two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

linear and nonlinear algorithms for identification in h sub infinity with error bounds a linear algorithm and a nonlinear algorithm for the problem of system identification in h sub infinity posed by helmicki et al 1990 for discrete time systems are presented the authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent however the worst case identification error is shown to grow as log n where n is the model order a robustly convergent nonlinear algorithm is derived and bounds on the worst case identification error in the h sub infinity norm are obtained

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

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

continuous time control model validation using finite experimental data the application of robust control theory requires models containing unknown bounded perturbations and unknown bounded input signals model validation is a means of assessing the applicability of a given model with respect to experimental data this paper develops a theoretical framework and a computational solution for the model validation problem in the case where the model including unknown perturbations and signals is given in the continuous time domain yet the experimental datum is a finite sampled signal the continuous nature of the unknown components is treated directly with a sampled data lifting theory this gives results which are valid for any sample period and any datum length explicit calculation of whether sufficient data for invalidation has been obtained arises naturally in this framework a common class of robust control models is treated and leads to a convex matrix optimization problem a simulation example illustrates the approach

nonparametric output prediction for nonlinear fading memory systems the authors construct a class of elementary nonparametric output predictors of an unknown discrete time nonlinear fading memory system their algorithms predict asymptotically well for every bounded input sequence every disturbance sequence in certain classes and every linear or nonlinear system that is continuous and asymptotically time invariant causal and with fading memory the predictor is based on k sub n nearest neighbor estimators from nonparametric statistics it uses only previous input and noisy output data of the system without any knowledge of the structure of the unknown system the bounds on the input or the properties of noise under additional smoothness conditions the authors provide rates of convergence for the time average errors of their scheme finally they apply their results to the special case of stable linear time invariant lti systems

sheaves and k theory for f1 schemes this paper is devoted to the open problem in f1 geometry of developing k theory for f1 schemes we provide all necessary facts from the theory of monoid actions on pointed sets and we introduce sheaves for m0 schemes and f1 schemes in the sense of connes and consani a wide range of results hopefully lies the background for further developments of the algebraic geometry over f1 special attention is paid to two aspects particular to f1 geometry namely normal morphisms and locally projective sheaves which occur when we adopt quillen s q construction to a definition of g theory and k theory for f1 schemes a comparison with waldhausen s s construction yields the ring structure of k theory in particular we generalize deitmar s k theory of monoids and show that k specf1 realizes the stable homotopy of the spheres as a ring spectrum

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

identification and adaptive control towards a complexity based general theory abstract two recent developments will be surveyed here which are pointing the way towards an input output theory of h l 1 adaptive feedback the solution of problems involving 1 feedback performance exact optimization under large plant uncertainty on the one hand the two disc problem of h and 2 optimally fast identification in h on the other taken together these are yielding adaptive algorithms for slowly varying data in h l 1 at a conceptual level these results motivate a general input output theory linking identification adaptation and control learning in such a theory the definition of adaptation is based on system performance under uncertainty and is independent of internal structure presence or absence of variable parameters or even feedback

order barriers for continuous explicit runge kutta methods in this paper we deal with continuous numerical methods for solving initial value problems for ordinary differential equations the need for which occurs frequently in applications whereas most of the commonly used multistep methods provide continuous extensions by means of an interpolant which is available without making extra function evaluations this is not always the case for one step methods we consider the class of explicit runge kutta methods and provide theorems used to obtain lower bounds for the number of stages required to construct methods of a given unifonn order p these bounds are similar to the butcher barriers known for the discrete case and are derived up to order p 5 as far as we know the examples we present of 8 stage continuous runge kutta methods of uniform order 5 are the first of their kind

h2 optimal control for generalized discrete time systems abstract for a generalized discrete time system whose transfer function matrix may be improper or polynomial we give realization based formulas for the h 2 optimal output feedback controller the formulas bear essentially the same elegant simplicity of the proper case

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

suboptimal algorithms for worst case identification in h sup spl infin and model validation new algorithms based on convex programming are proposed for worst case system identification the algorithms are optimal within a factor of two asymptotically further model validation or data consistency is embedded in the identification process explicit worst case identification error bounds in the h sup spl infin norm are also derived for both uniformly and nonuniformly spaced frequency response samples

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

ℋ2 control of siso fractional order systems abstract in this paper we propose a systematic method to design the optimal 2 output feedback controller for single input single output plants of fractional order based on wiener hopf spectral factorization the plant is allowed to be unstable non minimum phase and incommensurate order using the fractional order youla parameterization the resulting controller satisfies the closed loop internal stability requirement because of the branch point singularities associated with fractional order transfer functions the spectral decompositions are effected via an integral technique an example is provided to demonstrate the design procedure

structure of model uncertainty for a weakly corrupted plant in this paper we investigate the structure of the transfer function set which includes all the transfer functions deduced from the plant available information it is shown that when an upper bound of the plant transfer function s h sup spl infin norm has been supplied and the noise contaminating the time domain identification experiment data is not too significant such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices one of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude the other is a norm bounded structure fixed free transfer function matrix moreover it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the spl mu synthesis problem

cohomology of toric line bundles via simplicial alexander duality we give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by blumenhagen jurke rahn and roschy arxiv 1003 5217 we actually prove not only the original algorithm but also a speed up version of it our proof is independent from in fact appeared earlier on the arxiv than the proof by roschy and rahn arxiv 1006 2392 and has several advantages such as being shorter and cleaner and can also settle the additional conjecture on serre duality for betti numbers which was raised but unresolved in arxiv 1006 2392

natural runge kutta and projection methods recently the author defined the class of natural runge kutta methods and observed that it includes all the collocation methods the present paper is devoted to a complete characterization of this class and it is shown that it coincides with the class of the projection methods in some polynomial spaces

from time series to linear system part iii approximate modelling abstract in the third part of this paper the problem of finding a linear time invariant complete system which models an observed time series will be continued however in this part it will be assumed that the model is required to explain the observations only approximately this raises the question of what is meant by an approximate model and how one should judge a model against data which in a strict sense falsify the model the initial sections of this paper introduce the methodology either the maximal admissible complexity is fixed and the best fitting model in the model class is sought or the maximally tolerated misfit is fixed and the least complex model in the model class is sought this is illustrated by means of finite dimensional models where natural complexity and misfit functions suggest themselves subsequently what is meant by the complexity of a linear time invariant complete system is discussed a concrete complexity function is proposed which is defined in terms of the richness of the behaviour on finite time intervals and is in one to one correspondence with the number of inputs the number of states and the observability indices of the underlying minimal i s o system the next definition is that of the misfit between an observed time series and a system a concrete misfit function is proposed which takes into consideration the lag structure of the system and in how far the observations fail to corroborate the ar equations which define the system s behaviour how the misfit may be computed by means of the correlation function of the data is then shown these concepts are subsequently used in order to set up two algorithms for approximate modelling of an observed q dimensional time series the first algorithm fixes the maximal complexity in a sense this comes down to fixing the number and the lags of the required ar equations the second algorithm fixes the tolerated misfit it is adaptive in nature in the sense that the number and the structure of the resulting ar equations will depend on the observations these ideas and algorithms are illustrated by means of two simulated examples

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

relationship between the trace and maximum eigenvalue norms for linear quadratic control design the use of a sum of squares h sub 2 norm is considered for optimal control system design the relative advantages of the linear quadratic gaussian lqg trace norm and the h sub infinity sup norm cost functions are discussed an argument is presented to show that the sum of squares norm ssn problem might be considered alongside the lqg and h sub infinity cost problems when exploring the relationship between the lqg and ssn problems it is found that an lqg controller could be found which correspond to an ssn problem with larger disturbance inputs this suggests that the lqg controller can be computed with the knowledge that it minimizes a well defined ssn problem with worst case uncertainty or disturbances the range of a certain set of eigenvalues is found to provide a measure of the difference between the lqg and ssn problem designs

a nearly interpolatory algorithm for h sub spl infin identification with mixed time and frequency response data a new algorithm is proposed for h sub spl infin identification with mixed time and frequency response data this algorithm shares similar properties to interpolatory algorithms and is nearly interpolatory meanwhile it greatly reduces the computational complexity of the interpolatory algorithm worst case identification error bounds are also characterized and derived for this nearly interpolatory algorithm a numerical example is used to illustrate the proposed identification algorithm

approximation of infinite dimensional systems a fourier series based method for approximation of stable infinite dimensional linear time invariant system models is discussed the basic idea is to compute the fourier series coefficients of the associated transfer function t sub d z and then take a high order partial sum two results on h sup infinity convergence and associated error bounds of the partial sum approximation are established it is shown that the fourier coefficients can be replaced by the discrete fourier transform coefficients while maintaining h sup infinity convergence thus a fast fourier transform algorithm can be used to compute the high order approximation this high order finite dimensional approximation can then be reduced using balanced truncation or optimal hankel approximation leading to the final finite dimensional approximation to the original infinite dimensional model this model has been tested on several transfer functions of the time delay type with promising results

robust identification and interpolation in h abstract we consider system identification in h in the framework proposed by helmicki jacobson and nett an algorithm using the jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems it is shown that this and similar identification algorithms can be successfully combined with a model reduction procedure to produce low order models connections with the nevanlinna pick interpolation problem are explored and an algorithm is given in which the identified model interpolates the given noisy data some numerical results are provided for illustration finally the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions

natural continuous extensions of runge kutta methods the present paper develops a theory of natural continuous extensions nces for the discrete approximate solution of an ode given by a runge kutta process these nces are defined in such a way that the continuous solutions furnished by the one step collocation methods are included

a globally optimal minimax solution for spectral overbounding and factorization in this paper an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified real valued nonparametric function of frequency this method has direct application to transforming nonparametric uncertainty bounds available from system identification experiments and or plant modeling into parametric representations required for modern robust control design software i e a minimum phase transfer function multiplied by a norm bounded perturbation

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

time domain identification for robust control abstract in this paper we are concerned with a problem of robust control oriented system identification in the time domain based on the well known schur takagi aak theorem we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by h norm it is also shown that in the model set defined by the nominal model and the uncertainty bound there exists at least one model which matches the prescribed input output data given in the time domain

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

construction of highly stable parallel two step runge kutta methods for delay differential equations it is shown that any a stable two step runge kutta method of order p and stage order q p for ordinary differential equations can be extended to the p stable method of uniform order p p for delay differential equations

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

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

exponentially fitted two step runge kutta methods construction and parameter selection abstract we derive exponentially fitted two step runge kutta methods for the numerical solution of y f x y specially tuned to the behaviour of the solution such methods have nonconstant coefficients which depend on a parameter to be suitably estimated the construction of the methods is shown and a strategy of parameter selection is presented some numerical experiments are provided to confirm the theoretical expectations

cech cohomology over f12 abstract in this text we generalize cech cohomology to sheaves f with values in blue b modules where b is a blueprint with 1 if x is an object of the underlying site then the cohomology sets h l x f turn out to be blue b modules for a locally free o x module f on a monoidal scheme x we prove that h l x f h l x f where x is the scheme associated with x and f is the locally free o x module associated with f in an appendix we show that the naive generalization of cohomology as a right derived functor is infinite dimensional for the projective line over f 1

stochastic and worst case system identification are not necessarily incompatible abstract stochastic and worst case approaches to system identification are different and are usually treated separately in this communique we investigate the effect that a projection operator has on the worst case behavior of estimates derived by stochastic identification algorithms we show that under certain assumptions the projections of the stochastic estimates are convergent in the worst case setting we illustrate this result by applying it to least squares and maximum likelihood algorithms

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

on the wiener hopf approach to optimal feedback design abstract a simple solution is given to the problem of designing a proper feedback which minimizes the h 2 norm of the sensitivity function multiplied by a suitable weighting function

two step almost collocation methods for volterra integral equations in this paper we construct a new class of continuous methods for volterra integral equations these methods are obtained by using a collocation technique and by relaxing some of the collocation conditions in order to obtain good stability properties

from time series to linear system part i finite dimensional linear time invariant systems abstract in the first part of this paper the definition of a dynamical system as simply consisting of a family of time series will be developed in this context the notions of linearity time invariance and finite dimensionality will be introduced it will be shown that a given family of time series may be represented by a system of ar equations riw t l rl 1w t l 1 r0w t 0 or equivalently by a finite dimensional linear time invariant system x t 1 ax t bu t y t cx t du t w u y if and only if this family is linear shift invariant and complete or as is equivalent closed in the topology of pointwise convergence this yields a very high level and elegant set of axioms which characterize these familiar objects it is emphasized however that no a priori choice is made as to which components of w are inputs and which are outputs such a separation always exists in any specific linear time invariant model starting from these definitions the structural indices of such systems are introduced and it is shown how an ar representation of a system having a given behaviour can be constructed these results will be used in a modelling context in part ii of the paper

optimality approximation and complexity in set membership h sub spl infin identification investigates the set membership identification of time invariant discrete time exponentially stable possibly infinite dimensional linear systems from time or frequency domain data corrupted by deterministic noise the aim is to deliver not a single model but a set of models whose size in h sub spl infin norm measures the uncertainty in the identification the main focus of the note is on the optimality properties for finite data and on the tradeoff between optimality and complexity of approximated low order model sets a method is given for evaluating convergent and computationally efficient inner and outer approximations of the value set for a given frequency such approximations allow one to compute within any desired accuracy the identification error of any identified model and to evaluate an optimal model at any given number of frequencies by suitably approximating these values model sets with nominal models in rh sub spl infin are then derived whose order is selected by trading off between model set complexity and identification accuracy degradation this degradation is evaluated by computing the optimality level defined as the ratio between the reduced model identification error and the optimal one a numerical example demonstrates the effectiveness of the presented results

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

cech cohomology of semiring schemes abstract a semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings we generalize cech cohomology theory and invertible sheaves to semiring schemes in particular when x p m n a projective space over a totally ordered idempotent semifield m we show that h m x o x is in agreement with the classical computation for all m finally we classify all invertible sheaves on x p m n by computing pic x explicitly

derivation of continuous explicit two step runge kutta methods of order three we describe a construction of continuous extensions to a new representation of two step runge kutta methods for ordinary differential equations this representation makes possible the accurate and reliable estimation of local discretization error facilitates the efficient implementation of these methods in variable stepsize environment and adapts readily to the numerical solution of a class of delay differential equations a number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state of the art dde23 code from matlab

identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors a procedure is developed for identification of probabilistic system uncertainty regions for a linear time invariant system with unknown dynamics on the basis of time sequences of input and output data the classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process given minor and verifiable prior information on the system and the noise process frequency response pulse response and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate in the model parametrizations use is made of general forms of basis functions conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed form expressions using an instrumental variable method for identification the procedure is suitable also for input output data obtained from closed loop experiments

on identification of stable systems and optimal approximation abstract approximative modelling of stable continuous time possibly infinite dimensional systems is studied based on an optimal approximation approach both approximation of analytical system representations system approximation as well as approximation of input output data based system estimates system identification are considered while special emphasis is given to approximative modelling in the h and hankel norms the l1 and l2 norm cases are also discussed the model sets considered here are finite dimensional systems and time shifted systems simple delay systems the theory of approximation numbers is shown to provide a convenient tool to study problems of identification of stable continuous time systems in a deterministic framework with close connections to complexity considerations laguerre fourier series methods and hankel operator techniques can be utilized to develop fully practical identification methods for continuous time possibly infinite dimensional systems

from time series to linear system part ii exact modelling abstract in the second part of this paper the problem of finding an exact model for a q dimensional infinite time series is considered first a mathematical vocabulary for discussing exact modelling is developed it is then shown how the results of part i guarantee the existence of a most powerful ar model for an observed time series two algorithms for obtaining such an ar model are subsequently derived one of these algorithms gives a shortest lag input output model the problem of obtaining a minimal state space realization of the observed time series is also considered in order to do that realization theory based on the truncated behaviour is developed as an extensive example the classical situation with impulse response measurements is discussed

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

a parametrization of all the unfalsified plant models for mimo systems the results of the parametrization of all the unfalsified models for single input single output systems are extended to multi input multi output mimo systems in this parametrization the assumed a priori plant and noise information are upper bounds of the h sub spl infin norm of the plant matrix valued transfer function and the noise magnitude the parametrization is on the basis of several series of plant time domain identification experiment data it is shown that for mimo systems all the unfalsified plant matrix valued transfer functions can still be expressed by the linear fractional transformation of a fixed matrix valued transfer function and an h sub spl infin norm bounded structure fixed but uncertain matrix valued transfer function however the high dimensions of the matrix valued transfer functions involved in the parametrization hamper the direct application of these results to robust controller design to overcome these difficulties further efforts are needed

numerical treatment of delay differential equations by hermite interpolation a class of numerical methods for the treatment of delay differential equations is developed these methods are based on the wellknown runge kutta fehlberg methods the retarded argument is approximated by an appropriate multipoint hermite interpolation the inherent jump discontinuities in the various derivatives of the solution are considered automatically problems with piecewise continuous right hand side and initial function are treated too real life problems are used for the numerical test and a comparison with other methods published in literature

numerical search for algebraically stable two step almost collocation methods we investigate algebraic stability of the new class of two step almost collocation methods for ordinary differential equations these continuous methods are obtained by relaxing some of the interpolation and collocation conditions to achieve strong stability properties together with uniform order of convergence on the whole interval of integration we describe the search for algebraically stable methods using the criterion based on the nyquist stability function proposed recently by hill this criterion leads to a minimization problem in one variable which is solved using the subroutine fminsearch from matlab examples of algebraically stable methods in this class are also presented

rational basis functions for robust identification from frequency and time domain measurements this paper investigates the use of general bases with fixed poles for the purposes of robust estimation these bases which generalise the common fir laguerre and two parameter kautz ones are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied it is also shown that by using a min max criterion these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified the key idea facilitating this analysis is to re parameterise the chosen model structures into a new one with equivalent fixed poles but for which the basis functions are orthonormal in h 2 d

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

cohomology of line bundles proof of the algorithm we present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by blumenhagen et al e print arxiv 1003 5217 and suggest a kind of serre duality for combinatorial betti numbers that we observed when computing examples

h sub spl infin identification of multivariable systems by tangential interpolation methods the purpose of this paper is to present an extension to some of the current work on worst case identification problems to multivariable systems we consider an h sub spl infin identification problem for a class of linear shift invariant multi input multi output systems our main results are an interpolatory algorithm and a number of bounds on the identification error this algorithm operates on available input and output data in the time domain and is constructed by solving an extended matrix tangential caratheodory fejer problem similar to its counterpart for scalar systems this interpolatory algorithm possesses certain desirable optimality properties and can be obtained via standard convex programming methods

deitmar s versus toen vaquie s schemes over mathbb f _ 1 deitmar introduced schemes over mathbb f 1 the so called field with one element as certain spaces with an attached sheaf of monoids generalizing the definition of schemes as ringed spaces on the other hand toen and vaquie defined them as particular zariski sheaves over the opposite category of monoids generalizing the definition of schemes as functors of points we show the equivalence between deitmar s and toen vaquies notions and establish an analog of the classical case of schemes over mathbb z this result has been assumed by the leading experts on mathbb f 1 but no proof was given during the proof we also conclude some new basic results on commutative algebra of monoids such as a characterization of local flat epimorphisms and of flat epimorphisms of finite presentation we also inspect the base change functors from the category of schemes over mathbb f 1 to the category of schemes over mathbb z

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam

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

a fully discrete spectral method for delay differential equations in this paper a new lanczos tau method for solving linear functional differential equations is introduced the scheme has infinite order of accuracy both in time and in the delayed argument the high accuracy in time is obtained without increasing the computational work and memory space which is needed for a one step explicit difference scheme the article demonstrates how to implement the algorithm in a robust and efficient manner and to treat problems with piecewise continuous initial function numerical results illustrating the behavior of the method when faced with difficult problems are presented and the numerical results are compared to those obtained by using two other methods

a parametric extension of mixed time frequency robust identification a parametric extension to the time frequency robust identification framework is presented the results can be applied to stable linear time invariant systems on which time and or frequency experiments have been performed the parametric portion of the model should be affine in the unknown parameters which includes practical applications such as flexible structures the consistency problem is cast as a constrained finite dimensional convex optimization problem that can be formulated as a linear matrix inequality the proposed procedure provides an interpolating identification algorithm convergent and optimal up to a factor of two with respect to central algorithms

discrete fourier transform and h sub infinity approximation it is shown that uniform rational approximation of nonrational transfer functions can always be obtained by means of the discrete fourier transform dft as long as such approximants exist based on this fact it is permissible to apply the fast fourier transform fft algorithm in carrying out rational approximations without being apprehensive of convergence the dft is used to obtain traditional approximations for transfer functions of infinite dimensional systems justification is provided for using the dft in such approximations it is established that whenever a stable transfer function can be approximated uniformly on the right half plane by a rational function its approximants can always be recognized by means of a dft

worst case system identification in l 1 ne equation 1 optimal algorithms and error bounds abstract this paper analyses worst case identification of linear shift invariant systems with an l 1 error criterion the assumed apriori information on the plant are bounds on the system gain and decay rate of the impulse response of the unknown system and the experimental data is assumed to be a finite set of corrupted impulse or step response samples of the system

model validation a connection between robust control and identification the gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data the model validation problem addressed is given experimental data and a model with both additive noise and norm bounded perturbations is it possible that the model could produce the observed input output data this problem is studied for the standard h sub infinity mu framework models a necessary condition for such a model to describe an experimental datum is obtained for a large class of models in the robust control framework this condition is computable as the solution of a quadratic optimization problem

model reference predictive lqg optimal control law for simo systems the design of linear quadratic gaussian lqg controllers for single input multiple output simo systems is considered this includes the class of multiloop control problems which are often solved using a classical nested loop structure many simplifications can be achieved over the more general multivariate problem which is important in self tuning control applications for example the tracking problem allows a model following capability to be introduced a predictive control feature is also available which enables the future values of the set point to be taken into account as in preprogrammed robot control

least squares methods for h sub infinity control oriented system identification a series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies is presented these algorithms are applicable to a broad class of stable distributed linear shift invariant plants the a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant an upper bound on a certain gain associated with the unknown plant and an upper bound on the noise level the a posteriori data information consists of a finite number of corrugated point frequency response estimates of the unknown plant the extent to which certain standard hilbert space or least squares method are applicable to the h sub infinity system identification problem considered is examined results are established that connect the h sub 2 error of the least squares methods to the h sub infinity error needed for control oriented system identification

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

cohomology of line bundles a computational algorithm we present an algorithm for computing line bundle valued cohomology classes over toric varieties this is the basic starting point for computing massless modes in both heterotic and type iib f theory compactifications where the manifolds of interest are complete intersections of hypersurfaces in toric varieties supporting additional vector bundles

a new approach to numerical solution of fixed point problems and its application to delay differential equations in this paper we consider a certain approximation of fixed points of a continuous operator a mapping the metric space into itself by means of finite dimensional e h fixed points of a these finite dimensional functions are obtained from functions defined on discrete space grid points related to a parameter h 0 by applying suitably chosen extension operators p h a theorem specifying necessary and sufficient conditions for existence of fixed points of a in terms of e h fixed points of a is given a corollary which follows the theorem yields an approximate method for a fixed point problem and determines conditions for its convergence an example of application of the obtained general results to numerical solving of boundary value problems for delay differential equations is provided numerical experiments carried out on three examples of boundary value problems for second order delay differential equations show that the proposed approach produces much more accurate results than many other numerical methods when applied to the same examples

approximation and identification of continuous time systems an approximation approach to the identification of stable continuous time possibly infinite dimensional systems is studied for this purpose concrete exponential leg endre series methods are proposed and analysed here for the l1 and l2 approximations of continuous time systems rate of approximation results are given for the proposed methods for an important class of delay systems the proposed exponential legendre series method for the l2 approximation has a certain optimal rate of approximation property for this class of delay systems these results show that exponential legendre series techniques have promising properties in connection with the l1 and l2 identifications of stable continuous time systems the proposed l1 identification method has a direct application to the robust design of control systems

parameter identification in the presence of non parametric dynamic uncertainty abstract this paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs but in the presence of non parametric dynamic uncertainty unmodelled dynamics this paper considers two non parametric uncertainty sets motivated by robust control the weighted ball in h and the weighted ball in the induced l2 norm the non parametric uncertainty produces signals which corrupt the signals used in identification this paper shows that the corruption is non conservatively bounded in an l2 sense this l2 bound is then compared with the signal energy with the result used to enable disable the parameter adjustment of a gradient least squares adjustment mechanism it is proved that the resulting parameter adjustment yields non increasing parameter errors with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

automatic selection of the initial step size for an ode solver abstract the choice of initial step size is critical for the reliable numerical solution of the initial value problem for a system of ordinary differential equations automatic selection of this step size may lead to a more robust and efficient integration than its provision by a user and is always more convenient it is especially important for the reliability of an ode solver used as a module in a larger software package previous approaches to making the selection are combined with some new ideas to produce an effective scheme for the automatic choice of the initial step size numerical results illustrate the roles played by the individual phases of the algorithm and show that the whole algorithm is both robust and efficient

h2 output feedback control for descriptor systems this paper solves the h 2 output feedback control problem for continuous time descriptor systems an existence condition of the h 2 optimal controller is derived based on the standard model matching technique and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic riccati equations it turns out that the optimal controller has an observer based structure well known in the state space case so that the results in this paper are natural extensions of the state space results to the descriptor systems a numerical example is also included to show the applicability of the proposed results

a note on h sub 2 optimal control problems with passivity constraints considers the problem of determining the closest function that has a positive real part on the unit disk to a given function in h sub 2 an explicit characterization of the projection is given remarks on potential applications using this projection result to control synthesis and system identification problems are made

dual criterion stochastic optimal control problem for robustness improvement the solution of the dual criterion linear quadratic stochastic optimal control problem is obtained by following a wiener type of solution procedure a stabilizing solution is guaranteed by parameterizing the controller using the desoer fractional representation approach the dual criterion includes sensitivity and complementary sensitivity weighting terms which provide a means of varying the robustness characteristics of the multivariable system

a general class of two step runge kutta methods for ordinary differential equations a general class of two step runge kutta methods that depend on stage values at two consecutive steps is studied these methods are special cases of general linear methods introduced by butcher and are quite efficient with respect to the number of function evaluations required for a given order general order conditions are derived using the approach proposed recently by albrecht and examples of methods are given up to the order 5 these methods can be divided into four classes that are appropriate for the numerical solution of nonstiff or stiff differential equations in sequential or parallel computing environments