natural type selection in adaptive lossy compression consider approximate lossy matching of a source string spl sim p with a random codebook generated from reproduction distribution q at a specified distortion d previous work determined the minimum coding rate r sub 1 r p q d for this setting we observe that for a large word length and with high probability the matching codeword is typical with a distribution q sub 1 which is different from q if a new random codebook is generated spl sim q sub 1 then the source string will favor codewords which are typical with a new distribution q sub 2 resulting in a minimum coding rate r sub 2 r p q sub 1 d and so on we show that the sequences of distributions q sub 1 q sub 2 and rates r sub 1 r sub 2 generated by this procedure converge to an optimum reproduction distribution q and the rate distortion function r p d respectively we also derive a fixed rate distortion slope version of this natural type selection process in the latter case an iteration of the process stochastically simulates an iteration of the blahut arimoto 1972 algorithm for rate distortion function computation without recourse to prior knowledge of the underlying source distribution to strengthen these limit statements we also characterize the steady state error of these procedures when iterating at a finite string length implications of the main results provide fresh insights into the workings of lossy variants of the lempel ziv algorithm for adaptive compression

on constrained randomized quantization randomized dithered quantization is a method capable of achieving white reconstruction error independent of the source dithered quantizers have traditionally been considered within their natural setting of uniform quantization in this paper we extend conventional dithered quantization to nonuniform quantization via a subterfage dithering is performed in the companded domain closed form necessary conditions for optimality of the compressor and expander mappings are derived for both fixed and variable rate randomized quantization numerically mappings are optimized by iteratively imposing these necessary conditions the framework is extended to include an explicit constraint that deterministic or randomized quantizers yield reconstruction error that is uncorrelated with the source surprising theoretical results show direct and simple connection between the optimal constrained quantizers and their unconstrained counterparts numerical results for the gaussian source provide strong evidence that the proposed constrained randomized quantizer outperforms the conventional dithered quantizer as well as the constrained deterministic quantizer moreover the proposed constrained quantizer renders the reconstruction error nearly white in the second part of the paper we investigate whether uncorrelated reconstruction error requires random coding to achieve asymptotic optimality we show that for a gaussian source the optimal vector quantizer of asymptotically high dimension whose quantization error is uncorrelated with the source is indeed random thus random encoding in this setting of rate distortion theory is not merely a tool to characterize performance bounds but a required property of quantizers that approach such bounds

strategic information transmission this paper develops a model of strategic communication in which a better informed sender s sends a possibly noisy signal to a receiver r who then takes an action that determines the welfare of both we characterize the set of bayesian nash equilibria under standard assumptions and show that equilibrium signaling always takes a strikingly simple form in which s partitions the support of the scalar variable that represents his private information and introduces noise into his signal by reporting in effect only which element of the partition his observation actually lies in we show under further assumptions that before s observes his private information the equilibrium whose partition has the greatest number of elements is pareto superior to all other equilibria and that if agents coordinate on this equilibrium r s equilibrium expected utility rises when agents preferences become more similar since r bases his choice of action on rational expectations this establishes a sense in which equilibrium signaling is more informative when agents preferences are more similar

aggregation of a class of interconnected linear dynamical systems abstract in this paper we introduce the notion of a meaningful average of a collection of dynamical systems as distinct from an ensemble average such a notion is useful for the study of a variety of dynamical systems such as traffic flow power systems and econometric systems we also address the associated issue of the existence and computation of such an average for a class of interconnected linear time invariant dynamical systems such an average dynamical system is not only attractive from a computational perspective but also represents the average behavior of the interconnected dynamical systems the problem of analysis and control of heirarchical large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system

sobolev lorentz spaces in the euclidean setting and counterexamples abstract this paper studies the inclusions between different sobolev lorentz spaces w 1 p q defined on open sets r n where n 1 is an integer 1 p and 1 q we prove that if 1 q r then w 1 p q is strictly included in w 1 p r we show that although h 1 p w 1 p where r n is open and n 1 there exists a partial converse namely we show that if a function u in w 1 p n 1 is such that u and its distributional gradient u have absolutely continuous p norm then u belongs to h 1 p as well we also extend the morrey embedding theorem to the sobolev lorentz spaces h 0 1 p q with 1 n p and 1 q namely we prove that the sobolev lorentz spaces h 0 1 p q embed into the space of holder continuous functions on with exponent 1 n p whenever r n is open 1 n p and 1 q

control design for large scale lur e systems with arbitrary information structure constraints abstract in this paper an lmi based approach is proposed for the design of static output feedback for multi nonlinear lur e postnikov systems the resulting control laws ensure absolute stability and at the same time maximize the size of the nonlinear sectors the proposed method is computationally efficient and can accommodate feedback laws with arbitrary information structure constraints the effectiveness of this approach is demonstrated on a large scale example with 100 state variables

decentralized techniques for the analysis and control of takagi sugeno fuzzy systems this paper discusses decentralized parallel distributed compensator design for takagi sugeno fuzzy systems the fuzzy system is viewed as an interconnection of subsystems some of which are strongly connected while others being weakly connected the necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional space the so called expanded space design decentralized parallel distributed compensators in the expanded space then contract the solution for implementation on the original fuzzy system in this respect connective stability of the open loop and closed loop of the interconnected system is analyzed via the concepts of vector lyapunov functions and m matrices different lyapunov functions generate different results for the discrete time fuzzy system quadratic lyapunov generating the superior of the two following a similar approach stabilization of the closed loop fuzzy system using local parallel distributed compensators is investigated

controllability observability of expanded composite systems abstract the relation between original and expanded systems within the inclusion principle from the point of view of controllability observability of both subsystems and composite systems is studied it is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable observable two practically important large classes of complementary matrices are identified to offer results computationally attractive first the existence of complementary matrices ensuring controllability observability of decoupled subsystems is proved then using this result the same property is proved for the composite expanded system

the empirical distribution of rate constrained source codes let x x sub 1 be a stationary ergodic finite alphabet source x sup n denote its first n symbols and y sup n be the codeword assigned to x sup n by a lossy source code the empirical kth order joint distribution q spl circ sup k x sup n y sup n spl rceil x sup k y sup k is defined as the frequency of appearances of pairs of k strings x sup k y sup k along the pair x sup n y sup n our main interest is in the sample behavior of this random distribution letting i q sup k denote the mutual information i x sup k y sup k when x sup k y sup k spl sim q sup k we show that for any sequence of lossy source code s of rate spl les r lim sup sub n spl rarr spl infin 1 k i q spl circ sup k x sup n y sup n spl rfloor spl les r 1 k h x sub 1 sup k h x a s where h x denotes the entropy rate of x this is shown to imply for a large class of sources including all independent and identically distributed i i d sources and all sources satisfying the shannon lower bound with equality that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve q spl circ sup k x sup n y sup n spl rfloor spl rarr sup d p x sup k y sup k a s whenever p sub x sup k sub y sup k is the unique distribution attaining the minimum in the definition of the kth order rate distortion function consequences of these results include a new proof of kieffer s sample converse to lossy source coding as well as performance bounds for compression based denoisers

dual inclusion principle for overlapping interconnected systems restriction and aggregation are two dual inclusion conditions which are revealed in the research field of inclusion principle for state space descriptions of overlapping interconnected systems an input state output dual inclusion principle is proposed for linear time invariant systems and their dual systems with the focus on restriction and aggregation in duality for direct contraction of control laws and state observers in these two special inclusion cases dual relationships of restriction and aggregation inclusion conditions are formulated between an original system and its dual system overlapping decentralized controller design problems are considered within the framework of the dual inclusion principle it is shown that if dual inclusion is satisfied in the same type of expansions restriction or aggregation for both original system and its dual system direct contraction can be applied to designed control laws or state observers from the expansion to the original space while dual informatio

dithered quantizers a theory of overall quantization noise for nonsubtractive dither was originally developed in unpublished work by j n wright and by t j stockham and subsequently expanded by l k brinton s p lipshitz j vanderkooy and r a wannamaker it is suggested that since these latter results are not as well known as the original results misunderstanding persists in the literature new proofs of the properties of quantizer dither both subtractive and nonsubtractive are provided the new proofs are based on elementary fourier series and rice s characteristic function method and do not require the use of generalized functions impulse trains of dirac delta functions and sampling theorem arguments the goal is to provide a unified derivation and presentation of the two forms of dithered quantizer noise based on elementary fourier techniques

decentralized estimation and control with overlapping information sets the objective of this note is to present a solution to the decentralized estimation and control problem for linear discrete time varying systems composed of overlapping subsystems the solution is based on the expansion contraction framework of the inclusion principle it is shown how decentralized estimation and control laws can be independently computed for the expanded system and then contracted for implementation in the original system to satisfy the overlapping information structure constraint

overlapping decompositions expansions contractions and stability of hybrid systems inclusion and extension principles are defined and studied for hybrid systems the controller design problem for hybrid systems is then considered within the framework of the extension principle it is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation the stability of hybrid systems is also considered a number of definitions of stability for hybrid systems are given and it is shown that if a system which includes another system is stable then the included system is also stable furthermore it is shown that if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system decentralized controller design with overlapping decompositions is also discussed within the framework of extension an example is provided to illustrate the proposed approach

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

generalized selection of complementary matrices in the inclusion principle this paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state lq optimal control of lti systems it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design

optimal sobolev imbeddings involving rearrangement invariant quasinorms let m and n be positive integers with n 2 and 1 m n 1 we study rearrangement invariant quasinorms r and d on functions f 0 1 view the mathml source such that to each bounded domain in view the mathml sourcen with lebesgue measure there corresponds c c 0 for which one has the sobolev imbedding inequality r u t c d mu t u cm0 involving the nonincreasing rearrangements of u and a certain mth order gradient of u when m 1 we deal in fact with a closely related imbedding inequality of talenti in which d need not be rearrangement invariant r u t c d d dt x view the mathml sourcen u x u t u x dx u c10 in both cases we are especially interested in when the quasinorms are optimal in the sense that r cannot be replaced by an essentially larger quasinorm and d cannot be replaced by an essentially smaller one our results yield best possible refinements of such limiting sobolev inequalities as those of trudinger strichartz hansson brezis and wainger

sliding mode control in discrete state and hybrid systems the sliding mode control approach is developed for a class of discrete state systems in a metric space a concept of trajectory continuity is introduced which allows the use of sliding mode design techniques similar to that in continuous state systems this approach is then applied to a class of hybrid systems which consists of a continuous plant an interface and a discrete state controller the introduction of the sliding mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem

decentralized estimation and control with overlapping input state and output decomposition abstract the extension principle which was introduced recently is generalized to the case of input state and output expansion estimator and controller design problems are considered within the framework of the extension principle decentralized estimator and controller design with overlapping decompositions is also discussed within the same framework it is shown that if the extension principle is used then any estimator or controller designed in the expanded spaces is contractible to the original spaces for implementation furthermore it is shown that if an estimator designed for the expanded system achieves good estimation and or asymptotic estimation then the contracted estimator also achieves good estimation and or asymptotic estimation for the original system similarly it is also shown that if a controller designed for the expanded system achieves stability and or good performance then the contracted controller achieves stability and or good performance for the original system

bounding bar d distance by informational divergence a method to prove measure concentration there is a simple inequality by pinsker between variational distance and informational divergence of probability measures defined on arbitrary probability spaces we shall consider probability measures on sequences taken from countable alphabets and derive from pinsker s inequality bounds on the bar d distance by informational divergence such bounds can be used to prove the concentration of measure phenomenon for some nonproduct distributions

finite wordlength controller realisations using the specialised implicit form a specialised implicit state space representation is introduced to deal with finite wordlength effects in controller implementations this specialised implicit form provides a macroscopic description of the algorithm to be implemented so it constitutes a unifying framework allowing to encompass various implementation forms such as the operator the direct form ii transposed observer based and many other realisations usually considered separately in the literature different measures quantifying the finite wordlength effects on the overall closed loop behaviour are defined in this new context they concern both stability and performance the gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis the problem of determining a realisation with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods the approach is illustrated with an example

consistent abstractions of affine control systems in this paper we consider the problem of constructing abstractions of affine control systems that preserve reachability properties and in particular local accessibility in this framework showing local accessibility of the higher level abstracted model is equivalent to showing local accessibility of the more detailed lower level model given an affine control system and a smooth surjective map we present a canonical construction for extracting an affine control system describing the trajectories of the abstracted variables we then obtain conditions on the abstraction maps that render the original and abstracted system equivalent from a local accessibility point of view such consistent hierarchies of accessibility preserving abstractions of nonlinear control systems are then considered for various classes of affine control systems including linear bilinear drift free and strict feedback systems

an optimal interpolation theorem of marcinkiewicz type in orlicz spaces abstract an extension of the marcinkiewicz interpolation theorem is proved yielding a necessary and sufficient condition for every quasilinear operator satisfying given endpoint estimates of weak type to be bounded from an orlicz space into another

stochastic link activation for distributed filtering under sensor power constraint we consider the problem of link activation for distributed estimation with power constraint to satisfy the requirement of power consumption we propose a stochastic link activation scheme where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities first we design the optimal estimator gain of each sensor to minimize the state estimation error covariance then we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator finally we formulate the link activation problem as an optimization problem and convert it to a convex optimization

weak type interpolation near endpoint spaces let t be an operator of weak types a b and p q where a p and b q the marcinkiewicz interpolation theorem and its generalizations due to boyd krein semenov and others show that t maps certain rearrangement invariant spaces e which are not too close to la or lp into certain spaces f in this paper we consider analogous results for such an operator t in the case where on the contrary e is close to lp in the sense that its fundamental function is t1 p for example e can be a lorentz space lp r for 1 r the corresponding range spaces f are explicitly described and shown to be optimal when e lp r then in some cases f is a member of the class of lorentz zygmund spaces lq r log l s which were introduced and studied by bennett and rudnick but in general f is strictly smaller than the corresponding lorentz zygmund space and belongs to an apparently new class of r i spaces necessary and sufficient conditiones are given for the members of this new class to coincide with lorentz zygmund spaces certain results of this paper can be applied to give an alternative proof and generalization of the optimal form of the limiting case of the sobolev embedding theorem due to hansson and brezis wainger

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

optimal sobolev trace embeddings optimal target spaces are exhibited in arbitrary order sobolev type embeddings for traces of n dimensional functions on lower dimensional subspaces sobolev spaces built upon any rearrangement invariant norm are allowed a key step in our approach consists in showing that any trace embedding can be reduced to a one dimensional inequality for a hardy type operator depending only on n and on the dimension of the relevant subspace this can be regarded as an analogue for trace embeddings of a well known symmetrization principle for first order sobolev embeddings for compactly supported functions the stability of the optimal target space under iterations of sobolev trace embeddings is also established and is part of the proof of our reduction principle as a consequence we derive new trace embeddings with improved optimal target spaces for classical sobolev lorentz sobolev and orlicz sobolev spaces

inclusion principle for descriptor systems the purpose of this paper is to propose an expansion contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected when a control law is formulated in the expanded space the proposed characterizations provide contractibility conditions for implementation of the control law in the original system a full freedom is provided for selecting appropriate matrices in the proposed expansion contraction control scheme in particular the derived theoretical framework serves as a flexible environment for expansion contraction control design of descriptor systems under overlapping information structure constraints

contractibility of overlapping decentralized control abstract the purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle after a system with overlapping subsystems is expanded into a larger space and decentralized control laws are formulated for the disjoint subsystems the laws need to be contracted for implementation in the original space we propose broader definitions of restriction and aggregation in the framework of inclusion which provide more flexibility in the contraction phase of the expansion contraction process in particular we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications

optimal chained aggregation for reduced order modeling in this paper a theory is proposed for a new optimal process to perform chained aggregation in reduced order modelling notions of almost invariant subspaces and approximate aggregation are introduced in the proposed theory and are shown to be useful concepts in model reduction to derive an exact aggregated model from the approximately aggregated model obtained by optimal chained aggregation an algorithm is presented which is a variant of the well known shifted qr algorithm examples are given to illustrate the theory and its superiority over a previous approach

an optimal control approach to the decentralized robust servomechanism problem a linear quadratic optimal control approach is presented for designing linear time invariant decentralized controllers to solve the robust servomechanism problem it is assumed that not only the plant and the measurements but also the controllers may be subject to certain disturbances a physically meaningful quadratic cost functional is defined making it possible to assign desired weights to the errors to their derivatives to the system effort and to the controller efforts it is shown that the resulting controlled system has many properties like asymptotic tracking stability and robustness the solution does not require much control effort at high frequencies and the system is guaranteed not to have high frequency oscillations

higher order sobolev embeddings and isoperimetric inequalities abstract optimal higher order sobolev type embeddings are shown to follow via isoperimetric inequalities this establishes a higher order analogue of a well known link between first order sobolev embeddings and isoperimetric inequalities sobolev type inequalities of any order involving arbitrary rearrangement invariant norms on open sets in r n possibly endowed with a measure density are reduced to much simpler one dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets as a consequence the optimal target space in the relevant sobolev embeddings can be determined both in standard and in non standard classes of function spaces and underlying measure spaces in particular our results are applied to any order sobolev embeddings in regular john domains of the euclidean space in maz ya classes of possibly irregular euclidean domains described in terms of their isoperimetric function and in families of product probability spaces of which the gauss space is a classical instance

generalized decompositions of dynamic systems and vector lyapunov functions the notion of decomposition is generalized to provide more freedom in constructing vector lyapunov functions for stability analysis of nonlinear dynamic systems a generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state space of a given system an inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system so that stabliity of the expansion implies stability of the original system stability of the expansion can then be established by standard disjoint decompositions and vector lyapunov functions the applicability of the new approach is demonstrated using the lotka voiterra equations

white noise representations in stochastic realization theory it is proved that any random sequence can be exhibited as the output of a stochastic dynamical system driven by white noise further refinements are obtained for markov stationary and ergodic sequences this settles some open problems in stochastic realization theory posed by willems and van schuppen nato asi ams seminar on algebraic and geometric methods in linear system theory harvard university cambridge ma 1979

the hierarchical lattices of a finite machine the concept of dynamical consistency is introduced to define a high level transition function for an arbitrary partition of the state space of a finite input state machine m the existence of a dynamically consistent transition from a partition member xi to a member xj corresponds to the existence for every state x in xi of some x dependent control sequence which takes that state directly into xj this paper analyses what are termed in block controllable partition machines and between block controllable partition machines and establishes the existence of the associated in block controllable hierarchical lattice ibcp m it is shown that any partition machine in ibcp m is between block controllable if and only if the base machine m is controllable this setting allows the specification of state to state control trajectories of m to be decomposed into high level and low level components

model abstraction and inclusion principle a comparison this paper discusses connections between the inclusion principle and model abstraction in large scale hierarchical control systems it also provides conditions for implementation of controllability and observability in linear continuous time dynamic systems satisfying either aggregation or restriction conditions as well as for observability implementation in linear continuous time dynamic systems satisfying conditions for abstraction

on the performance of data compression algorithms based upon string matching lossless and lossy data compression algorithms based on string matching are considered in the lossless case a result of wyner and ziv 1989 is extended in the lossy case a data compression algorithm based on approximate string matching is analyzed in the following two frameworks 1 the database and the source together form a markov chain of finite order 2 the database and the source are independent with the database coming from a markov model and the source from a general stationary ergodic model in either framework it is shown that the resulting compression rate converges with probability one to a quantity computable as the infimum of an information theoretic functional over a set of auxiliary random variables the quantity is strictly greater than the rate distortion function of the source except in some symmetric cases in particular this result implies that the lossy algorithm proposed by steinberg and gutman 1993 is not optimal even for memoryless or markov sources

hierarchically consistent control systems large scale control systems typically possess a hierarchical architecture in order to manage complexity higher levels of the hierarchy utilize coarser models of the system resulting from aggregating the detailed lower level models in this layered control paradigm the notion of hierarchical consistency is important as it ensures the implementation of high level objectives by the lower level system in this paper we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives as an interesting byproduct we obtain a hierarchical controllability criterion for linear systems from which we recover the best of the known controllability algorithms from numerical linear algebra

on the stability and control of nonlinear dynamical systems via vector lyapunov functions vector lyapunov theory has been developed to weaken the hypothesis of standard lyapunov theory in order to enlarge the class of lyapunov functions that can be used for analyzing system stability in this paper we extend the theory of vector lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states furthermore we present a generalized convergence result which in the case of a scalar comparison system specializes to the classical krasovskii lasalle invariant set theorem in addition we introduce the notion of a control vector lyapunov function as a generalization of control lyapunov functions and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector lyapunov function moreover using control vector lyapunov functions we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel furthermore we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law finally the proposed control framework is used to construct decentralized controllers for large scale nonlinear systems with robustness guarantees against full modeling uncertainty

multiple description distribution preserving quantization the notion of a multiple description quantizer mdq includes providing multiple distortion levels if a human observer is involved the design of mdq requires a suitable distortion measure to achieve a graceful quality degradation in the case of description losses while the mean squared error is a ubiquitous distortion measure for many classic mdq schemes it is known to be perceptually relevant only at low distortions we propose a new mdq designed according to an unconventional distortion criterion that combines the mean squared error with a constraint on the probability distribution of the reconstructed signal the performance of the new mdq is shown to approach that of the classic mdq asymptotically as rate increases however once applied in the context of transform audio coding the new mdq significantly outperforms a classic mdq in perceptual tests the new scheme is suitable for a wide range of distortions and renders a seamless transition between coding that preserves signal features and coding of a waveform

pair wise decomposition and coordinated control of complex systems pair wise decomposition and coordinated control for complex interconnected systems with any information structure constraints are proposed in this paper based on the inclusion principle a permuted inclusion principle is presented to expand the system into an expanded space from which a recurrent reverse order of pair wise subsystems is extracted by a standard lq control pair wise controllers can be designed to stabilize and coordinate the pair wise subsystems according to these controllers a coordinated compensator of subsystem interconnections is introduced in order to obtain a coordination based controller for the expanded system therefore a coordinated controller of the system can be contracted from the expanded space under the conditions of the inclusion principle moreover a sufficient condition of connective stability for the system is also proved by the lyapunov function and m matrix a main advantage of the proposed decomposition and control is that it allows any variation of information structure constraints of the system especially the increase and decrease of subsystem numbers finally the effectiveness of the proposed methodology is demonstrated by an application of automatic generation control to a four area electric power system

randomized quantization and source coding with constrained output distribution this paper studies fixed rate randomized vector quantization under the constraint that the quantizer s output has a given fixed probability distribution a general representation of randomized quantizers that includes the common models in the literature is introduced via appropriate mixtures of joint probability measures on the product of the source and reproduction alphabets using this representation and results from optimal transport theory the existence of an optimal minimum distortion randomized quantizer having a given output distribution is shown under various conditions for sources with densities and the mean square distortion measure it is shown that this optimum can be attained by randomizing quantizers having convex codecells for stationary and memoryless source and output distributions a rate distortion theorem is proved providing a single letter expression for the optimum distortion in the limit of large blocklengths

a quotient space analysis of aggregated models the aggregation method in model reduction is reexamined using a quotient space approach the controllability of the aggregated model is then easily established the result is used to find the output matrix of the aggregated model for the matching of markov parameters and time moments

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

sobolev embeddings in orlicz and lorentz spaces with measures abstract embedding theorems for orlicz sobolev spaces into orlicz or orlicz lorentz spaces in domains in r n endowed with a frostman measure are offered parallel embeddings for lorentz sobolev spaces into generalized lorentz spaces are also established the relevant embeddings yield an optimal target norm in the relevant classes whenever it does exist in particular various results available in the literature are improved by special choices of the function spaces and of the measure

contractible controller design and optimal control with state and input inclusion abstract a new inclusion concept which involves both state and input expansion is introduced it is shown that with the approach undertaken here any control law designed in the expanded spaces is always contractible to the original spaces the inclusion of the cost functions is also discussed and necessary and sufficient conditions are derived it is shown that unlike the case when the two input spaces are identical the inclusion conditions must in general depend on the control laws however certain sufficient conditions which do not involve final control laws can be found if the inclusion is taken with respect to the optimal control finally controller design with overlapping decompositions is discussed within the framework of the new inclusion concept and optimal control

robust exponential stabilization for large scale uncertain impulsive systems with coupling time delays abstract in this paper we aim to study robust exponential stabilization for a large scale uncertain impulsive system with coupling time delays furthermore we also provide an estimation of the rate of convergence of exponential stabilization by utilizing the lyapunov method and razumikhin technique we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed loop large scale uncertain impulsive system with coupling time delays moreover we shall also use the results obtained to design impulsive controllers for a large scale uncertain continuous system under which the closed loop continuous system achieves robust and exponential stability to illustrate our results one example is solved

on optimal zero delay coding of vector markov sources optimal zero delay coding quantization of a vector valued markov source driven by a noise process is consid ered using a stochastic control problem formulation the exis tence and structure of optimal quantization policies are studied for a finite horizon problem with bounded per stage distortion measure the existence of an optimal zero delay quantization policy is shown provided that the quantizers allowed are ones with convex codecells the bounded distortion assumption is relaxed to cover cases that include the linear quadratic gaussian problem for the infinite horizon problem and a stationary markov source the optimality of deterministic markov coding policies is shown the existence of optimal stationary markov quantization policies is also shown provided randomization that is shared by the encoder and the decoder is allowed

overlapping decompositions and expansions of petri nets overlapping decompositions and expansions are considered to design decentralized controllers for discrete event systems dess modeled by petri nets the inclusion principle for petri nets is first defined it is shown that properties like boundedness reversibility and liveness with a mild additional condition carry over from the including net to the included net moreover a new property called obstruction is introduced for the including net and it is shown that if obstruction does not occur in the including net then deadlock does not occur in the included net an expansion procedure which guarantees inclusion for an overlappingly decomposed petri net is then introduced

orlicz sobolev boundary trace embeddings we prove a sharp trace embedding theorem for orlicz sobolev spaces into orlicz spaces on the boundary an optimal trace embedding into more general rearrangement invariant spaces on the boundary is also established

on universal quantization the quantization of n dimensional vectors in r n with an arbitrary probability measure under a mean square error constraint is discussed it is demonstrated that a uniform one dimensional quantizer followed by a noiseless digital variable rate encoder entropy encoding can yield a rate that is for any n no more than 0 754 bit per sample higher than the rate associated with the optimal n dimensionai quantizer regardless of the probabilistic characterization of the input n vector for the allowable mean square error

on the sufficiency of c cyclical monotonicity for optimality of transport plans we consider a mass transport problem among polish spaces and we show that a transport plan concentrated in a c cyclical monotone set is optimal if the cost function is continuous and possibly valued the same result is proved for a generic l s c cost function in the case when the measures are purely atomic this generalizes the previously known results

optimization and convergence of observation channels in stochastic control this paper studies the optimization of observation channels stochastic kernels in partially observed stochastic control problems in particular existence and continuity properties are investigated mostly but not exclusively concentrating on the single stage case continuity properties of the optimal cost in channels are explored under total variation setwise convergence and weak convergence sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented and applications to quantization are explored

a canonical form for the inclusion principle of dynamic systems the inclusion principle provides a mathematical framework for comparing behavior of dynamic systems having different dimensions our main objective is to derive a canonical form for larger systems expansions that are obtained by expanding smaller systems contractions the form offers full freedom in selecting appropriate matrices for the expansion contraction process we will broaden the form to include feedback and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints

an inclusion principle for hereditary systems abstract given two hereditary dynamic systems having different dimensions the conditions are provided under which a part of the motion of the larger system is reproduced by the smaller system that is the larger system includes the smaller one the conditions for inclusion are useful in applying the concept of vector liapunov functions to stability analysis of systems composed of overlapping subsystems by expanding the systems into a larger space the overlapping subsystems appear as disjoint and standard methods can be used to conclude stability of the expanded system under the inclusion conditions stability of the expansion implies stability of the original system an example is provided to show stability where the standard disjoint decompositions fail

sequential design of multi overlapping controllers for longitudinal multi overlapping systems in this paper a strategy to design multi overlapping controllers for systems with longitudinal multi overlapping structure is presented the design process uses the inclusion principle to carry out a multi step expansion that allows the decentralized design of a sequence of expanded local controllers these expanded local controllers are subsequently contracted to produce a multi overlapping controller that can be implemented in the original system to illustrate the proposed methodology the response of a four story building under a seismic excitation is considered

preservation of controllability observability in expanded systems the result contributed by the article is that controllability observability of an original continuous time lti dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices this new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases such as aggregations and restrictions which enable such preservation only in certain special cases a complete unrestricted transmission of these qualitative properties from the original controllable observable system to its expansion is a basic requirement on the expansion contraction process mainly when controllers observers are designed in expanded systems to be consequently contracted for implementation in initially given systems an original system composed of two overlapped subsystems is adopted as a general prototype ease a numerical example is supplied

decentralized control and overlapping decomposition of mechanical systems part 1 system decomposition this paper improves a new inclusion concept called txtension to mechanical systems described by matrix second order equations recent work on specialization of the inclusion principle has been generalized to the expansion and contraction of input state and output spaces but without the possibility of constructing completely general contractible controllers in this paper necessary and sufficient conditions for extensions and contractible feedback controllers are proved they enable the construction of general contractible controllers without any constraint on the structure of controllers for mechanical systems

embeddings for spaces of lorentz sobolev type the purpose of this paper is to characterize all embeddings for versions of besov and triebel lizorkin spaces where the underlying lebesgue space metric is replaced by a lorentz space metric we include two appendices one on the relation between classes of endpoint mikhlin hormander type fourier multipliers and one on the constant in the triangle inequality for the spaces l p r when p 1

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

a new approach to control design with overlapping information structure constraints in this paper a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints the method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space this approach can be extended to include an important class of uncertain nonlinearities and its validity is demonstrated through applications to strings of moving vehicles

compactness for sobolev type trace operators abstract compactness of arbitrary order sobolev type embeddings for traces of n dimensional functions on lower dimensional subspaces is investigated sobolev spaces built upon any rearrangement invariant norm are allowed in particular we characterize compactness of trace embeddings for classical sobolev lorentz sobolev and orlicz sobolev type spaces

stabilization of fixed modes in expansions of lti systems the objective of this note is to propose a method for stabilization of structurally fixed modes in expansions of lti dynamic systems in the scope of overlapping decentralized control design based on the expansion contraction framework enabling successful design for a broader class of problems than considered so far the method is based on a judicious choice of complementary matrices in the expanded space numerical examples are provided to illustrate simplicity and efficiency of the proposed approach

decentralized control using quasi block diagonal dominance of transfer function matrices the purpose of this paper is to present a generalization of the nyquist array method to blockwise decompositions which is based upon a new version of block diagonal dominance an additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices which increases considerably the class of control systems which can be designed via block diagonal dominance within this framework the controllers for individual subsystems can be designed independently of each other so that their union represents a decentralized controller for the overall system