a geometric approach to variance analysis in system identification this paper addresses the problem of quantifying the model error variance error in estimates of dynamic systems it is shown that under very general conditions the asymptotic in data length covariance of an estimated system property represented by a smooth function of estimated system parameters can be interpreted in terms of an orthogonal projection of a certain function associated with the property of interest onto a subspace determined by the model structure and experimental conditions the presented geometric approach simplifies structural analysis of the model variance and this is illustrated by analyzing the influence of inputs and sensors on the model accuracy

simultaneous stabilization using evolutionary strategies in this work a new procedure is presented for the simultaneous stabilization of linear time invariant siso plants evolutionary strategies and substitutions by polynomials and rational functions are used the algorithm presented requires minimal computational resources for its execution in addition it is possible to work with some types of plants that could not be simultaneously stabilized until now and there are many more of these than is described in the literature the restrictions are minimal and the method can be extended with little difficulty to mimo plants moreover a mechanism of substitutions by polynomials and rational function is presented and this mechanism preserves simultaneously stabilizable plants and their controllers several examples are given showing the advantages of these procedures

covariance analysis in siso linear systems identification in this paper we analyze the asymptotic covariance of models of causal single input single output linear time invariant systems expressions for the asymptotic co variance of system properties es

variance error quantification for identified poles and zeros this paper deals with quantification of noise induced errors in identified discrete time models of causal linear time invariant systems where the model error is described by the asymptotic in data length variance of the estimated poles and zeros the main conclusion is that there is a fundamental difference in the accuracy of the estimates depending on whether the zeros and poles lie inside or outside the unit circle as the model order goes to infinity the asymptotic variance approaches a finite limit for estimates of zeros and poles having magnitude larger than one but for zeros and poles strictly inside the unit circle the asymptotic variance grows exponentially with the model order we analyze how the variance of poles and zeros is affected by model order model structure and input excitation we treat general black box model structures including armax and box jenkins models

variance error quantifications that are exact for finite model order this paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order in the interests of improved accuracy this paper provides new expressions whose accuracy depends only on data length they are therefore exact for arbitrarily small true model order other authors have recognized the importance of such expressions and have derived them for the case of finite impulse response like model structures in which denominators are fixed at true values and only numerator terms are estimated this paper progresses beyond this situation to address the more general output error and box jenkins structures in which full dynamics models both numerator and denominator terms and noise models may be estimated a key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed

an indirect method for transfer function estimation from closed loop data abstract an indirect method is introduced that is able to estimate consistently the transfer function of a linear plant on the basis of data obtained from closed loop experiments even in the situation where the model of the noise disturbance on the data is not accurate moreover the method allows approximate identification of the open loop plant with an explicit and tunable expression for the bias distribution of the resulting model

a general multirate approach for direct closed loop identification to the nyquist frequency and beyond without injecting any external persistently exciting signals a general multirate approach is proposed for direct closed loop identification first an extended least squares algorithm is designed to identify the mixed rate model after polynomial transformation next the identified mixed rate model is used to compute the fast rate model from which system dynamics to the nyquist frequency and beyond can be obtained identifiability is mathematically proven if the plant output sampling rate is non integer multiples of the controller sampling rate the effectiveness of the proposed approach is evaluated by both the simulation and experimental results in a hard disk drive

optimal policies for controlled markov chains with a constraint abstract the time average reward for a discrete time controlled markov process subject to a time average cost constraint is maximized over the class of al causal policies each epoch a reward depending on the state and action is earned and a similarly constituted cost is assessed the time average of the former is maximized subject to a hard limit on the time average of the latter it is assumed that the state space is finite and the action space compact metric an accessibility hypothesis makes it possible to utilize a lagrange multiplier formulation involving the dynamic programming equation thus reducing the optimization problem to an unconstrained optimization parametrized by the multiplier the parametrized dynamic programming equation possesses compactness and convergence properties that lead to the following if the constraint can be satisfied by any causal policy the supremum over time average rewards respective to all causal policies is attained by either a simple or a mixed policy the latter is equivalent to choosing independently at each epoch between two specified simple policies by the throw of a biased coin

preserving synchronization under matrix product modifications abstract in this article we present a methodology under which stability and synchronization of a dynamical master slave system configuration are preserved under modification through matrix multiplication the objective is to show that under a defined multiplicative group hyperbolic critical points are preserved along the stable and unstable manifolds the properties of this multiplicative group were determined through the use of simultaneous jordan decomposition it is also shown that a consequence of this approach is the preservation of the signature of the jacobian matrix associated with the dynamical system to illustrate the results we present several examples of different modified systems

preservation of spr functions and stabilization by substitutions in siso plants in this paper we present sufficient conditions to preserve stability by rational function substitutions it is proved that by making substitutions with strictly positive real spr zero relative degree functions it is possible to preserve the stability and coprime factorization of transfer functions it is also proved that these functions are closed under function composition finally we prove some results about robust stabilization using constant compensators spr robust functions and robust stability based on the result over closure of spr functions

information matrix and d optimal design with gaussian inputs for wiener model identification we present a closed form expression for the fischer s information matrix associated with the identification of wiener models in the derivation we assume that the input signal is gaussian the analysis allows the linear sub system in the wiener model to have a generic rational transfer function of arbitrary order it also allows the static nonlinearity of the wiener model to be a polynomial of arbitrary degree in addition we show how this analysis can be used to design tractable algorithms for d optimal input design the idea is further extended to design optimal inputs consisting of a sequence of gaussian signals with different mean values and variances by combining gaussian inputs with different means we can tune the amplitude distribution of the input to achieve the best identification accuracy in d optimal sense the analytical results are also illustrated with some numerical simulations

asymptotic variance of closed loop subspace identification methods in this paper the asymptotic properties of a version of the innovation estimation algorithm by qin and ljung as well as of a version of the whitening filter based algorithm introduced by jansson are studied expressions for the asymptotic error as the sum of a bias term plus a variance term are given the analysis is performed under rather mild assumptions on the spectrum of the joint input output process however in order to avoid unnecessary complications the asymptotic variance formulas are computed explicitly only for finite memory systems i e of the arx type this assumption could be removed at the price of some technical complications the simulation results confirm that when the past horizon is large enough as compared to the predictor dynamics the asymptotic expressions provide a good approximation of the asymptotic variance also for armax systems

technical communique asymptotic variance expressions for closed loop identification asymptotic variance expressions are analyzed for models that are identified on the basis of closed loop data the considered methods comprise the classical direct method as well as the more recently developed indirect methods employing coprime factorized models dual youla kucera parametrizations and the two stage approach the variance expressions are compared with the open loop situation and evaluated in terms of their relevance for subsequent model based control design

frequency domain conditions for strictly positive real functions frequency domain conditions for strictly positive real spr functions which appear in literature are often only necessary or only sufficient this point is raised in 1 2 where necessary and sufficient conditions in the s domain are given for a transfer function to be spr in this note the points raised in 1 i2 are clarified further by giving necessary and sufficient conditions in the frequency domain for transfer functions to be spr these frequency domain conditions are easier to test than those given in the s domain or time domain 1 2

on the frequency domain accuracy of closed loop estimates it has been argued that the frequency domain accuracy of high model order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used the analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order and hence are approximations when either of these are finite however recent work has provided variance expressions that are exact for finite possibly low model order and hence can potentially deliver more accurate quantification of estimation accuracy this paper and a companion one revisits the study of identification from closed loop data in light of these new quantifications and establishes that under certain assumptions there can be significant differences in the accuracy of frequency response estimates these discrepencies are established here and in the companion paper to be dependent on what type of direct indirect or joint input output identification strategy is pursued

synthesis of positive real spl hscr sub 2 controllers this paper describes a synthesis procedure for strictly positive real observer based controllers in particular we address the standard spl hscr sub 2 optimal control problem with the additional constraint on the strict positive realness of the controller a suboptimal version of this problem is shown to be a convex optimization problem and a linear matrix inequality based solution is provided one example illustrates the main results

the fundamental role of general orthonormal bases in system identification the purpose of this paper is threefold firstly it is to establish that contrary to what might be expected the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure secondly it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros this is achieved by employing certain new results on generalized fourier series and the asymptotic properties of toeplitz like matrices in such a way that the new variance expressions presented here encompass pre existing ones as special cases via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification namely that orthonormal bases are much more than an implementational option offering improved numerical properties in fact they are an intrinsic part of estimation since as shown here orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them

closed loop identification revisited identification of systems operating in closed loop has long been of prime interest in industrial applications the problem offers many possibilities and also some fallacies and a wide variety of approaches have been suggested many quite recently the purpose of the current contribution is to place most of these approaches in a coherent framework thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates the common framework is created by the basic prediction error method and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models the so called indirect methods e g are indeed direct methods employing noise models that contain the regulator the asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations we also study a new projection approach to closed loop identification with the advantage of allowing approximation of the open loop dynamics in a given and user chosen frequency domain norm even in the case of an unknown nonlinear regulator

characterizing families of positive real matrices by matrix substitutions on scalar rational functions abstract this paper concerns the characterization of positive real pr matrices generated by substitutions of the laplace variable s in scalar rational transfer functions by matrix pr functions our main results are restricted to both strongly strictly pr matrices sspr and strictly bounded real matrices as a way to illustrate our main results we also include here a partial extension of both the kalman yakubovich popov lemma for sspr systems of zero relative degree and the circle criterion for strictly pr systems of zero relative degree

discounted markov decision processes with utility constraints we consider utility constrained markov decision processes the expected utility of the total discounted reward is maximized subject to multiple expected utility constraints by introducing a corresponding lagrange function a saddle point theorem of the utility constrained optimization is derived the existence of a constrained optimal policy is characterized by optimal action sets specified with a parametric utility

variance error interpolation and experiment design we investigate how the variance error associated with the prediction error identification is related to the power spectral densities of the input and the additive noise at the output let f e i w be the ratio of the input power spectral density psd to the output noise psd we characterize the set of all functions f for which the variance error remains constant this analysis results a minimal finite dimensional affine parameterization of the variance error this parameterization connects our analysis with the theory of nevanlinna pick interpolation it is shown that the set of all f for which the variance error remains constant can be characterized by the solutions of a nevanlinna pick interpolation problem this insight has interesting consequences in optimal input design where it is possible to use some recent tools in analytic interpolation theory to tune shape of the input psd to suit certain needs

an exact iterative search algorithm for constrained markov decision processes abstract this communique provides an exact iterative search algorithm for the np hard problem of obtaining an optimal feasible stationary markovian pure policy that achieves the maximum value averaged over an initial state distribution in finite constrained markov decision processes it is based on a novel characterization of the entire feasible policy space and takes the spirit of policy iteration pi in that a sequence of monotonically improving feasible policies is generated and converges to an optimal policy in iterations of the size of the policy space at the worst case unlike pi an unconstrained mdp needs to be solved at iterations involved with feasible policies and the current best policy improves all feasible policies included in the union of the policy spaces associated with the unconstrained mdps

brief paper on the accuracy in errors in variables identification compared to prediction error identification errors in variables estimation problems for single input single output systems with gaussian signals are considered in this contribution it is shown that the fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated furthermore it is shown that whittle s formula for the fisher information matrix can be represented as a gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators finally the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases i when the model includes white measurement noise on the input and the variance of the noise is estimated and ii when the model includes only measurement noise on the output in both cases asymptotically efficient estimators are assumed an explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output

h robustness properties preservation in siso systems when applying spr substitutions the preservation of both robust stability and weighted robust performance properties of controlled linear time invariant single input single output siso systems is studied when performing substitutions of the complex laplace variable s by a particular class of rational strictly positive real functions spr functions the so called strictly positive real functions of zero relative degree spr0 functions concerning weighted robust performance and model matching we provide some results on preservation of controller optimality

splitting randomized stationary policies in total reward markov decision processes this paper studies a discrete time total reward markov decision process mdp with a given initial state distribution a randomized stationary policy can be split on a given set of states if the occupancy measure of this policy can be expressed as a convex combination of the occupancy measures of stationary policies each selecting deterministic actions on the given set and coinciding with the original stationary policy outside of this set for a stationary policy necessary and sufficient conditions are provided for splitting it at a single state as well as sufficient conditions for splitting it on the whole state space these results are applied to constrained mdps the results are refined for absorbing including discounted mdps with finite state and actions spaces in particular this paper provides an efficient algorithm that presents the occupancy measure of a given policy as a convex combination of the occupancy measures of finitely many stationary deterministic policies this algorithm generates the splitting policies in a way that each pair of consecutive policies differs at exactly one state the results are applied to constrained problems to efficiently compute an optimal policy by computing and splitting a stationary optimal policy