a note on node aggregation and benders decomposition node aggregation methods have been previously studied as a means for approximating large scale transportation problems in this paper we show how the approximations inherent in benders decomposition method can be combined with node aggregation in optimizing large scale capacitated plant location problems

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

brief paper the extended periodic lyapunov lemma in this paper the so called lyapunov lemma for linear systems with periodically time varying coefficients is dealt with by this lemma the asymptotic stability of a given periodic system is linked with the existence of a periodic positive definite solution of the associated lyapunov equation under the assumption on the system being observable by relaxing the observability assumption to detectability an extended version of the lemma is obtained where the system stability is linked with the existence of a periodic positive semidefinite solution of the lyapunov equation

reachability and controllability of discrete time linear periodic systems in this paper we consider discrete time linear systems with periodic coefficients two necessary and sufficient conditions for complete controllability and reachability are given the conditions are stated in terms of the reachability gramian and hold for both reversible and nonreversible systems

a harmonic framework for controllability in linear continuous time periodic systems controllability of linear continuous time periodic systems is dealt with via a harmonic analysis approach for the first time in this paper this approach reveals that controllability of continuous time periodic systems can be connected to necessary and sufficient conditions expressed explicitly with fourier coefficients of the system matrices which can be interpreted in a way similar to what we have seen in linear time invariant cases these controllability conditions shed new light upon structural characteristics of continuous time periodic systems that are hard to know by means of existing time domain controllability criteria in the literature controllability canonical decomposition of linear continuous time periodic systems is revisited through state coordinate transforms of strong analytic features the results are heuristic and significant for examining structural characteristics of continuous time periodic systems and extending controllability related techniques that are widely employed in linear time invariant systems to linear continuous time periodic systems

the control of linear time periodic systems using floquet lyapunov theory in this paper we use floquet lyapunov theory to derive the floquet factors of the state transition matrix of a given linear time periodic system we show how the periodicity of one of the factors can be determined a priori using a constant matrix which we call the yakubovich matrix based upon the signs of the eigenvalues of the monodromy matrix we then describe a method for the numerical computation of the floquet factors relying upon a boundary value problem formulation and the yakubovich matrix further we show how the invertibility of the controllability gramian and a specific form for the feedback gain matrix can be used to derive a control law for the closed loop system the controller can be full state or observer based it also allows the engineer to assign all the invariants of the system i e the full monodromy matrix deriving the feedback matrix requires solving a matrix integral equation for the periodic floquet factor of the new state transition matrix of the closed loop system this is

direct sampling method for retrieving small perfectly conducting cracks abstract in this paper direct sampling method is considered for determining the location of a set of small linear perfectly conducting cracks from the collected far field data corresponding to an incident field to show the feasibility of the direct sampling method this study proves that the indicator function of the direct sampling method can be represented by the bessel function of order zero and the crack lengths the results of the numerical simulations are shown to support the fact that the imaging performance is highly dependent on the crack lengths to explain the fact that the imaging performance is highly dependent on the rotation of the cracks the direct sampling method is further analyzed by establishing a representation using bessel functions of orders zero and one based on the derived representation of indicator function we design improved direct sampling methods by applying incident fields with multiple directions and multiple frequencies corresponding analysis of indicator functions and simulation results are shown for demonstrating the effectiveness and improvements

discrete time linear periodic systems gramian and modal criteria for reachability and controllability this paper deals with the reachability and controllability of periodic discrete time systems first we supply two necessary and sufficient complete reachability conditions which apply to reversible and non reversible systems respectively then a necessary and sufficient complete controllability condition is provided this condition as well as the complete reachability criteria is given in terms of the reachability gramian matrix equivalent modal criteria for reachability and controllability are established in the second part of the paper

robust disturbance rejection problems for linear spl omega periodic discrete time systems two robust disturbance rejection problems with state feedback and with incomplete state feedback for linear spl omega periodic discrete time systems are studied in the framework of the so called geometric approach also some necessary conditions and or sufficient conditions for the problems to be solvable are presented

a forward simplex method for staircase linear programs modelling planning problems that extend over many time periods as linear programs leads to a special structure called a staircase or dynamic linear program in this special structure the nonzero coefficients of the linear program appear in blocks along the main diagonal of the coefficient matrix such problems are commonly found in economic planning structural design agricultural planning dynamic traffic assignment production planning and scheduling models forward algorithms provide an approach to solving these dynamic problems by solving successively longer finite horizon subproblems terminating when a stopping rule can be invoked or a decision horizon found such algorithms are available for a large number of specific models here we discuss the implementation and testing of a forward algorithm for solving general dynamic staircase linear programs tests reported indicate that the solution time is linear in the number of periods of the staircase problem as compared to a quadratic or cubic relationship for standard linear programming codes computational decision horizons are often found and are responsible for the good performance of the algorithm

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

the linear periodic output regulation problem the problem of asymptotic output regulation for linear systems driven by time varying t periodic exosystems is considered in this paper necessary and sufficient condition for its solvability based on the existence of periodic solutions of differential sylvester equations are derived these conditions constitute a generalization to the periodic case of the celebrated algebraic regulator equations of francis a general algorithm for the synthesis of an error feedback regulator is given for the case of minimum phase systems it is shown that the regulator design can be carried out without the knowledge of the floquet decomposition of the exosystem thus extending significantly the applicability of the general result the more challenging issue of robust regulation by error feedback is also addressed and solved under a stronger observability condition

solving staircase linear programs by the simplex method 2 pricing this and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged or staircase structure the preceding paper considered inversion routines that factorize the basis and solve linear systems the present paper examines pricing routines that compute reduced costs for nonbasic variables and that select a variable to enter the basis at each iteration both papers describe extensive although preliminary computer experiments and can point to some quite promising results for pricing in particular staircase computation strategies appear to offer modest but consistent savings staircase selection strategies properly chosen may offer substantial savings in number of iterations time per iteration or both

direct sampling method for identifying magnetic inhomogeneities in limited aperture inverse scattering problem abstract the direct sampling method dsm in limited aperture inverse scattering problems for transverse electric te polarization is considered based on the asymptotic expansion formula in the presence of small targets we demonstrate that the indicator function of dsm can be represented by an infinite series of bessel functions of integer order and correspondingly examine various properties of dsm simulation results with noisy data are created to support theoretical results based on the identified structure of the indicator function we design a new indicator function of dsm analyze its mathematical structure and generate simulation results to demonstrate its effectiveness and improvement

a multilevel sampling method for detecting sources in a stratified ocean waveguide in the reconstruction process of sound waves in a 3d stratified waveguide a key technique is to effectively reduce the huge computational demand in this work we propose an efficient and simple multilevel reconstruction method to locate the accurate position of a point source in a stratified ocean the proposed method can be viewed as a direct sampling method since no solutions of optimizations or linear systems are involved the novel method exhibits several strengths fast convergence robustness against noise advantages in computational complexity and applicability for a very small number of receivers

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

monodromy eigenvalue assignment in linear periodic systems this note addresses the problem of assigning the eigenvalues of the monodromy matrix of a linear continuous time periodic system by periodic state feedback a controllability criterion is given which slightly strengthens known results an explicit expression for a periodic feedback gain which performs the pole assignment is given when the system is controllable over one period the whole monodromy matrix is assignable by periodic feedback an example is given

disturbance localization and pole shifting by dynamic compensation this paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector a necessary and sufficient condition for the solvability of the problem is given two synthesis procedures of the compensator are presented one is based on an observer and the other is based on a dual observer the observer designed by the proposed procedure acts as as unknown input observer for a linear function an improved procedure of designing a reduced order unknown input observer is also given the result may be applicable to reducing the compensator order

characteristic multiplier assignment in continuous time linear periodic systems a characteristic multiplier assignment problem for continuous time periodic systems with analytic coefficients is considered first the necessary and sufficient condition for controllability is shown under this condition an algorithm for assigning a set of characteristic multipliers is proposed the algorithm is constructed by a simple repetitive procedure and is suited to computer programming the given feedback gain matrix is composed of a sequence of dirac delta functions such a feedback system can easily be implemented using proper approximation to the delta function lastly the design method is applied to the attitude control problem of a spin stabilized satellite and some simulation results are given

minimal time minimal order deadbeat regulator with internal stability this paper is concerned with the output deadbeat finite settling time regulation with internal stability for linear discrete time multivariable systems the two cases are treated separately the one is the regulation by state feedback and the other is the regulation through function observers for both cases the basic solvability conditions the minimal settling time and the characterizations of the minimal time regulators are derived throughout the paper the well posedness condition plays a fundamental role a deterministic version of the so called separation theorem in lqg problem is derived namely the minimal time state feedback regulator combined with the minimal time minimal order function observer yields the overall minimal time minimal order regulator by output feedback

a gramian based controller for linear periodic systems this note proposes a new design method for the control of linear time periodic systems the method is based on the reachability gramian and a specific form for the feedback gain matrix to build a novel control law for the closed loop system the new controller allows assignment of all the invariants of the system calculating the feedback requires solving a matrix integral equation for the periodic floquet factor of the state transition matrix of the closed loop system

regulator synthesis using c a b pairs the concept of a c a b pair of subspaces was introduced in an earlier paper by the author to study problems of compensator design here it is shown that the same concept plays a basic role in the theory of tracking and regulation from a few fundamental properties the main results of regulator theory are derived in a relatively simple and straightforward manner another new feature is that we are able to allow the presence of an unknown input thereby unifying the fields of tracking and regulation and disturbance decoupling all results are fully constructive and an example is given to illustrate the theory

multirate control a new approach abstract a new multirate digital control of linear periodic and time invariant systems is proposed an explicit multirate law is given which transforms the overall control design into that of a relatively small dimensional discrete time invariant system for which standard design techniques can be used it is shown that the proposed multirate scheme is in general more effective as a design tool than current multirate designs the controllability properties of the multirate system are studied consequently necessary and sufficient conditions for pole placement and stabilizability of the multirate system are given in terms of the continuous plant matrices moreover the multirate lqr problem is solved in this case the solution is obtained by solving an algebraic discrete riccati equation here necessary and sufficient conditions for the existence of a unique nonnegative definite solution of the riccati equation and the asymptotic stability of the corresponding closed loop multirate system are obtained these conditions are given in terms of the continuous time parameters

inertia theorems for the periodic lyapunov difference equation and periodic riccati difference equation abstract the periodic lyapunov difference equation plde and periodic riccati difference equation prde are dealt with the inertia i e the number of positive null and negative eigenvalues of any symmetric periodic solution of such equations is linked with the pattern of eigenvalues of the monodromy matrix associated with the open loop for plde or closed loop for prde underlying systems different results are obtained by imposing requirements with decreasing strength to the original system precisely assumptions of observability reconstructibility and detectability are successively introduced some results are also given for the particular case of positive semidefinite periodic solutions

a new optimal multirate control of linear periodic and time invariant systems the optimal multirate design of linear continuous time periodic and time invariant systems is considered it is based on solving the continuous linear quadratic regulation lqr problem with the control being constrained to a certain piecewise constant feedback necessary and sufficient conditions for the asymptotic stability of the resulting closed loop system are given an explicit multirate feedback law that requires the solution of an algebraic discrete riccati equation is presented such control is simple and can be easily implemented by digital computers when applied to linear time invariant systems multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly compared to the classical single rate sampled data feedback in which the state is always sampled at the same rate the multirate system can provide a better response with a considerable reduction in the optimal cost in general the multirate scheme offers more flexibility in choosing the sampling rates

an improved disaggregation method for transportation problems a method is given to disaggregate the solution to an aggregated transportation problem the resulting solution to the original problem is feasible all integer and has lower cost that those of solutions produced by earlier methods

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

cyclomonotonicity riccati equations and periodic receding horizon control abstract in this paper periodic receding horizon control of periodic and time invariant systems is considered this type of receding horizon control is based on the periodic extension of the control law that solves a finite horizon optimal control problem it is shown that cyclomonotonicity of the solution of the differential riccati equation entails stability of the closed loop system stability analysis hinges on the so called fake two point boundary riccati equation a differential riccati equation whose solution is constrained to satisfy a two point boundary condition in the case of time invariant systems cyclomonotonicity is always achievable by a proper scaling of the terminal condition of the riccati equation it is also proven that cyclomonotonic solutions of the riccati equation not only yield stabilizing controllers but also constant and stabilizing control laws

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

direct recovery of wave penetrable scatterers in a stratified ocean waveguide abstract we shall derive a direct sampling method for the recovery of wave penetrable inhomogeneous scatterers in a three dimensional stratified ocean waveguide the proposed method is simple straightforward and computationally efficient since no matrix inversions optimizations or solutions of ill posed linear systems are involved moreover it is highly tolerant to noise and is applicable with a few scattered fields corresponding to only two or four incidences in addition a priori knowledge of either the number of disconnected components or the physical features of the unknown obstacles is not required by the direct sampling method a mathematical derivation is provided for its validation and several extensive numerical experiments are shown to evaluate the effectiveness and feasibility of the newly proposed method

on the stabilization of a class of bilinear systems abstract in this paper the problem of the stabilization of a class of continuous time bilinear systems containing the class of the homogeneous ones is studied and simple stabiliza bility conditions are derived expressed in terms of the stability or stabilizability of some linear or homogeneous bilinear subsystems of the given system on this basis it is shown that this problem can be decomposed into subproblems and reduced to the stabilization of homogeneous subsystems of the system obtained through successive decompositions of it a sufficient condition for the stabilization of a homogeneous bilinear system is also given

stabilizability and detectability of linear periodic systems abstract in this paper four characterizations of stabilizability and detectability of linear periodic systems are considered two of them look as natural extensions of the classical definitions given for time invariant systems the remaining two are modal characterizations which turn out to be useful in the analysis of the periodic lyapunov and riccati equations it is shown that all these notions of stabilizability and detectability are in fact equivalent to each other one of the various definitions calls for the existence of the kalman canonical decomposition of periodic systems this issue is addressed in the appendix

structural properties of a class of linear hybrid systems and output feedback stabilization in this paper we deal with the problem of output feedback stabilization for a class of linear hybrid systems this problem is addressed by characterizing the structural properties of such a class of systems namely reachability controllability stabilizability observability constructibility and detectability are framed in terms of algebraic and geometric conditions on the data of the system two canonical forms recalling the classical kalman decompositions with respect to reachability and observability are given by taking advantage of this characterization duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time invariant output feedback compensator are stated compared with previous results no assumption is needed on the plant about minimum phaseness relative degree or squareness

periodic solutions of periodic riccati equations for periodically time varying matrix riccati equations controllability and observability in the usual sense are shown to be sufficient for the existence of a unique positive definite periodic solution

periodic output regulation for general linear heterodirectional hyperbolic systems abstract this paper presents a backstepping solution of the periodic output regulation problem for general linear heterodirectional hyperbolic systems by utilizing a time varying signal model regulators are determined for a general class of periodic reference inputs and disturbances a systematic design procedure is developed for the state feedback regulator by solving the periodic regulator equations in order to obtain an output feedback regulator a time varying finite dimensional reference observer and a time varying infinite dimensional disturbance observer are determined for this a systematic backstepping approach is provided the results of the paper are illustrated for a 4 4 hyperbolic system with periodic triangle reference inputs and sinusoidal disturbances subject to time varying frequencies

convexification of a 3 d coefficient inverse scattering problem abstract a version of the so called convexification numerical method for a coefficient inverse scattering problem for the 3d helmholtz equation is developed analytically and tested numerically backscattering data are used which result from a single direction of the propagation of the incident plane wave on an interval of frequencies the method converges globally the idea is to construct a weighted tikhonov like functional the key element of this functional is the presence of the so called carleman weight function cwf this is the function which is involved in the carleman estimate for the laplace operator this functional is strictly convex on any appropriate ball in a hilbert space for an appropriate choice of the parameters of the cwf thus both the absence of local minima and convergence of minimizers to the exact solution are guaranteed numerical tests demonstrate a good performance of the resulting algorithm unlikeprevious the so called tail functions globally convergent method we neither do not impose the smallness assumption of the interval of wavenumbers nor we do not iterate with respect to the so called tail functions

h controllability and observability of linear periodic systems with reference to linear periodic systems the classical notion of controllability introduced by kalman k controllability is shown to be equivalent to the characterization of controllability h controllability first proposed by hewer as a natural extension to the periodic case of an eigenvalue eigenvector controllability condition independently introduced by several authors for time invariant systems only the proof of such an equivalence also leads to the conclusion that if a t periodic system s is k controllable and k is the degree of the minimal polynomial of the monodromy matrix associated with s then at any time t s is controllable over t t kt since k is lower than or equal to the system order a well known result due to brunovsky is slightly strengthened by duality the corresponding observability results follow

lyapunov and riccati equations periodic inertia theorems the lyapunov and riccati differential equations with periodically time varying coefficients are considered under the assumption of detectability of the underlying periodic system two inertia theorems are provided linking the inertia of the solution to the one of the so called monodromy matrix

the solution of multiperiod network models with bundle constraints by aggregation we present a new network aggregation disaggregation approach for solving a multiperiod network model with bundle generalized upper bounding side constraints the model describes production planning and distribution problems instead of solving the original multicommodity problem we transform it so that a pair of single commodity network flow problems can be solved the original network is aggregated and the resulting problem is solved its solution determines a disaggregated problem that yields a feasible near optimal solution to the original problem we describe the determination of theoretical a priori and a posteriori bounds we also introduce a very tight computational error bound the implementation of the algorithm was tested against mpsx 370 and the specialized code for solving networks with side constraints netside the proposed solution method was found to be much more efficient with negligible error

direct sampling method for diffusive optical tomography in this work we are concerned with the diffusive optical tomography dot problem in the case when only one or two pairs of cauchy data are available we propose a simple and efficient direct sampling method to locate inhomogeneities inside a homogeneous background and solve the dot problem in both full and limited aperture cases this new method is easy to implement and less expensive computationally numerical experiments demonstrate its effectiveness and robustness against noise in the data this provides a new promising numerical strategy for the dot problem

a canonical decomposition of linear periodic discrete time systems in this paper a linear periodic discrete time system is studied on the basis of simple properties of the subspaces of controllable states and of unreconstructible ones a canonical structure theorem is derived this generalizes 1o such a system the classical kalman decomposition while preserving the constant dimensionality of the four subsystems which arise when a periodic continuous time system is decomposed the dynamic matrices of the non controllable and or non reconstructible subsystems are shown to be non singular at each time instant as those for a time invariant discrete time system are

solving staircase linear programs by the simplex method 1 inversion this and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged or staircase structure the present paper looks at inversion routines within the simplex method particularly those for sparse triangular factorization of a basis by gaussian elimination and for solution of triangular linear systems the succeeding paper examines pricing routines both papers describe extensive though preliminary computational experience and can point to some quite promising results

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

the multiperiod assignment problem a multicommodity network flow model and specialized branch and bound algorithm abstract the multiperiod assignment problem a specialization of the three dimensional assignment problem is an optimization model that describes the situation of assigning people to activities or jobs over time we consider the most general case which has both a cost of assigning a person to an activity in each time period and a cost of transferring the person from one activity in each period to another activity in the next period in general the number of time periods need not equal the number of persons and activities we present a new formulation of the multiperiod assignment problem that of an integer multicommodity network flow model the special structure of the model allows us to find a good feasible solution relatively quickly by a shortest path heuristic algorithm we discuss a new branch and bound algorithm for solving this problem to optimality the subproblems of the branch and bound tree are evaluated by solving a set of special structured shortest path problems all of which can be solved in order n 2 t time where n is the number of persons and activities and t is the number of time periods we present computational tests of the algorithm on moderately sized problems

nonlinear multigrid algorithms for bayesian optical diffusion tomography optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem bayesian approaches are effective but are computationally expensive especially for three dimensional 3 d imaging this paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems this multigrid method is applied to compute the maximum a posteriori map estimate of the reconstructed image in the optical diffusion tomography problem the proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality