an algebraic approach to the time optimal output regulator the time optimal output regulator is considered for a special class of linear time invariant discrete time systems it is shown that a simple state feedback law achieves time optimal output regulator response in one sampling period for a square system the state feedback law always assigns the invariant zeros as closed loop poles for a non square system time optimal regulator response is achieved even if the set of invariant zeros is empty if the set of invariant zeros is not empty the control law always assigns these zeros as closed loop poles the method of this paper for the discrete system described by the state and output equations x k 1 ax k bu k and z k cx k does not require that a be invertible and that the open loop system s a b c be state controllable furthermore the only requirement is the existence of a right inverse for the matrix cb which is sufficient for output controllability

a note on parameterization of the class of deadbeat controllers the problem of parameterizing the class of deadbeat controllers for a given discrete time system through the minimum number of parameters was solved by schlegel 1 this note shows how to utilize the above solution to study some problems in designing deadbeat controllers first an algorithm is developed to compute a controller which minimizes in an average sense a given objective function second a necessary and sufficient condition is given for the existence of an output deadbeat controller finally the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase variable block canonical form is reconsidered

distributed finite time calculation of node eccentricities graph radius and graph diameter abstract the distributed calculation of node eccentricities graph radius and graph diameter are fundamental steps to tune network protocols e g setting an adequate time to live of packets to select cluster heads or to execute distributed algorithms which typically depend on these parameters most existing methods deal with undirected topologies and have high memory and or bandwidth requirements or simply provide a bound on the diameter to reduce such costs other approaches instead require nodes able to communicate with their neighbors on a point to point basis thus requiring each node to be aware of its neighbors in this paper we consider strongly connected directed graphs or connected undirected graphs and we develop an algorithm that takes advantage of the robustness and versatility of the max consensus algorithm and has low computational memory and bandwidth requirements moreover the agents communicate by broadcasting messages to their out neighbors without requiring any knowledge on them or needing point to point communication capability specifically each node has memory occupation proportional to the number of its neighbors while the bandwidth for each link at each time instant is o log n bits where n is the number of nodes the completion time of the proposed algorithm is o n for undirected graphs and o n 2 for directed graphs where is the network diameter

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

multiscattering inversion for low model wavenumbers abstracta successful full waveform inversion implementation updates the low wavenumber model components first for a proper description of the wavefield propagation and slowly adds the high wavenumber potentially scattering parts of the model the low wavenumber components can be extracted from the transmission parts of the recorded wavefield emanating directly from the source or the transmission parts from the single or double scattered wavefield computed from a predicted scatter field acting as secondary sources we use a combined inversion of data modeled from the source and those corresponding to single and double scattering to update the velocity model and the component of the velocity perturbation responsible for the single and double scattering the combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data a scattering angle filter is used to divide the gradient of the combined inversion so initially the high wavenumber low scatterin

application of the finite difference contrast source inversion algorithm to seismic full waveform data we have applied the finite difference contrast source inversion fdcsi method to seismic full waveform inversion problems the fdcsi method is an iterative nonlinear inversion algorithm however unlike the nonlinear conjugate gradient method and the gauss newton method fdcsi does not solve any full forward problem explicitly in each iterative step of the inversion process this feature makes the method very efficient in solving large scale computational problems it is shown that fdcsi with a significant lower computation cost can produce inversion results comparable in quality to those produced by the gauss newton method and better than those produced by the nonlinear conjugate gradient method another attractive feature of the fdcsi method is that it is capable of employing an inhomogeneous background medium without any extra or special effort this feature is useful when dealing with time lapse inversion problems where the objective is to reconstruct changes between the baseline and the monitor model by using the baseline model as the background medium in crosswell seismic monitoring problems high quality time lapse inversion results are obtained

comments on minimum gain minimum time deadbeat controllers abstract we point out that the problem formulated in the above paper by elabdalla and amin 1 was solved in an earlier paper 3 using a direct approach

use of the design freedom of time optimal control abstract a method for synthesizing a state feedback time optimal controller for linear n state r input discrete time systems is developed the nonuniqueness of the solution is organized in such a way as to select the controller with the minimum value of the frobenius norm of the feedback gain matrix k it is shown that among the rn design parameters in the parametric form of k only r n rp r need to be considered in the search technique where p r is the order of the smallest jordan block in the jordan form of the closed loop system

author s reply to comments on eigenstructure assignment in linear multivariable systems a parametric solution by m m fahmy and j o reilly the authors reply that klein is correct in his observation that the approaches to eigenstructure assignment in earlier articles by b c moore 1976 g klein and moore 1977 are equivalent to those of the authors they assert however that their philosophies are quite different these differences are then described

deadbeat algorithms for output controllers in discrete time multivariable systems abstract this paper studies the problem of designing output deadbeat controllers to force the state of discrete time multivariable systems to zero in a finite number of samples two algorithms are considered the first is based on the fact that the closed loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces in the second algorithm the output gain matrix is computed through the optimization of certain parameters of the controller while maintaining its structural constraints computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques

on output deadbeat control of discrete time multivariable systems a necessary extension to the output deadbeat control algorithm of m r marrani et al see ibid vol ac 34 p 644 8 1989 is presented this extension is shown to provide particular theoretical insights when dealing with the case of a system with multiple stable transmission zeros it is numerically straightforward to implement once the zeros have been calculated the state zero directions can be determined independently this method has particular advantages when dealing with the case of a plant with multiple stable transmission zeros

comments on design of optimal dead beat controllers it is shown that the system considered in the numerical example of the above paper belongs to a class of systems with n states and r inputs for which the set of all minimum time dead beat mtdb controllers is parameterized by an arbitrary matrix of order lambda 1 r n x n lambda r where is the greatest integer less than the ratio n r since the example treats the case of n 3 r 2 the mdtb controller is parameterized by a single scalar element

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

minimum gain minimum time deadbeat controllers abstract this paper considers the design of minimum gain minimum time deadbeat controllers mgmtdc for linear discrete time systems a new direct method for constructing the mgmtdc of minimum frobenius norm is developed compared with many existing techniques the proposed method gives analytic expressions for the constructed mgmtdc requires less computational effort and does not require that the transition matrix be nonsingular

construction and parameterization of a class of minimum time deadbeat controllers abstract a method for constructing and parametrizing a class of minimum time deadbeat controllers mtdc for a discrete time system is presented the number of construction steps is equal to the controllability index of the controllable part of the system the method reduces the considered problem to that of solving at most r linear equations at each step where r is the input dimension the minimum number of free parameters that characterizes the constructed class of mtdc is specified and arranged in a new compact linear parametric form of mtdc contrary to many existing methods the presented method does not require the system to be controllable

an algorithm for minimizing the norm of state feedback controllers in eigenvalue assignment abstract minimization of the norm of parametric feedback controllers which assign desired eigenvalues to the closed loop system is achieved by implementation of vector companion forms described in an earlier paper the simple algorithm which emerges gives insight into the mechanism by which parametric eigenvalue assignment is affected a couple of numerical examples are presented to illustrate advantages of this algorithm which easily computes the controller gain matrix with minimum norm

joint migration inversion simultaneous determination of velocity fields and depth images using all orders of scattering the future in seismic exploration and seismic monitoring is the inclusion of all orders of scattering in the imaging and inversion algorithms using the full wavefield in an inversion process allows us to surpass imprints provided by incomplete acquisition and provide more accurate information on the subsurface as noise becomes signal we describe an inversion process that does not use the standard parameters from finite difference type modeling being local velocity and density but that describes the seismic data in terms of elastic reflectivity operators and propagation operators with these operators our full wavefield modeling process builds the complete two way seismic response a major advantage of our alternative to the traditional full waveform inversion methodology is that reflectivity operators are traveltime free and propagation operators are scattering free making the inversion problem significantly more linear a major advantage of our algorithm is 1 that multiples are utilized to impro

dead beat observers of reduced order for linear periodic discrete time systems with inaccessible inputs in this paper necessary and sufficient conditions are given for the existence of a dead beat observer for a linear periodic discrete time system subject to immeasurable periodic disturbances the conditions express in terms of the disturbed system the reconstructibility of the augmented system obtained by connecting the former with the disturbance generator a synthesis procedure of the observer is also provided

shaping of the output response in a class of linear multivariable systems a state feedback controller is designed to regulate as desired the output response of minimum phase linear multivariable square plants with cb having full rank b input matrix and c output matrix properties of the controller are given and an example is worked out for illustration

deadbeat characteristic of one step ahead control abstract the deadbeat characteristic of one step ahead control is examined in detail it has been clarified that the plant output y k coincides with the reference output y m k for all k n 1 n m where n is the order of the plant and n m is the relative degree of the plant transfer function

output controllability in a long time horizon abstract in this article we consider a linear finite dimensional system our aim is to design a control such that the output of the system reach a given target at a final time t 0 this notion is known as output controllability we extend this notion to the one of long time output controllability more precisely we consider the question is it possible to steer the output of the system to some prescribed value in time t 0 and then keep the output of the system at this prescribed value for all times t t we provide a necessary and sufficient condition for this property to hold once the condition is satisfied one can apply a feedback control that keeps the average fixed during a given time period we also address the l 2 norm optimality of such controls we apply our results to long time averaged control problems

regulation of time invariant discrete time descriptor systems time invariant discrete time descriptor systems of the form exk 1 axk buk where e and a are n n matrices and e may be singular are considered the problem is to find a feedback law uk kxk that drives the descriptor from x 0 to the origin in less than n time steps

time optimal output deadbeat regulators with internal stability for invertible systems abstract hassan and amin 1987 and amin and hassan 1987 have presented a simple algebraic solution for the time optimal output deadbeat tood regulator problem this solution which consists of a state feedback control law has been obtained for right invertible systems these results are generalized here to accom modate all classes of output controllable left invertible systems s a b c e the design of tood regulators with internal stability for all classes of right or output controllable left invertible systems s a b c e is also considered it is shown that the right wiener hopf factorization at infinity of h z the transfer function matrix of s is the key tool for solving all tood regulator problems moreover the internal stability problem which will arise if any invariant zero of s is unstable is solved by designing a tood regulator with internal stability finally numerical examples are worked out to illustrate the generality of the proposed method

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

a least deviation method to obtain a priority vector of a fuzzy preference relation based on the transfer relationship between fuzzy preference relation and multiplicative preference relation this paper proposes a least deviation method to obtain a priority vector of a fuzzy preference relation and studies its desirable properties a simple convergent iterative algorithm is given and its practicality is shown by two numerical examples

decision making with the ahp why is the principal eigenvector necessary in this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix a aij when a is a small perturbation of a consistent matrix when providing numerical judgments an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios near consistent matrices are essential because when dealing with intangibles human judgment is of necessity inconsistent and if with new information one is able to improve inconsistency to near consistency then that could improve the validity of the priorities of a decision in addition judgment is much more sensitive and responsive to large rather than to small perturbations and hence once near consistency is attained it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one if such perturbations were forced they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

incomplete pairwise comparison and consistency optimization this paper proposes a new method for calculating the missing elements of an incomplete matrix of pairwise comparison values for a decision problem the matrix is completed by minimizing a measure of global inconsistency thus obtaining a matrix which is optimal from the point of view of consistency with respect to the available judgements the optimal values are obtained by solving a linear system and unicity of the solution is proved under general assumptions some other methods proposed in the literature are discussed and a numerical example is presented

a generalization of rosenbrock s theorem this note presents the simple generalization of rosenbroek s theorem concerning the limits of linear state variable feedback in modifying the dynamics of constant linear multivariable systems

recursive eigenstructure assignment in linear systems in arbel and rath 1985 an iterative eigenvalue assignment algorithm was presented this algorithm has the shortcomings of clustering most of the closed loop eigenvalues on the real axis a general method is given here for recursive eigenstructure assignment in linear systems the method eliminates the shortcomings of the algorithm of arbel and rath it is shown that the right and left eigenvectors of the closed loop system matrix can be determined in terms of those of a small dimension matrix a c it is also shown that the results of arbel and tse 1980 are special cases of those of the proposed method moreover the arbitrary parameters beyond eigenvalue assignment are shown to be embedded in the choice of a certain arbitrary invertible matrix s furthermore computer oriented steps are outlined for recursive eigenstructure assignment in large scale systems numerical examples are worked out to illustrate the generality and feasibility of the proposed method

double objective optimal multivariable ripple free deadbeat control this paper presents novel results on optimal multivariable deadbeat control given a discrete time stable linear time invariant plant model we give a simple parameterization of all stabilizing ripple free deadbeat controllers of a given order the free parameter is then optimized in the sense that a quadratic index is kept minimal the optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort the proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor simulation results are included to illustrate the effectiveness of the proposed design algorithm

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

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

combining full wavefield migration and full waveform inversion a glance into the future of seismic imaging the next generation seismic migration and inversion technology considers multiple scattering as vital information allowing the industry to derive significantly better reservoir models with more detail and less uncertainty while requiring a minimum of user intervention three new insights have been uncovered with respect to this fundamental transition unblended or blended multiple scattering can be included in the seismic migration process and it has been proposed to formulate the imaging principle as a minimization problem the resulting process yields angle dependent reflectivity and is referred to as recursive full wavefield migration wfm the full waveform inversion process for velocity estimation can be extended to a recursive optionally blended anisotropic multiple scattering algorithm the resulting process yields angle dependent velocity and is referred to as recursive full waveform inversion wfi the mathematical equations of wfm and wfi have an identical structure but the physical meaning behind the expressions is fundamentally different in wfm the reflection process is central and the aim is to estimate reflection operators of the subsurface using the up and downgoing incident wavefields including the codas in each gridpoint in wfi however the propagation process is central and the aim is to estimate velocity operators of the subsurface using the total incident wavefield sum of up and downgoing in each gridpoint angle dependent reflectivity in wfm corresponds with angle dependent velocity anisotropy in wfi the algorithms of wfm and wfi could be joined into one automated joint migration inversion process in the resulting hybrid algorithm being referred to as recursive joint migration inversion jmi the elaborate volume integral solution was replaced by an efficient alternative wfm and wfi are alternately applied at each depth level where wfm extrapolates the incident wavefields and wfi updates the velocities without any user interaction the output of the jmi process offers an integrated picture of the subsurface in terms of angle dependent reflectivity as well as anisotropic velocity this two fold output reflectivity image and velocity model offers new opportunities to extract accurate rock and pore properties at a fine reservoir scale

parameterization of the class of deadbeat controllers via the theory of decoupling a novel approach is presented for parameterizing the class of minimum time deadbeat controllers mtdc through the minimum number of parameters the approach is based on the theory of decoupling and the properties of square decouplable systems the main result is a compact parametric form for the class of mtdc of a discrete time system contrary to many existing techniques no special assumption on the invertibility of the transition matrix is required

the effect of sampling period on the behaviour of systems incorporating state feedback an exposition of the effects of sampling on the controllability characteristics and the kronecker invariants of the plant and the input matrices of sampled data systems is presented in particular the effect of sampling period on the feedback matrix for time optimal control of sampled data systems is investigated in detail and it is shown that different classes of systems produce different response characteristics as the sampling period becomes large also simple expressions for a nt in terms of a t and b nt as a function of a t and b t are derived these expressions are computationally attractive and therefore facilitate the study of the effect of sampling period on system behaviour by applying these expressions the effects of sampling period on the feedback matrices for time optimal control of three classes of systems whose open loop plants are asymptotically stable marginally stable and unstable are illustrated by numerical examples

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

design of precompensators via infinite zero structure for dynamic decoupling of linear invertible systems the problem of designing precompensators necessary for decoupling invertible systems having weak inherent coupling is considered a simple algorithm which is directly applicable to systems characterized by square proper transfer function matrices t s is proposed for such design in the proposed algorithm the concept row reducedness at infinity of t s is utilized as an alternative necessary and sufficient condition for the decouplability of t s in addition to the simple design procedure of the compensator the algorithm yields the infinite zero structure of both t s and the resulting compensated system

deadbeat control of linear multivariable generalized state space systems the classic idea of deadbeat control is extended to linear multivariable discrete time generalized state space systems using algebraic methods the asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers using stabilizing full semistate feedback the solution is constructed from a cheap control problem both semistate and output deadbeat control laws are considered the main design criteria are to drive the semistate and or outputs of the system to zero in minimum time and that the closed loop system be internally stable unique properties of these types of control laws are discussed for semistate deadbeat control all the dynamic poles including the ones at infinity are moved to the origin whereas for output deadbeat some of the finite transmission zeros are canceled numerically reliable algorithms are developed to solve both problems

output regulator problem of time invariant discrete time descriptor systems linear time invariant discrete time systems of the form exk 1 axk buk yk cxt are considered where e and a are square matrices and e may be singular the investigations are restricted to systems for which there exist non singular matrices and such that e diag lr 0 and a equation pending where f 2 has full row rank such systems are termed regular by luenberger 1977 and can be decomposed into two equations of the respective forms k 1 1 k 2 k and 2uk 0 where k k and xk are related by the equation xk equation pending thus the descriptor system might be reduced to a state space system whose state vector is k a reasonable choice for c is c i 0 1where is some m x r matrix of full row rank which yields yk k the problem is this given an initial descriptor vector xo find without reducing the descriptor system to a state space system a sequence of control vectors u o u 1 un 1 hy that will yield yn 0 for some n a necessary and sufficie

time optimal output regulators for linear multivariate discrete time systems part 2 all classes of right invertible systems in part 1 of this paper hassan and amin 1987 a simple algebraic solution for the time optimal output regulator problem was presented this solution which consists of a state feedback control law has been obtained for all classes of right invertible decouplable systems s a b c e the results of part 1 are here extended to all classes of right invertible systems s a b c e a set of optimal output deadbeat indices called the optimal set is defined and related to the observability indices of the optimal closed loop system the time optimal output regulator problem for a right invertible non decouplable system s a b c e is resolved by transforming s into a decouplable system sc a b cc ec having the optimal output deadbeat index of s first an algorithm is presented to construct iteratively in a well defined optimal sense a unimodular left compensator l z and a compensated decouplable system sc a b cc ec from the state space parameters of s then a family of optimal state fee

on the general solution of the state deadbeat control problem in this note the state deadbeat control problem is considered it is shown that after appropriate change of basis of input and state spaces the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix this result yields a very simple procedure for the calculation of a state feedback deadbeat control gain it also provides the number of free parameters which could be used for further design purposes the results are illustrated by an example at the end of the note

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

comments on eigenstructure assignment in linear multivariable systems a parametric solution the approaches to eigenstructure assignment in 1 3 and the above paper are shown to be equivalent

parameterizations of the state feedback controllers for linear multivariable systems abstract a general framework is constructed upon which an explicit parametric formula can be derived for state feedback controllers containing all the possible combination of parameters the relation between the parameters is nonlinear in general and therefore many different constraint may be imposed by the designer to obtain desired performance criteria a couple of illustrative examples are presented

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

elastic reflection based waveform inversion with a nonlinear approach abstractfull waveform inversion fwi is a highly nonlinear problem due to the complex reflectivity of the earth and this nonlinearity only increases under the more expensive elastic assumption in elastic media we need a good initial p wave velocity and even better initial s wave velocity models with accurate representation of the low model wavenumbers for fwi to converge however inverting for the low wavenumber components of p and s wave velocities using reflection waveform inversion rwi with an objective to fit the reflection shape rather than produce reflections may mitigate the limitations of fwi because fwi performing as a migration operator is preferred of the high wavenumber updates along reflectors we have developed an elastic rwi that inverts for the low wavenumber and perturbation components of the p and s wave velocities to generate the full elastic reflection wavefields we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields w

eigenstructure assignment via linear state feedback control in fahmy and o reilly 1982 a b a parametric solution for the linear state feedback eigenstructure assignment problem is developed this approach is here modified in such a way as to accommodate the case where the set of closed loop eigenvalues and the set of open loop eigenvalues have elements in common it is particularly shown that each common eigenvalue introduces a number of partially free design parameter vectors in addition to the original free ones the paper concludes with illustrative numerical examples

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

multidimensional linearized inversion and seismic migration this paper discusses the close relationship between seismic migration and multidimensional inversion according to the linearized inverse scattering theory the linearized inverse scattering approach represents a mixed modeling inversion procedure unlike seismic migration the actual inversion process is carried out on the difference between a modeled reference response and the actually measured data the output is generally presented in terms of the elastic parameters of the medium seismic migration represents a direct inversion method the downward extrapolation process is carried out directly on the measured data output is presented in terms of reflectivity if the reference medium has been chosen in such a way that 1 the total wave field in the reference medium can be split into a downward traveling source wave field and an upward traveling response the propagation of both wave fields being defined by the one way wave equation and that 2 the upward traveling response in the reference medium can be neglected with respect to the upward traveling response in the actual medium then seismic migration and linearized inversion define identical inversion processes typically the above conditions are fulfilled in a homogeneous reference medium in iterative multidimensional inversion the full inverse scattering problem is approached by a number of linearized inversion steps i show that each linear step consists of a prestack migration process and a prestack modeling process the modeling output being used to remove the contribution of multiple scattering finally i argue that for a proper inversion process information on the elastic parameters outside the seismic frequency bandwidth temporally and spatially should be accounted for in the reference medium

a monte carlo investigation of incomplete pairwise comparison matrices in ahp the analytic hierarchy process ahp is a decision analysis technique used to evaluate complex multiattribute alternatives among one or more decision makers it imposes a hierarchical structure on any complex multicriterion problem however a major drawback of the ahp is that a large number of pairwise comparisons is needed to calibrate the hierarchy when there are a few levels and sublevels the ahp can be applied in a straightforward manner to derive the weights relative preference for each alternative as the size of the hierarchy increases the number of pairwise comparisons increases rapidly it is well established in the marketing and consumer behavior literature that in a very long interview even under the best circumstances the respondent is likely to suffer from information overload recognition of this problem was the motivation which led to the investigation of a modification of ahp which required less data collection i e a reduction in the threat of information overload the first question to be answered is the effect on ahp weights due to different patterns of missing data likely to result from reallife data collection in this study a monte carlo simulation was conducted which uses the incomplete pairwise comparisons ipc algorithm 14 to investigate the effect of reduced sets of pairwise comparisons in the ahp data for the study were generated with known structure and comparisons made between complete and incomplete matrices the results of the simulation suggest that incomplete sets of pairwise comparison matrices can capture the attribute level weights without significant loss of accuracy and independent of decision model form and amount of error considered

multiperson decision making based on multiplicative preference relations abstract a multiperson decision making problem where the information about the alternatives provided by the experts can be presented by means of different preference representation structures preference orderings utility functions and multiplicative preference relations is studied assuming the multiplicative preference relation as the uniform element of the preference representation a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives in this decision model several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations the decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives quantifier guided dominance degree and quantifier guided non dominance degree the consistency of the model is analysed to prove that it acts coherently

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

subsurface reflectivity estimation from imaging of primaries and multiples using amplitude normalized separated wavefields abstractseveral studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors however to characterize the reflector properties there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples from this perspective and based on the wave equation and rayleigh s reciprocity theorem recent works have suggested computing the subsurface image from the green s function reflection response or reflectivity by inverting a fredholm integral equation in the frequency space domain by following claerbout s imaging principle and assuming locally reacting media the integral equation may be reduced to a trace by trace deconvolution imaging condition for a complex overburden and considering that the structure of the subsurface is angle dependent this trace by trace deconvolution does not properly solve the fredholm integral equation we

parametrization of minimum time output deadbeat controllers for all classes of invertible systems this paper considers the problem of parametrizing through the minimum number of parameters the minimum time output deadbeat controller mtodc for a given linear multivariable output controllable system s a b c e having n states m inputs p outputs and a transfer function matrix h z of full rank r the main result is a new compact linear parametric form for a class of mtodc that zeros the outputs of the system s in the minimum number of control iterations 1 where 1 i 1 2 r assumed to be decreasingly ordered are equal lo the negatives of the right factorization indices at infinity of h z the developed parametric class is a linear function in effective free parameters the principal benefits of this explicit parametrization of mtodcs lie in the ability to accommodate directly various different design criteria

sparse and distributed analytic hierarchy process abstract the analytic hierarchy process ahp is a de facto standard technique in centralized decision making consider a situation where there is a need to rank a set of elements or alternatives based on their value or utility of which we just know pairwise relative information i e the ratio of their values ahp proved an effective tool to retrieve the value of each element being able to handle also relative information affected by distortions subjective biases and intransitivity a downside of ahp however is that it requires complete information i e knowledge on all pairs in this paper we extend the applicability of the ahp technique to the case of sparse information i e when only a limited amount of information is available and such an information corresponds to an undirected connected graph we complement our sparse framework by developing novel criteria and metrics to evaluate the degree of consistency of the data at hand moreover exploiting the proposed framework we also provide a distributed formulation of ahp in which a set of agents interacting through an undirected graph are able to compute their own values e g for ranking or leader election purposes by only knowing the ratio of their values with respect to their neighbors to this end we develop a novel algorithm to let each agent i compute the dominant eigenvalue and the i th component of the corresponding eigenvector of the sparse ahp matrix we conclude the paper with a simulation campaign that numerically demonstrates the effectiveness of the proposed approach

time optimal output regulators for linear multivariable discrete time systems part 1 right invertible decouplable systems corsetti and houpis 1985 presented a simple algebraic solution for the timeoptimal output regulator problem this solution has been obtained for a special class of right invertible decouplable systems s a b c satisfying the condition that cb is of full rank in this paper a general method is presented to extend the results of corsetti and houpis to all classes of right invertible decouplable systems s a b c e it is shown that a simple state feedback control law drives each output of s a b c e in a minimum number of steps equal to the order of the associated infinite zero this state feedback represents the optimal solution for the considered time optimal output regulator problem a class of optimal solutions parametrized by a free parameter matrix k is obtained for non square systems the properties of the resulting optimal closed loop system is given and a numerical example is worked out to illustrate the generality and feasibility of the proposed method

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

explicit parameterization of state deadbeat controllers a general state deadbeat control problem not restricted to the controllability indexes is posed and solved a result for the explicit parameterization of deadbeat controllers is obtained with the parameterization only the genuine independent free parameters appear in the deadbeat controllers

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed