limitations of robust adaptive pole placement control in this paper we investigate the limitations of adaptive pole placement control of ar systems when an additive disturbance is present the magnitude of the disturbance is dependent on past input and output values it is shown that the control objective of robust stabilization restricts the set of systems one can deal with we subsequently propose and analyze an adaptive algorithm which can be applied to convex not necessarily bounded subsets of the aforesaid set in particular it is shown that all signals in the control loop remain bounded

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

closed loop identification for the best asymptotic performance of adaptive robust control discrete linear systems subjected to both additive and parametric deterministic disturbances are considered the certainty equivalence principle is used for the design of adaptive control two different estimation algorithms are proposed to meet different control objectives in the regulation problem with the worst case limsup performance index

unbiased identification of systems with nonparametric uncertainty the set membership identification of systems with parametric and nonparametric uncertainty is studied the bias induced by the additive noise is eliminated by using the bias eliminated least squares method proposed previously by us 1991 a prefilter is connected to the input terminal of the system so that some zeros are inserted to the system by using the information obtained from these known zeros the bias induced by the additive noise is eliminated

worst case input output identification we consider worst case l1 identification of causal linear shift invariant systems from time series many results are given on general aspects of identification algorithm performance existence of optimal algorithms robust convergence and input experiment design the identification methodology studied here is compatible with the modelling requirements of modern robust control design

the einstein equation for signature type changing spacetimes we give a local existence and uniqueness theorem for solutions of einstein s equations with dust energy momentum tensor in the class of m dimensional analytic transverse signature type changing spacetimes where the initial condi tions are given on the hypersurface of signature type change we also prove a similar theorem in the case that the energy momentum tensor represents a scalar field

performance limitations of adaptive parameter estimation and system identification algorithms in the absence of excitation we address the problem of fundamental performance limitations in adaptive parameter estimation and system identification occurring in environments where perturbations are present but there is lack of sufficient excitation we construct a simple yet general bursting scenario to derive an analytical lower bound on the worst case peak steady state error for a wide class of parameter estimation and system identification algorithms our results show that in the absence of any input constraints arbitrarily small perturbations impose a serious performance limitation in the sense that the worst case performance deteriorates proportionally with the size of the parametric uncertainty set

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

stable on line parameter identification algorithms for systems with non parametric uncertainties and disturbances an on line parameter identification problem is formulated for linear time invariant continuous time systems with bounded input output disturbances as well as non parametric uncertainties characterized either by h2 or h norms based on the formulation a switching type gradient algorithm is proposed to estimate the parameters of the system from the available input output data in spite of the existence of non parametric uncertainties and disturbances this on line algorithm guarantees that the estimation error is monotonically decreasing with respect to time and the parameter estimate is convergent to a steady state value under a mild condition furthermore the algorithm is stable in the sense that the estimation error will converge to zero as both non parametric uncertainties and disturbances gradually diminish to evaluate the accuracy of the identified parameters an upper bound on the estimation error is given

transverse type changing pseudo riemannian metrics and the extendability of geodesics we study the geodesics and pre geodesics of a smooth manifold with smooth pseudo riemannian metric which changes bilinear type i e the signature changes on a hypersurface we classify all geodesics and pre geodesics that cross the hypersurface of type change transversely we then apply these results to the eikonal partial differential equation to find geometric conditions for the local existence or non existence of smooth transverse solutions

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

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

recursive prediction error identification using the nonlinear wiener model the nonlinear wiener model consisting of a linear dynamic block in cascade with a static nonlinearity is considered a recursive prediction error identification algorithm based on the wiener model is derived the linear dynamic block is modelled as a siso transfer function operator and the static nonlinearity is approximated with a piecewise linear function a theoretical analysis of the method is carried out and conditions for local convergence to the true parameter vector are given in particular the analysis shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation a numerical example illustrates the performance of the algorithm further practical guidelines on how to apply the algorithm are also included in the paper

modelling of uncertain systems via linear programming abstract real plants are in general time varying and uncertain yet most industrial control loops are designed using linear time invariant lti plant models the present work formalizes the problem of best approximate lti modelling of bibo stable linear time varying ltv systems in a way that is compatible with the notion of induced l norm used in robust l 1 control this setup is closely associated with certain identification methods and controlmotivated model validation invalidation procedures that can be efficiently implemented with special purpose linear programming lp techniques results are given for approximate modelling of bibo stable ltv and lti systems using lti models especially bibo stable fixed pole state space model parametrizations it is shown that such parametrizations are satisfactory from an approximate modelling point of view and can be used in output error type lp identification techniques and in lp model validation procedures various useful constraints on model parameters etc can be included as long as they are linear in the unknown parameters and both insensitive statistically robust and sensitive criteria can be used in identification and model validation simulation examples are included to illustrate that such techniques indeed give good results and can be used to solve problems of realistic size

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

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

a comparison of classical stochastic estimation and deterministic robust estimation the formulation and solution of two linear parameter estimation problems are compared the basic distinction in the problem formulation is the nature of the uncertainty in one case the uncertainty is generated by white gaussian noise and the solution is the kalman filter in the other case the uncertainty is unmodeled dynamics in the unit ball in h sup infinity or its nonlinear cover and the particular solution studied is a deterministic robust estimator certain parallels between classical stochastic estimation kalman filtering and the deterministic robust estimation are examined the similarities and differences are discussed in geometric terms in philosophical terms and in terms of the estimator s recursive implementation

the role of signal processing methods in the robust design of predictive control abstract this paper blends the ideas of estimation of model plant uncertainty from process data with the robust design of generalized predictive control gpc based on the small gain theorem classical signal processing methods with appropriate smoothing techniques are used for the estimation of model plant uncertainty and its upper bound for siso linear time invariant systems the choice of proper input excitation in the estimation of uncertainty spectrum in the presence of additive noise is also discussed the estimated uncertainty spectrum with the stability bounds are then used to provide simple graphical based tuning guidelines for robust design of gpc a more accurate estimate of the uncertainty bound allows one to trade off robustness with performance the use of important gpc tuning parameters that allow one to shape the stability bound for robust performance is highlighted evaluation of this technique is illustrated via simulation and experimental application

sequential approximation of feasible parameter sets for identification with set membership uncertainty in this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered the system model is linear in the unknown parameters a recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented and an efficient algorithm is proposed its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm

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

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

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

parameter set estimation for non linear systems models of dynamical systems are instrumental for many purposes prediction control simulation tracking and so on in this paper we will show how parameter set estimation pse can be applied to non linear systems parameter set estimation identifies a set of estimates which are feasible with respect to the measured data and a priori information this set of parameters feasible for the given model structure can then be used for system tracking or robust control designs for application to robust control it is important that the size of this set be as small as possible in order to apply parameter set estimation techniques to a non linear system the system function is expressed in a tensor parameterization which is linear in the parameters lp then it is shown how an optimum volume ellipsoid strategy for linear time invariant systems can be extended to this tensor parameterization of a non linear system the methodology is illustrated on two examples the second of which uses data obtained from an

recursive system identification in the presence of noise and model uncertainties the main contribution of this paper is a recursive algorithm for parametric system identification in the presence of both noise and model uncertainties the estimates provided by this algorithm are not invalidated after a learning period by the observed input output data and the assumed system and uncertainty structures a complementary off line algorithm derived from the on line algorithm is also presented

some computations of non abelian tensor products of groups on considere le produit tensoriel generalise g h des groupes g h on presente le calcul de g g

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

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

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

optimal nonparametric identification from arbitrary corrupt finite time series formulates and solves a worst case system identification problem for single input single output linear shift invariant distributed parameter plants the available a priori information in this problem consists of time dependent upper and lower bounds on the plant impulse response and the additive output noise the available a posteriori information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input signal the authors present a novel identification method for this problem this method maps the available a priori and a posteriori information into an uncertain model of the plant which comprises a nominal plant model a bounded additive output noise and a bounded additive model uncertainty the upper bound on the model uncertainty is explicit and expressed in terms of both the l sub 1 and h sub spl infin system norms the identification method and the nominal model possess certain well defined optimality properties and are computationally simple requiring only the solution of a single linear programming problem

separable dynamic programming and approximate decomposition methods we consider control planning and resource allocation problems involving several independent subsystems that are coupled through a control decision constraint we discuss one step lookahead methods that use an approximate cost to go function derived from the solution of single subsystem problems we propose a new method for constructing such approximations and derive bounds on the performance of the associated suboptimal policies we then specialize this method to problems of reachability of target tubes that have the form of a box a cartesian product of subsystem tubes we thus obtain inner approximating tubes which are the union of a finite number of boxes each involving single subsystem calculations

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

set membership identification of systems with parametric and nonparametric uncertainty a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented in the disturbance free case the parameter set estimate is guaranteed to contain the parameter set of the true plant in the presence of stochastic disturbances the parameter set estimate obtained from finite data records is shown to have the property that it contains the true plant parameter set with probability one as the data length tends to infinity

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

robust convergence of two stage nonlinear algorithms for identification in h two stage nonlinear algorithms for the problem of identification in are analyzed in terms of the fourier transform of the window function conditions characterizing the robust convergence of the two stage nonlinear algorithm are derived the sufficiency of the conditions holds for a general class of window functions while the necessity is proved for robust convergence of the first stage of the algorithm under the mild additional restriction that the window function is even symmetric some improved upper bounds for the worst case identification error are also obtained

closed loop system identification using the dual youla control parametrization identification of an unknown plant operated in a closed loop environment in the presence of external disturbance is considered under closed loop experiment the objectives of system identification are not only to obtain a best fit of the unknown plant but also to make close prediction or estimation of closed loop system responses by using the a priori information of a known stabilizing controller and the dual youla control parametrization identification of an unknown plant in a closed loop system can be simplified to that of an open loop reduced system it is shown that the output prediction errors of the estimates for both the original plant and the reduced system are equal furthermore if the feedback controller is of normalized coprime factorization then to find a best fit of the reduced system amounts to establishing a nominal closed loop system with which the signals of the true closed loop system can be predicted in a least squares sense in addition the optimal experimental designs for reduci

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

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

the construction of spinor fields on manifolds with smooth degenerate metrics we examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric we concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into lorentzian and euclidean domains we introduce the notion of a complex spinor fibration to make precise the meaning of continuity of a spinor field and give an express ion for the components of a local spinor connection that is valid in the absence of a frame of local orthonormal vectors these considerations enable one to construct a dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy we conclude that the theory contains more freedom than the spacetime dirac theory and we discuss some of the implications of this for the continuity of conserved currents

autocommutator subgroups of finite groups abstract we present some new results about the absolute center and autocommutator subgroup of a group concepts which were introduced in an earlier paper

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

asymptotic properties of set membership identification algorithms this paper addresses the asymptotic worst case properties of set membership identification smid algorithms we first present a set membership identification algorithm which can be used with a model structure consisting of parametric and nonparametric uncertainty as well as output additive disturbances this algorithm is then studied in the context of asymptotic worst case behavior we derive lower bounds on the worst case achievable identification error measured by the volume as well as the sum of sidelengths of the identified ellipsoidal uncertainty sets we then show that there exist inputs which can shrink the uncertainty sets to these lower bounds

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

mixed type surfaces with bounded gaussian curvature in three dimensional lorentzian manifolds abstract a mixed type surface is a connected regular surface in a lorentzian 3 manifold with non empty spacelike and timelike point sets the induced metric of a mixed type surface is a signature changing metric and their lightlike points may be regarded as singular points of such metrics in this paper we investigate the behavior of gaussian curvature at a non degenerate lightlike point of a mixed type surface to characterize the boundedness of gaussian curvature at a non degenerate lightlike points we introduce several fundamental invariants along non degenerate lightlike points such as the lightlike singular curvature and the lightlike normal curvature moreover using the results by pelletier and steller we obtain the gauss bonnet type formula for mixed type surfaces with bounded gaussian curvature

a time domain approach to model validation in this paper we offer a novel approach to control oriented model validation problems the problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input output data our approach directly uses time domain input output data to validate uncertainty models the algorithms we develop are computationally tractable and reduce to generally nondifferentiable convex feasibility problems or to linear programming problems in special cases we give analytical solutions to these problems

selection rules for topology change it is shown that there are restrictions on the possible changes of topology of space sections of the universe if this topology change takes place in a compact region which has a lorentzian metric and spinor structure in particular it is impossible to create a single wormhole or attach a single handle to a spacetime but it is kinematically possible to create such wormholes in pairs another way of saying this is that there is a 2 invariant for a closed oriented 3 manifold which determines whether can be the spacelike boundary of a compact manifoldm which admits a lorentzian metric and a spinor structure we evaluate this invariant in terms of the homology groups of and find that it is the mod2 kervaire semi characteristic

reformulation of the parameter identification problem for systems with bounded disturbances abstract the problem of deriving parameter identification algorithms that incorporate prior knowledge of a bound on the disturbance is studied particular emphasis is given to the following aspects firstly to motivate from geometrical and optimization considerations the modifications dead zones required to cope with the disturbances secondly to guarantee the convergence properties which are essential in the establishment of stability of identification based adaptive control systems projection and least squares algorithms are studied in both cases an interpretation is given to the new dead zone that has proven to be a key ingredient in recent robustness studies e g goodwin et al 1986 automatica 22 199 207 kreisselmeier and anderson 1985 ieee trans aut control 31 127 133 and lozano leal and ortega 1986 2nd ifac workshop on adapt syst in control and signal proc lund sweden

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

on the autocommutator subgroup and absolute centre of a group abstract we show that if the quotient of a group by its absolute centre is locally finite of exponent n then the exponent of its autocommutator subgroup is n bounded that is bounded by a function depending only on n if the group itself is locally finite then its exponent is n bounded as well under some extra assumptions the exponent of its automorphism group is n bounded we determine the absolute centre and autocommutator subgroup for a large class of infinite abelian groups

consistency of open loop experimental frequency response data with coprime factor plant models the model data consistency problem for coprime factorization considered is given some possibly noisy frequency response data obtained by running open loop experiments on a system show that these data are consistent with a given family of perturbed coprime factor models and a time domain spl lscr sub spl infin noise model in the noise free open loop case the model data consistency problem boils down to the existence of an interpolating function in spl rscr spl hscr sub spl infin that evaluates to a finite number of complex matrices at a finite number of points on the imaginary axis a theorem on boundary interpolation in spl rscr spl hscr sub spl infin is a building block that allows one to devise computationally simple necessary and sufficient tests to check if the perturbed coprime factorization is consistent with the data for standard coprime factorizations the test involves the computation of minimum norm solutions to underdetermined complex matrix equations the schmidt mirsky theorem is used in the case of special factorizations of flexible systems for spl lscr sub spl infin noise corrupting the frequency response measurements a complete solution to the open loop noisy siso problem using the structured singular value spl mu is given

robust stability with structured real parameter perturbations this paper considers the problem of robust stabilization of a linear time invariant system subject to variations of a real parameter vector for a given controller the radius of the largest stability hypersphere in this parameter space is calculated this radius is a measure of the stability margin of the closed loop system the results developed are applicable to all systems where the closed loop characteristic polynomial coefficients are linear functions of the parameters of interest in particular this always occurs for single input multioutput or single output multiinput systems where the transfer function coefficients are linear or affine functions of the parameters many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters the largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined based on these calculations a design procedure is proposed to robustify a given stabilizing controller this algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller io stabilize a plant subject to given ranges of parameter excursions these results are illustrated by an example

the non abelian tensor product of finite groups is finite si m et n sont des groupes finis ou p groupes agissant l un sur l autre et si leurs actions sont compatibles alors m n est fini ou un p groupe

stable model reference adaptive control in the presence of bounded disturbances the adaptive control of a linear time invariant plant in the presence of bounded disturbances is considered in addition to the usual assumptions made regarding the plant transfer function it is also assumed that the high frequency gain k p of the plant and an upper bound on the magnitude of the controller parameters are known under these conditions the adaptive controller suggested assures the boundedness of all signals in the overall system

the role of model validation for assessing the size of the unmodeled dynamics the problem of assessing the quality of a given or estimated model is a central issue in system identification various new techniques for estimating bias and variance contributions to the model error have been suggested in recent literature in this contribution classical model validation procedures are placed at the focus of our attention we discuss the principles by which we reach confidence in a model through such validation techniques and also how the distance to a true description can be estimated this way in particular we stress how the typical model validation procedure gives a direct measure of the model error of the model test without referring to its ensemble properties several model error bounds are developed for various assumptions about the disturbances entering the system

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

on the structure of groups whose exterior or tensor square is a p group it is well known that if g is a nilpotent infinite p group of bounded exponent then g g resp g g is also an infinite p group we study the converse under some restrictions we also prove that if g is a finitely generated group with gab capable then the finiteness of g g implies that of g

identification in the presence of classes of unmodeled dynamics and noise identification involves obtaining a model from an a priori chosen model class es using finite corrupted data the corruption may be due to several reasons ranging from noise to unmodeled dynamics since the real system may not belong to the model class two popular approaches probabilistic and set membership identification deal with this problem by imposing temporal constraints on the noise sample paths we differentiate between the two sources of error by imposing different types of constraints on the corruption if the source of corruption is noise we model it by imposing temporal constraints on the possible realizations of noise on the other hand if it results from unmodeled dynamics informational constraints are imposed contrary to probabilistic identification where the parameters of the identified model converge to the true parameters in the presence of noise current results in set membership identification do not have this convergence property our approach leads to bridging this gap between probabilistic and set membership identification when the source of corruption is noise for the case when both unmodeled dynamics and noise are present we derive consistency results for the case when the unmodeled dynamics can be described either by a linear time invariant system or by a static nonlinearity

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

identification in h using pick s interpolation the problem of system identification in h is studied using the pick interpolation theorem a tuned nonlinear interpolation algorithm is proposed and the resulting error bound in h norm is derived an example is used to illustrate the use of the interpolation algorithm

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

mapping frequency response bounds to the time domain a rigorous method of converting a transfer function description with any shaped uncertainty region in the complex frequency domain to input specific guaranteed time domain bounds is derived periodic input signals are considered first followed by an extension to aperiodic input such as a step the results can be used with confidence in controller design techniques that make use of the complex frequency plane and require translation to the time domain

robust approximate modelling of stable linear systems robust approximation and worst case approximate modelling of stable shift invariant systems from corrupted transfer function estimates are studied in the h sense connections between the problem formulations of the present work and certain problems of worst case system identification notably the helmicki jacobson nett problem formulation for identification in h are established issues of model set selection are addressed using the n width concept a concrete result establishes a priori knowledge for which a certain rational model set is optimal in then width sense a notion of robust convergence is defined so that any untuned approximation method satisfying it has a generic well posedness property for systems in the disk algebra the existence of robustly convergent approximation methods based on any complete model set in the disk algebra is shown in a constructive way a framework is given in which approximate models can be obtained as stable perturbations of the true system these can be combined

model uncertainty in frequency response based system identification abstract determination of plant nominal model error bound is one of the most essential topics in robust control oriented identification the objective of this paper is to investigate the structure of plant model uncertainties when a set of corrupted plant frequency response samples are supplied it is shown that the plant model uncertainties which result from the partialness and corruptedness of the provided plant information can be represented by structure fixed norm bounded but uncertain matrix valued functions that perturb a plant nominal model through a linear fractional transformation these results are very similar to those when plant time domain identification experiment data have been provided

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

a framework for robust parametric set membership identification this paper proposes a new framework for studying robust parametric set membership identification the authors derive some new results on the fundamental limitations of algorithms in this framework given a particular model structure the new idea is to quantify uncertainty only with respect to the finite dimensional parametric part of the model and not the fixed size unmodeled dynamics thus the measure of uncertainty is different from the measures used in previous robust identification work where system norms are used to quantify uncertainty as an example the results are used to assess the fidelity of a certain approximate robust parametric set membership identification algorithm

brief a convex approach to the characterization of the frequency response of ellipsoidal plants this paper deals with the frequency domain properties of an ellipsoidal family of rational functions i e a family of rational functions whose coefficients depend affinely on an ellipsoidal parameter set the considered problems are relevant to several recently developed techniques in the identification for control research area a complete characterization of the frequency plots of such a family is provided and an efficient algorithm for computing the envelope of the bode plots is devised in particular it is shown that the extremal values of the magnitude and phase of the family frequency response which in general involve non convex optimization problems can be computed via a sequence of simple algebraic tests