

self convergence of weighted least squares with applications to stochastic adaptive control a recursive least squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self convergence property i e it converges to a certain random vector almost surely irrespective of the control law design such algorithms enjoy almost the same nice asymptotic properties as the standard least squares this universal convergence result combined with a method of random regularization then easily can be applied to construct a self convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive moving average with exogenous input armax systems as an application we give a simple solution to the well known stochastic adaptive pole placement and linear quadratic gaussian lqg control problems in the paper

measures of controllability and observability and residues the relationship between two measures of controllability and observability is derived given a linear time invariant system both of the measures are based on angles between various subspaces of the state space it is shown that these measures can be used to bound the norm of the residues of the transfer function

improved l sub 2 sensitivity for state space digital system an improved l sub 2 sensitivity measure for linear state space digital systems is presented it gives a more precise evaluation of the transfer function deviation spl delta h z between the infinite wordlength system and the finite wordlength system when the structure matrices a b c contain 0 and spl plusmn 1 coefficients this measure can be applied in the system optimization resulting in a computationally efficient and very low l sub 2 sensitivity structure the theoretical result is verified by a numerical example

the effect of identifier structure on parameter convergence the effects of a chosen system structure on the identification of its parameters are considered in particular convergence rates are compared for the parameters of three state space structures direct form ii parallel and dual generalized hessenberg representation structures it is shown that the chosen structure does influence identification algorithms and that this influence is measured by examining the information contained in the structural parameters a conjecture about the relative convergence of the parameters is offered and evidence in its support is provided an important result is that identification of the usually identified direct from ii parameters the standard arma parameters does not necessarily yield the fastest parameter convergence for the system being identified

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

posterior sampling based reinforcement learning for control of unknown linear systems we propose a posterior sampling based learning algorithm for the linear quadratic lq control problem with unknown system parameters the algorithm is called posterior sampling based reinforcement learning for lq regulator psrl lq where two stopping criteria determine the lengths of the dynamic episodes in posterior sampling the first stopping criterion controls the growth rate of episode length the second stopping criterion is triggered when the determinant of the sample covariance matrix is less than half of the previous value we show under some conditions on the prior distribution that the expected bayesian regret of psrl lq accumulated up to time t is bounded by tilde o sqrt t here tilde o cdot hides constants and logarithmic factors numerical simulations are provided to illustrate the performance of psrl lq

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

stable adaptation in the presence of input constraints abstract for a class of linear dynamical systems with unknown parameters a direct model reference adaptive control framework is developed that provides stable adaptation in the presence of input constraints the proposed design methodology termed positive modification has the ability to protect the control law from actuator position saturation the reference system is adaptively modified to ensure global asymptotic tracking for open loop stable systems for unstable systems an estimate for the domain of attraction is derived based on the input saturation magnitude and system parameters simulation of a benchmark example verifies the theoretical statements

optimal adaptive control and consistent parameter estimate for deterministic systems with quadratic cost in this paper an adaptive control is designed for deterministic systems on the basis of the projection algorithm so that the quadratic loss function approaches its minimum at a rate of n e e 0 and the parameter estimate converges to its true value with a near exponential rate

convergence rates of continuous time stochastic els parameter estimation discrete time convergence rates for extended least squares els algorithms are generalized to the continuous time case an essential difference in the estimation is the appropriate prefiltering while in the theory the existence of solutions of the stochastic equations is a concern

identification and adaptive control for systems with unknown orders delay and coefficients an analysis that gives recursive estimates for time delay system orders and coefficients of single input single output linear discrete time deterministic and stochastic systems with uncorrelated noise is presented it is assumed that a lower bound for the time delay and upper bounds for system order are known the optimal adaptive control is designed for both tracking and linear quadratic regulation when the system parameters including time delay orders and coefficients are unknown the rates of convergence are derived the coefficient estimates to their true values and the loss functions to their minima

low gain integral control of well posed linear infinite dimensional systems with input and output nonlinearities abstract time varying low gain integral control strategies are presented for asymptotic tracking of constant reference signals in the context of exponentially stable well posed linear infinite dimensional single input single output systems subject to globally lipschitz nondecreasing input and output nonlinearities it is shown that applying error feedback using an integral controller ensures that the tracking error is small in a certain sense provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the positive gain function t k t is ultimately sufficiently small and not of class l 1 under a weak restriction on the initial data it is shown that a b and c ensure asymptotic tracking if additionally the impulse response of the linear part of the system is a finite signed borel measure the global lipschitz assumption on the output nonlinearity may be considerably relaxed

generalized hicks contractions an extension of a result of žikic abstract in a recent paper of this journal ikic dosenovic has established a coincidence point theorem for three mappings in menger spaces we relax some conditions of ikic s theorem in order to connect it to some known results in fixed point theory in probabilistic metric spaces among consequences an improvement of a theorem from the book o had ic e pap fixed point theory in probabilistic metric spaces kluwer academic publishers dordrecht 2001 concerning generalized hicks c contractions is obtained

generalised modal realisation as a practical and efficient tool for fwl implementation finite word length fwl effects have been a critical issue in digital filter implementation for almost four decades although some optimisations may be attempted to get an optimal realisation with regards to a particular effect for instance the parametric sensitivity or the round off noise gain the purpose of this article is to propose an effective one i e taking into account all the aspects based on the specialised implicit form a new effective and sparse structure named modal realisation is proposed this realisation meets simultaneously accuracy low sensitivity round off noise gain and overflow risk few and flexible computational efforts with a good readability thanks to sparsity and simplicity no tricky optimisation is required to obtain it as well two numerical examples are included to illustrate the modal realisation s interest

the strong consistency of the stochastic gradient algorithm of adaptive control by use of a technique due to chen sufficient conditions are established for the strong consistency of the stochastic gradient sg algorithm for mimo armax stochastic systems without monitoring this result is then used in conjunction with the method of disturbed adaptive controls introduced in 1 2 hence it is shown that the sg algorithm generates strongly consistent parameter estimates while it is operating as a part of the sg algorithm of adaptive control of goodwin ramadge and caines

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

will the pls criterion for order estimation work with aml and a posteriori prediction error the general formula of the pls predictive least squares criterion for order estimation is worked out under the assumption that the parameter estimates are calculated via the aml approximate maximum likelihood a particular case is then carefully analysed and it is shown that depending on the system generating the data the pls critetion using the a posteriori prediction error can surprisingly almost surely overestimate the true order

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

steady state and parameter tracking properties of self tuning minimum variance regulators abstract the self tuning regulator with a fixed gain and a fixed forgetting factor applied to control of an arx plant is considered the ordinary differential equation analysis of the closed loop system is performed in the neighbourhood of the stable equilibrium point and the approximate expressions for the steady state mean square parameter tracking and regulation errors are derived for the adaptive regulators based on the exponentially weighted least squares and stochastic approximation identification respectively it is shown that the concept of the effective memory length of the estimation algorithm has to be revised if the closed loop system identification with the gain fixing technique is used

adaptive control in the presence of input constraints this paper deals with the problem of adaptively controlling a linear time invariant plant in the presence of constraints on the input amplitude we introduce a new adaptive algorithm which ensures that the plant can be locally stabilized in addition to the standard assumptions which are required for adaptive control in the ideal case an upper bound on the plant control parameter is required to be known the results are evaluated by simulation studies

common fixed point theorems under strict contractive conditions in menger spaces abstract the main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property e a in menger probabilistic metric spaces as applications we obtain the corresponding common fixed point theorems under strict contractive in metric spaces

a stopping rule for least squares identification a stopping rule for least squares identification is developed the stopping rule is determined by the construction of a confidence ellipsoid for any predetermined estimation error epsilon 0 if the iterates are inside of an ellipsoidal confidence region with volume less than or equal to epsilon sup r then the recursive online algorithm will be terminated with high probability

roundoff noise analysis of two efficient digital filter structures in this correspondence two efficient structures are analyzed for the implementation scheme of rounding before multiplication rbm the first one is the direct form ii transposed structure in spl rho operator spl rho dfiit recently proposed in the expression of roundoff noise gain is derived based on which a revised spl rho dfiit structure denoted as spl rho rdfiit is obtained it is shown that the spl rho rdfiit structure having the same implementation complexity yields a smaller roundoff noise gain than the spl rho dfiit the roundoff noise gain for the spl rho rdfiit structure with error feedbacks is also derived each structure can be optimized with regard to the free parameters it possesses with a genetic algorithm numerical examples are presented which show that the optimized structures are very competitive because they can even outperform the traditional optimal state space realization in terms of the roundoff noise performance as well as the implementation simplicity

nonstationary time series identification abstract in this paper strongly consistent estimates are given for both unknown parameters and orders of the nonstationary time series where the nonstationarity arises because 1 at any time n a feedback control is added to the usual arma process which is successfully applied to modelling economic systems and 2 det a z may have zeros on the unit circle in addition to those located outside the unit disk where a z is the matrix polynomial corresponding to the ar part of the arma process

low gain integral control for multi input multioutput linear systems with input nonlinearities we consider the inclusion of a static antiwindup component in a continuous time low gain integral controller in feedback with a multi input multi output stable linear system subject to an input nonlinearity from a class of functions that includes componentwise diagonal saturation we demonstrate that the output of the closed loop system asymptotically tracks every constant reference vector which is feasible in a natural sense provided that the integrator gain is sufficiently small robustness properties of the proposed control scheme are investigated and three examples are discussed in detail

robust recursive identification of multidimensional linear regression models stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not too coloured as when a positive real condition on the noise mode is satisfied moreover the whiter the noise environment the more robust are the algorithms this paper shows that for linear regression signal models the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates indeed there are guaranteed attractive convergence rates independent of the process noise colour no positive real condition is imposed on the noise model

perturbation analysis of an svd based linear prediction method for estimating the frequencies of multiple sinusoids a linear prediction approach is studied for estimating the frequencies of sinusoids in white noise it is shown that in the first step the continuity of the generalized inverse and the concept of angle between subspaces play an important role the continuity concept helps explain the need for a low rank approximation and the quality of the approximation is appraised by using the notion of angle between subspaces for the second step the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined it is shown that increasing the order of the predictor polynomial and computing the minimum norm solution provides a mechanism to reduce parameter sensitivity

adaptation rates for mrac systems abstract a method for predicting the adaptation rate of a single input hyperstability based mrac system is developed assuming a slowly changing input and output this rate follows well defined root loci a straightforward method for choosing adaptation gains results the derived theory was applied to a laboratory experiment which involved a dc motor driving an inverted pendulum here the adaptation rates were accurately pedicted in spite of imperfect model following due to the presence of unmodelled static friction

strongly consistent estimation of the order of stochastic control systems carma model abstract in this paper a variant of the plc predictive least squares criterion for order estimation is combined with an adaptive control strategy and applied to multidimensional carma systems it is shown that with this combination we can estimate recursively and in a strongly consistent way both the order and coefficients of the controlled system while achieving asymptotically optimal cost

consistent estimation of the order of stochastic control systems a consistent estimate of the order of feedback control systems with unknown matrix coefficients estimated by the least squares method is derived by minimizing a modified version of the bayesian information criterion

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

on the convergence of the self tuning algorithms based on nonmodified least squares self tuning servo control based on a nonmodified least squares algorithm is considered the fundamental result of the analysis is that the passivity of the two time varying operators depending on the noise process dynamics regression vector and the ponderation matrix sequence of the algorithm is essential for the global stability of the self tuning regulator the methodology can be applied to problems of adaptive prediction based on a nonmodified least squares algorithm and system parameter identification by a least squares algorithm with a priori prediction

a fixed point theorem in probabilistic metric spaces and an application abstract the notion of a c contraction type multivalued mapping is introduced this notion is a generalization of the notion of c contraction introduced by t l hicks univ u novom sadu zb rad prirod mat fak ser mat 13 1983 63 72 a fixed point theorem for c contraction is proved an application on the existence of a random fixed point for random operator f m m where m d is a separable metric space and a m a measure space with a decomposable measure of nsa type is given

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

least squares identification for armax models without the positive real condition recursive identification problems of linear stochastic feedback control systems described by armax models are studied without imposing the strictly positive real condition on the noise model an increasing lag least squares is used in the first step to estimate the noise process while the parameter estimate is formed in the second step by an extended least squares in the algorithm there is an increase in computational cost in comparison to traditional algorithms however the results of this note do not need any a priori information or conditions on the noise model except that of stability and they are applicable to the identification of general feedback control systems

generation of a time series having a specified power spectrum with minimum roundoff noise the problem of determining a shaping filter which minimized the output roundoff noise variance is discussed it is shown that in the family of shaping filters of an identical mcmillan degree having an identical power spectrum the shaping filter of minimum phase attains a minimum output roundoff noise variance in either the case of optimal word lengths or the case of equal word lengths it is shown out by examples that this is not valid in the family of shaping filters having an identical power spectrum and different mcmillan degrees

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

a note on continuous time els abstract the parameter estimation of continuous time finite dimensional linear stochastic systems is a problem of long standing interest the method usually used is the extended least squares els algorithm described by a nonlinear stochastic differential equation sld with the existence of the global strong solution assumed this paper shows that the els estimate does exist in 0 and at the same time presents a number of convergence results paralleling those for the discrete time case

low roundoff noise augmented realizations of iir filters the scaling factor in a direct form ii infinite impulse response iir digital filter depends on only the system poles not its zeros adding pole zero cancellation pairs changes the scaling factor and the associated roundoff noise without affecting the transfer function it is shown that with l sub 2 scaling the upper bound of the noise reduction for direct form ii iir digital filters using k pole zero cancellation pairs is about 6k db the authors consider parallel form 3p to be the basic structure in which each subfilter is augmented with one or two pole zero cancellation pairs and realized in direct form ii they seek an iterative optimization process for each subfilter to find the optimal pole zero cancellation pairs that minimize the roundoff noise experimental results indicate the global optimal solution for these augmented subfilters can be obtained by using simple criteria to determine the starting points of the iterative processes alternative structures illustrative examples and overflow limit cycles are examined

unified adaptive control of non minimum phase systems part 1 weighted control effort and pole placement for stochastic systems global convergence of a class of unified adaptive control algorithms for discrete time non minimum phase stochastic linear systems is established it is shown that the algorithms ensure that the system inputs and outputs are sample mean bounded the minimum variance cost function with weighted control effort achieves its minimum possible values the weighted factors adjusted on line eventually converge to expected values and the closed loop poles arise at prespecified locations

digital methods for conversion between arbitrary sampling frequencies the paper presents filtering methods for interfacing time discrete systems with different sampling frequencies the methods are applicable for sampling rate conversion between any two sampling frequencies the conversion ratio may even be irrational or slowly time varying interpolation by irrational factors requires digital filters with nonperiodically varying coefficients this is dealt with in two ways 1 all possible coefficient values are precalculated this is in a sense possible because of the finite resolution needed or 2 the coefficients can be updated in real time using either fir or iir filters the first solution requires a huge coefficient memory the second scheme on the other hand is computationally intensive while discussing both of these solutions more practical intermediate schemes incorporating both fir and iir type filters are suggested the suggested practical implementations are either based on analog reconstruction filters where the derived digital filter coefficients are functions of the distances between current input and output samples or digital interpolators combined with simple analog interpolation schemes for finding the desired values in between the uniform output samples from the digital interpolator

brief on line order estimation and parameter identification for linear stochastic feedback control systems carma model this paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems carma model under the assumption that the upper bounds of system orders are known the strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained the estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients the resulting closed loop systems are then globally stable and the tracking sample mean square error is minimized as well simultaneously the estimates of the adaptive tracking for orders and coefficients are also strongly consistent the simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective

coincidence point theorems in probabilistic and fuzzy metric spaces in this paper we prove some new coincidence point theorems for a hybrid pair of single and multi valued mappings under more generalized contractive conditions in menger spaces and generalized menger spaces our results can be applied to the theory of the fuzzy metric spaces by relaxing some conditions several recent results given by zikic dos enovic mihet and ghaemi and razani are extended

adaptive lqg control of input output systems a cost biased approach in this paper we consider linear systems in input output form and introduce a new adaptive linear quadratic gaussian lqg control scheme which is shown to be self optimizing the identification algorithm incorporates a cost biasing term which favors the parameters with smaller lqg optimal cost and a second term that aims at moderating the time variability of the estimate the corresponding closed loop scheme is proven to be stable and to achieve an asymptotic lqg cost equal to the one obtained under complete knowledge of the true system self optimization the results of this paper extend in a nontrivial way previous results established along the cost biased approach in other settings

positive μ modification as an anti windup mechanism abstract this paper proposes a simple anti windup mechanism for a model reference adaptive control scheme subject to saturation constraints the anti windup compensator has in essence the same structure as positive modification for the same class of systems it is shown how this structure can under certain circumstances display characteristics similar to anti windup schemes proposed for linear control systems in particular it is shown that if the unknown ideal control signal eventually lies within the control constraints then the response of the adaptive control system will converge to that of the reference system provided certain conditions are satisfied the paper illustrates the challenge of designing anti windup compensators for model reference adaptive control systems

measures for controllability observability and fixed modes measures are introduced that provide quantitative information about relative controllability and observability of a linear multivariable system the proposed measures are directly related to frequency domain characteristics such as zeros and residues and to time domain characteristics such as eigenvectors controllability and observability gramians and eigenvalue sensitivity a simple and computationally efficient formula involving a quadratic form in the input output matrix and the left right eigenvector is presented for the calculation of controllability observability measure for systems with repeated eigenvalues the measures are shown to be proportional to the distances of transmission zeros of certain subsystems and the eigenvalues the results are extended to decentralized systems where a measure for fixed modes is proposed

adaptive low gain integral control of multivariable well posed linear systems the principle of low gain integral control for finite dimensional systems is well known more recently low gain integral control results have been obtained for classes of infinite dimensional systems in this paper we show that integral control with a simple and natural adaptation of the integrator gain achieves tracking of constant reference signals for every exponentially stable multivariable well posed infinite dimensional linear system whose steady state gain matrix has its spectrum in the open right half plane our results considerably extend improve and simplify previous work by the authors siam j control optim 35 1997 pp 78 116