a global rational arnoldi method for model reduction abstract in this paper we propose two new approaches for model order reduction of large scale multi input multi output mimo linear time invariant dynamical systems lti these methods are based on a generalization of the global arnoldi algorithm which is used to generate projection subspaces an adaptive procedure for the selection of shift parameters is proposed and some simple arnoldi relations are established in order to compute error bounds on the transfer function numerical experiments showing the effectiveness of these approaches are provided

algebraic foundations for qualitative calculi and networks abstract binary constraint problems have traditionally been considered as network satisfaction problems over some relation algebra a constraint network is satisfiable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved a qualitative representation is like an ordinary representation but instead of requiring that a b is the composition a b of the relations a and b as we do for ordinary representations we only require that c a b c a b for each c in the algebra a constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation preserving the constraints if a constraint network is satisfiable then it is clearly qualitatively satisfiable but the converse can fail as we show however for a wide range of relation algebras including the point algebra the allen interval algebra rcc8 and many others a network is satisfiable if and only if it is qualitatively satisfiable unlike ordinary composition the weak composition arising from qualitative representations need not be associative so we can generalise by considering network satisfaction problems over non associative algebras we prove that computationally qualitative representations have many advantages over ordinary representations whereas many finite relation algebras have only infinite representations every finite qualitatively representable algebra has a finite qualitative representation the representability problem for the atom structures of finite non associative algebras is np complete the network satisfaction problem over a finite qualitatively representable algebra is always in np the validity of equations over qualitative representations is co np complete on the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras

comparison between h sub 2 and h sub infinity controllers the h sub infinity performances of a controller designed by h sub 2 methodology and a controller designed by h sub infinity methodology are quantitatively compared it is shown that the ratio of the h sub infinity performance of the two is no greater than 2k for the one block problem where k is the total number of right half plane transmission zeros for two subsystems namely the subsystem between the disturbance and the measurement and the subsystem between the control signal and the controlled output it is also shown that there are systems which can give a ratio arbitrarily close to the upper bound however those systems are of a pathological type some possible generalizations to two and four block problems are discussed

learning efficiency of very simple grammars from positive data the class of very simple grammars is known to be polynomial time identifiable in the limit from positive data this paper gives an even more general discussion on the efficiency of identification of very simple grammars from positive data which includes both positive and negative results in particular we present an alternative efficient inconsistent learning algorithm for very simple grammars

characterization of the solution to the optimal h model reduction problem abstract in this paper the h norm approximation of a given stable proper rational transfer function by a lower order stable proper rational transfer function is studied the solution method is based on the authors observation that the h model reduction problem can be converted into a hankel norm model reduction problem a simple characterization of the solution to the optimal h model reduction problem is developed

frequency weighted spl lscr sub spl infin norm and optimal hankel norm model reduction a new relative error model reduction method is proposed using frequency weighted balanced realization and explicit spl lscr sub spl infin norm error bounds are also derived for the relative error and multiplicative error the method only needs to solve two lyapunov equations it is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase this paper also gives a complete solution to the frequency weighted hankel norm approximation with antistable weighting these results are then applied to spl lscr sub spl infin norm model reduction and several numerically effective algorithms are proposed it is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions

rich classes inferable from positive data inductive inference from positive data is shown to be remarkably powerful using the framework of elementary formal systems an elementary formal system efs for short is a kind of logic program on consisting of finitely many axioms any context sensitive language is definable by a restricted efs called a length bounded efs length bounded efss with at most n axioms are considered and it is shown that inductive inference from positive data works successfully for their models as well as for their languages from this it follows that any class of logic programs such as prolog programs corresponding to length bounded efss can be inferred from positive facts

a relation algebraic approach to the region connection calculus abstract we explore the relation algebraic aspects of the region connection calculus rcc of randell et al proceedings of the cade vol 11 pp 786 790 springer berlin 1992a in particular we present a refinement of the rcc8 table which shows that the axioms provide for more relations than are listed in the present table we also show that each rcc model leads to a boolean algebra finally we prove that a refined version of the rcc5 table has as models all atomless boolean algebras b with the natural ordering as the part of relation and that the table is closed under first order definable relations iff b is homogeneous

reasoning about cardinal directions between extended objects the np hardness result the cardinal direction calculus cdc proposed by goyal and egenhofer is a very expressive qualitative calculus for directional information of extended objects early work has shown that consistency checking of complete networks of basic cdc constraints is tractable while reasoning with the cdc in general is np hard this paper shows however that if some constraints are unspecified then consistency checking of incomplete networks of basic cdc constraints is already intractable this draws a sharp boundary between the tractable and intractable subclasses of the cdc the result is achieved by a reduction from the well known 3 sat problem

some computational results on size reduction in h sup infinity design the authors explore the properties of the algebraic riccati equation new results on the rank of the solution to the algebraic riccati equation are obtained and lead to an efficient algorithm for reducing the size of the antistable transfer function matrix in the model matching problem in the 1 block problem the method is taken further to obtain explicit formulas for a minimal realization of the matrix the approach is direct and numerically reliable as it is based almost entirely on orthogonal transformations

polynomial time identification of very simple grammars from positive data this paper concerns a subclass of simple deterministic grammars called very simple grammars and studies the problem of identifying the subclass in the limit from positive data the class of very simple languages forms a proper subclass of simple deterministic languages and is incomparable to the class of regular languages this class of languages is also known as the class of left szilard languages of context free grammars after providing some properties of very simple languages we show that the class of very simple grammars is polynomial time identifiable in the limit from positive data in the following sense that is we show that there effectively exists an algorithm that given a target very simple grammar g over alphabet identifies a very simple grammar g equivalent to g in the limit from positive data satisfying the property that the time for updating a conjecture is bounded by o m and the total number of prediction errors made by the algorithm is bounded by o n where n is the size of g m max n 1 3 and n is the total length of all positive data provided

l sub 2 optimal filter reduction a closed loop approach this paper is concerned with the problem of order reduction of a full order kalman filter for a stable linear signal model so that the steady state filtering error variance associated with the reduced order filter is minimized by an orthogonal parameterization the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices both continuous and iterative algorithms are derived to compute an optimal reduced order filter the algorithms are shown to possess good properties including the desirable convergence property the proposed algorithms are simple and effective numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open loop methods such as the well known balanced truncation method

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

on the convexity of h sup infinity riccati solutions and its applications the authors consider the two riccati equation solution to a standard h sup infinity control problem which can be used to characterize all possible stabilizing optimal or suboptimal h sup infinity controllers if the optimal h sup infinity norm or gamma an upper bound of a suboptimal h sup infinity norm is given some eigen properties of these h sup infinity riccati solutions are revealed the most prominent one is that the spectral radius of the product of these two riccati solutions is a continuous nonincreasing convex function of gamma on the domain of interest based on these properties a quadratically convergent algorithm is developed to compute the optimal h sup infinity norm

spectral analysis in linear process identification a new look at an old problem the problem of estimating the transfer function frequency response of a linear process by means of a modified spectral analysis method is treated a method of determining the maximum time lags of the correlation functions which makes use of the available a priori physical knowledge about the process and the input signal is proposed this leads in a natural way to the use of an asymmetrical window technique some simulation results are used to illustrate the method based on the asymptotic properties of the estimate the input design is studied finally it will be shown that this work can be used for the estimation of an upper bound of the model uncertainty in the frequency domain

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

region connection calculus its models and composition table originating in allen s analysis of temporal relations the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence this paper is mainly about the consistency based composition table rcc8 ct of the region connection calculus rcc raised by randell cui and cohn first we show each rcc model is a consistent model of the rcc8 ct then after an exhaustive analysis we show that no rcc model can be interpreted extensionally anyway and hence give a negative answer to a conjecture raised by bennett all these results are given in an extensional rcc8 composition table where we attach to each cell entry in the rcc8 ct a superscript to indicate in what circumstances an extensional interpretation is possible

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

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

probability one homotopy algorithms for solving the coupled lyapunov equations arising in reduced order h2 h modeling estimation and control optimal reduced order modeling estimation and control with respect to combined h 2 h criteria give rise to coupled lyapunov and riccati equations to develop reliable numerical algorithms for these problems this paper focuses on the coupled lyapunov equations which appear as a subset of the synthesis equations in particular this paper systematically examines the requirements of probability one homotopy algorithms to guarantee global convergence homotopy algorithms for nonlinear systems of equations construct a continuous family of systems and solve the given system by tracking the continuous curve of solutions to the family the main emphasis is on guaranteeing transversality for several homotopy maps based upon the pseudogramian formulation of the coupled lyapunov equations and variations based upon canonical forms these results are essential to the probability one homotopy approach by guaranteeing good numerical properties in the computational implementation of the homotopy algorithms

approximation of fir by iir digital filters an algorithm based on balanced model reduction an algorithm for the approximation of finite impulse response fir filters by infinite impulse response iir filters is presented the algorithm is based on a concept of balanced model reduction the matrix inversions normally associated with this procedure are notoriously error prone due to ill conditioning of the special matrix forms required this difficulty is circumvented here by directly formulating a reduced state space system description which is input output equivalent to the system that would more conventionally be obtained following the explicit step of constructing an interim balanced realization examples of fir by iir filter approximations are included

computation of generalized h 2 optimal controllers the generalized h 2 optimal control problem for a linear time invariant system is one in which the conventional h 2 norm is replaced by an operator norm the closed loop system is described in terms of a mapping between the space of time domain input disturbances in l 2 and the space of time domain regulated outputs in l a minimum of this norm is then sought over all stabilizing controllers it is shown that optimal controllers for such problems have the structure of a kalman filter with estimated state feedback where the feedback gains are obtained from the solution to a weighted lqr problem a computational algorithm is presented to determine the weights in this lqr problem and examples are given which demonstrate various problems which may arise in obtaining the optimal weights in particular it is shown that the generalized h 2 problem may involve the solution to a singular lqr problem

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

h optimal control part 1 model matching our aim in this paper is to develop a new approach for solving the h optimal control problem where the feedback arrangement takes the form of a linear fractional transformation the paper is in two parts in part 1 a basic kind of model matching problem is considered given rational matrices m s and n s the h norm of an error function defined as e s m s n s q s is minimized or bounded subject to e s and q s being stable closed form state space characterizations are obtained for both e s and q s the results established here will be used in part 2 of the paper hung 1989 to solve the h optimal control problem

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

rcc8 binary constraint network can be consistently extended the rcc8 constraint language developed by randell et al has been popularly adopted by the qualitative spatial reasoning and gis communities the recent observation that rcc8 composition table describes only weak composition instead of composition raises questions about renz and nebel s maximality results about the computational complexity of reasoning with rcc8 this paper shows that any consistent rcc8 binary constraint network rcc8 network for short can be consistently extended given an rcc8 network and z a fresh variable suppose xty and t is contained in the weak composition of r and s this means that we can add two new constraints xrz and zsy to without changing the consistency of the network the result guarantees the applicability to rcc8 of one key technique theorem 5 of j renz b nebel on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus artificial intelligence 108 1999 69 123 which allows the transfer of tractability of a set of rcc8 relations to its closure under composition intersection and converse

learning local languages and their application to dna sequence analysis this paper presents an efficient algorithm for learning in the limit a special type of regular languages called strictly locally testable languages from positive data and its application to identifying the protein spl alpha chain region in amino acid sequences first we present a linear time algorithm that given a strictly locally testable language learns its deterministic finite state automaton in the limit from only positive data this provides one with a practical and efficient method for learning a specific concept domain of sequence analysis we then describe several experimental results using the learning algorithm developed above following a theoretical observation which strongly suggests that a certain type of amino acid sequences can be expressed by a locally testable language we apply the learning algorithm to identifying the protein spl alpha chain region in amino acid sequences for hemoglobin experimental scores show an overall success rate of 95 correct identification for positive data and 96 for negative data

formulation and solution of structured total least norm problems for parameter estimation the total least squares tls method is a generalization of the least squares ls method for solving overdetermined sets of linear equations ax spl ap b the tls method minimizes spl par e r spl par sub f where r b a e x so that b r spl isin range a e given a spl isin c sup m spl times n with m spl ges n and b spl isin c sup m spl times 1 the most common tls algorithm is based on the singular value decomposition svd of a b however the svd based methods may not be appropriate when the matrix a has a special structure since they do not preserve the structure previously a new problem formulation known as structured total least norm stln and the algorithm for computing the stln solution have been developed the stln method preserves the special structure of a or a b and can minimize the error in the discrete l sub p norm where p 1 2 or spl infin in this paper the stln problem formulation is generalized for computing the solution of stln problems with multiple right hand sides ax spl ap b it is shown that these problems can be converted to ordinary stln problems with one right hand side in addition the method is shown to converge to the optimal solution in certain model reduction problems furthermore the application of the stln method to various parameter estimation problems is studied in which the computed correction matrix applied to a or a b keeps the same toeplitz structure as the data matrix a of a b respectively in particular the l sub 2 norm stln method is compared with the ls and tls methods in deconvolution transfer function modeling and linear prediction problems

model reduction of large scale systems by least squares abstract in this paper we introduce an approximation method for model reduction of large scale dynamical systems this is a projection which combines aspects of the svd and krylov based reduction methods this projection can be efficiently computed using tools from numerical analysis namely the rational krylov method for the krylov side of the projection and a low rank smith type iteration to solve a lyapunov equation for the svd side of the projection for discrete time systems the proposed approach is based on the least squares fit of the r 1 th column of a hankel matrix to the preceding r columns where r is the order of the reduced system the reduced system is asymptotically stable matches the first r markov parameters of the full order model and minimizes a weighted h 2 error the method is also generalized for moment matching at arbitrary interpolation points application to continuous time systems is achieved via the bilinear transformation numerical examples prove the effectiveness of the approach the proposed method is significant because it combines guaranteed stability and moment matching together with an optimization criterion

arma spectral estimation of narrow band processes via model reduction the problem of estimating autoregressive moving average arma models for narrowband processes is considered the following approach is proposed estimate a high order autoregressive ar approximation of the process by model reduction based on a truncated internally balanced realization or optimal hankel norm model reduction reduce the order of this high order ar estimate to find a lower order arma model this algorithm gives arma spectral estimates with excellent resolution properties without using iterative numerical minimization methods as for the maximum likelihood method how to take the narrowband assumption into account in the model reduction step is discussed in detail

state space approach to discrete time super optimal h control problems abstract an algorithm is presented for solving the strengthened discrete time 1 block model matching problem all the steps of the algorithm are performed using state space models and each step has a closed form solution the uniqueness of the super optimal solution follows from the constructions in the algorithm although the problem is analogous to the continuous time case and the strategy used is the same there are some intricate differences in detail which make the derivation of one from the other non trivial by working completely in discrete time the super optimal controller can be analysed explicitly in the z domain and implemented directly on a digital computer

learning in the limit with lattice structured hypothesis spaces we define a collection of language classes which are txtex learnable learnable in the limit from positive data the learners map any data input to an element of a fixed lattice and keep the least upper bound of all lattice elements thus obtained as the current hypothesis each element of the lattice is a grammar for a language and the learner climbs the lattice searching for the right element we call these classes in our collection lattice classes we provide several characterizations of lattice classes and their learners which suggests they are very natural in particular we show that any class of languages is a lattice class iff it is txtex learnable consistently conservatively set drivenly and strongly monotonically we show several language classes previously discussed in the literature to be lattice classes including the locally k testable classes the piecewise k testable classes the k reversible languages and the pattern languages we also show that lattice classes contain three previously known collections of language classes string extension language classes function distinguishable language classes and closed set systems finally the lattice perspective helps analyze the learning of these classes illustrations include query learning results in dependence on the lattice structure characterizations of closure properties and the vc dimension of lattice classes in terms of lattice properties

a semi dynamical approach for solving qualitative spatial constraint satisfaction problems in this paper we solve the problem of determining a consistent instantiation of any finite path consistent and atomic network of rcc8 base relations we already know that such networks that contain a finite number of variables have a realization in any dimension d 1 the novelty of our work is that given any path consistent and atomic constraint rcc8 network we are able to construct in polynomial time a realization that satisfies it for this purpose we suitably instantiate the variables of such a network by associating to them some regular closed sets of the set of real numbers

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

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

a lyapunov theory for linear time delay systems some relationships between a lyapunov based stability test and linear control system models with time delays are explored the main result is a generalization of the result that if a b is a reachable pair of matrices then square a is a stability matrix if and only if there is a positive definite matrix k such that ak ka bb

a representation theorem for boolean contact algebras we prove a representation theorem for boolean contact algebras which implies that the axioms for the region connection calculus rcc d a randell a g cohn z cui computing transitivity tables a challenge for automated theorem provers in d kapur ed proceedings of the 11th international conference on automated deduction cade 11 lecture notes in artificial intelligence vol 607 springer saratoga springs ny 1992 pp 786 790 are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected t1 spaces

inference of k testable languages in the strict sense and application to syntactic pattern recognition the inductive inference of the class of k testable languages in the strict sense k tssl is considered a k tssl is essentially defined by a finite set of substrings of length k that are permitted to appear in the strings of the language given a positive sample r of strings of an unknown language a deterministic finite state automation that recognizes the smallest k tssl containing r is obtained the inferred automation is shown to have a number of transitions bounded by o m where m is the number of substrings defining this k tssl and the inference algorithm works in o kn log m where n is the sum of the lengths of all the strings in r the proposed methods are illustrated through syntactic pattern recognition experiments in which a number of strings generated by ten given source non k tssl grammars are used to infer ten k tssl stochastic automata which are further used to classify new strings generated by the same source grammars the results of these experiments are consistent with the theory and show the ability of stochastic k tssls to approach other classes of regular languages

on the complexity of qualitative spatial reasoning a maximal tractable fragment of the region connection calculus the computational properties of qualitative spatial reasoning have been investigated to some degree however the question for the boundary between polynomial and np hard reasoning problems has not been addressed yet in this paper we explore this boundary in the region connection calculus rcc 8 we extend bennett s encoding of rcc 8 in modal logic based on this encoding we prove that reasoning is np complete in general and identify a maximal tractable subset of the relations in rcc 8 that contains all base relations further we show that for this subset path consistency is sufficient for deciding consistency

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

a new approach to the discretization of continuous time controllers a new method for discretizing continuous time controllers is derived using principles of controller approximation it focuses on the closed loop use of the discrete time controller the resulting approximation criterion is a measure for stability of the control system provides an upper bound on the sampling time for which stability can be guaranteed and because it is based on continuous time controller approximation it indicates the cost of discretization in terms of performance degradation the discrete time controller is obtained through minimization of this criterion which can be performed with standard software used in h sub infinity controller design

using contextual representations to efficiently learn context free languages we present a polynomial update time algorithm for the inductive inference of a large class of context free languages using the paradigm of positive data and a membership oracle we achieve this result by moving to a novel representation called contextual binary feature grammars cbfgs which are capable of representing richly structured context free languages as well as some context sensitive languages these representations explicitly model the lattice structure of the distribution of a set of substrings and can be inferred using a generalisation of distributional learning this formalism is an attempt to bridge the gap between simple learnable classes and the sorts of highly expressive representations necessary for linguistic representation it allows the learnability of a large class of context free languages that includes all regular languages and those context free languages that satisfy two simple constraints the formalism and the algorithm seem well suited to natural language and in particular to the modeling of first language acquisition preliminary experimental results confirm the effectiveness of this approach

brief paper on the stability of a reduced order filter based on dominant singular value decomposition of the system dynamics the stability of a reduced order filter rof the gain of which is constructed on the basis of a subspace of dominant singular vectors of the system dynamics is examined a definition of s detectability is introduced it is found that the observability of all unstable and neutral singular vectors s detectability is a sufficient condition for the existence of a stable filter

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

hankel norm approximation for well posed linear systems the sub optimal hankel norm approximation problem is solved for a well posed linear system with generating operators a b c and transfer function g satisfying some mild assumptions in the special case of the sub optimal nehari problem an explicit parameterization of all solutions is obtained in terms of the system parameters a b c and g 0

model reduction for state space symmetric systems in this paper the model reduction problem for state space symmetric systems is investigated first it is shown that several model reduction methods such as balanced truncation balanced truncation which preserves the dc gain optimal and suboptimal hankel norm approximations inherit the state space symmetric property furthermore for single input and single output siso state space symmetric systems we prove that the h norm of its transfer functions can be calculated via two simple formulas moreover the siso state space symmetric systems are equivalent to systems with zeros interlacing the poles zip under mild conditions

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

squaring down and the problems of almost zeros for continuous time systems abstract in this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains we derive the minimal gain of the precompensator to achieve such a square system if the gain of this precompensator is too large then we derive an explicit trade off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system

a stable state space realization in the formulation of h norm computation in the two block hinftyoptimization problem usually we are given the state space realizations of the proper rational matrices r 1 s and r 2 s whose poles are all the open right half plane two problems are studied in the note the first is the evaluation of phi s r 1 s at s s k k 1 2 n where phi s is an inner function whose zeros s k k 1 2 n are the poles of r 1 s this evaluation is essential if chang and pearson s method is used for computing the optimal hinftynorm the problem is solved in state space via the solutions of lyapunov equations neither polynomial matrix manipulations nor numerical pole zero cancellations are involved in the evaluation the second problem is to find a stable state space realization of s s u s r 2 s where u s is an inner matrix this problem arises in the spectral factorization of gamma 2 r 2 ast r 2 doyle and chu had a method for constructing stable s s based on a minimal realization of r 2 s an alternate method is proposed the alternate method does not require a minimal realization of r 2 s and only a lyapunov equation is involved

optimal hankel norm identification of dynamical systems abstract the problem of optimal approximate system identification is addressed with a newly defined measure of misfit between observed time series and linear time invariant models the behavioral framework is used as a suitable axiomatic setting for a non parametric introduction of system complexity and allows for a notion of misfit of dynamical systems that is independent of system representations the misfit function introduced here is characterized in terms of the induced norm of a hankel operator associated with the data and a co inner kernel representation of a model sets of pareto optimal models are defined as feasible trade offs between complexity and misfit of models and it is shown how all pareto optimal models are characterized as exact models of compressed data sets obtained from hankel norm approximations of data matrices this leads to new conceptual algorithms for optimal approximate identification of time series 1997 elsevier science ltd

learning regular sets from queries and counterexamples the problem of identifying an unknown regular set from examples of its members and nonmembers is addressed it is assumed that the regular set is presented by a minimamy adequate teacher which can answer membership queries about the set and can also test a conjecture and indicate whether it is equal to the unknown set and provide a counterexample if not a counterexample is a string in the symmetric difference of the correct set and the conjectured set a learning algorithm l is described that correctly learns any regular set from any minimally adequate teacher in time polynomial in the number of states of the minimum dfa for the set and the maximum length of any counterexample provided by the teacher it is shown that in a stochastic setting the ability of the teacher to test conjectures may be replaced by a random sampling oracle ex a polynomial time learning algorithm is shown for a particular problem of context free language identification

directional interpolation approach to h optimization and robust stabilization it is shown that under a mild condition h infty optimization and robust stabilization are equivalent to a directional interpolation problem which is a matrix extension of the classical pick nevanlinna interpolation problem a classical iterative method which is an extension of the schur nevanlinna algorithm is given for solving the problem this method does not require the inner outer factorization nor the balanced realization of the original plant a circuit theoretical parameterization of all solutions is derived that is expected to enhance the physical insight to the h infty optimal control and robust stabilization this parameterization has the degree much less than the one obtained previously

brief paper balanced truncation model reduction for systems with inhomogeneous initial conditions we present a rigorous approach to extend balanced truncation model reduction btmr to systems with inhomogeneous initial conditions we provide an estimate for the error between the input output maps of the original and of the reduced initial value system and we illustrate numerically the superiority of our approach over the naive application of btmr when btmr is applied to linear time invariant systems with inhomogeneous initial conditions it is crucial that the initial data are well represented by the subspaces generated by btmr this requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero to ensure that the initial data are well represented by the btmr subspaces we add auxiliary inputs determined by the initial data

qualitative constraint satisfaction problems an extended framework with landmarks dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity the qualitative approach to spatial and temporal reasoning known as qualitative spatial and temporal reasoning qstr typically represents spatial temporal knowledge in terms of qualitative relations e g to the east of after and reasons with spatial temporal knowledge by solving qualitative constraints when formulating qualitative constraint satisfaction problems csps it is usually assumed that each variable could be here there and everywhere practical applications such as urban planning however often require a variable to take its value from a certain finite domain i e it is required to be here or there but not everywhere entities in such a finite domain often act as reference objects and are called landmarks in this paper the paper extends the classical framework of qualitative csps by allowing variables to take values from finite domains the computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi viz point algebra interval algebra cardinal relation algebra rcc5 and rcc8 we show that all these consistency problems remain in np and provide under practical assumptions efficient algorithms for solving basic constraints involving landmarks for all these calculi

convolution and hankel operator norms for linear systems some norms are derived for convolution and hankel operators associated with linear time invariant systems in certain cases these norms are shown to be identical the tightest possible bound has been obtained for the absolute magnitude of the euclidean 2 or infinity norm of the time domain response of a multioutput system to certain classes of input disturbance

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

generalized region connection calculus the region connection calculus rcc is one of the most widely referenced system of high level qualitative spatial reasoning rcc assumes a continuous representation of space this contrasts sharply with the fact that spatial information obtained from physical recording devices is nowadays invariably digital in form and therefore implicitly uses a discrete representation of space recently galton developed a theory of discrete space that parallels rcc but question still lies in that can we have a theory of qualitative spatial reasoning admitting models of discrete spaces as well as continuous spaces in this paper we aim at establishing a formal theory which accommodates both discrete and continuous spatial information and a generalization of region connection calculus is introduced grcc the new theory takes two primitives the mereological notion of part and the topological notion of connection rcc and galton s theory for discrete space are both extensions of grcc the relation between continuous models and discrete ones is also clarified by introducing some operations on models of grcc in particular we propose a general approach for constructing countable rcc models as direct limits of collections of finite models compared with standard rcc models given rise from regular connected spaces these countable models have the nice property that each region can be constructed in finite steps from basic regions two interesting countable rcc models are also given one is a minimal rcc model the other is a countable sub model of the continuous space r 2

reasoning about cardinal directions between extended objects direction relations between extended spatial objects are important commonsense knowledge recently goyal and egenhofer proposed a relation model known as the cardinal direction calculus cdc for representing direction relations between connected plane regions the cdc is perhaps the most expressive qualitative calculus for directional information and has attracted increasing interest from areas such as artificial intelligence geographical information science and image retrieval given a network of cdc constraints the consistency problem is deciding if the network is realizable by connected regions in the real plane this paper provides a cubic algorithm for checking the consistency of complete networks of basic cdc constraints and proves that reasoning with the cdc is in general an np complete problem for a consistent complete network of basic cdc constraints our algorithm returns a canonical solution in cubic time this cubic algorithm is also adapted to check the consistency of complete networks of basic cardinal constraints between possibly disconnected regions

boolean connection algebras a new approach to the region connection calculus abstract the region connection calculus rcc is a well established formal system for qualitative spatial reasoning it provides an axiomatization of space which takes regions as primitive rather than as constructions from sets of points the paper introduces boolean connection algebras bcas and proves that these structures are equivalent to models of the rcc axioms bcas permit a wealth of results from the theory of lattices and boolean algebras to be applied to rcc this is demonstrated by two theorems which provide constructions for bcas from suitable distributive lattices it is already well known that regular connected topological spaces yield models of rcc but the theorems in this paper substantially generalize this result additionally the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations