line search acceleration of iterative methods abstract this paper describes and analyzes a simple technique that accelerates the convergence of iterative methods for solving large linear systems the proposed technique can be used with any convergent method however it is especially useful when solving unstructured systems since in this case traditional methods as sor or chebyshev semiiteration have difficulty in obtaining optimal parameters special attention is given to column relaxation and row relaxation it is demonstrated experimentally that an accelerated gauss seidel scheme runs faster than an optimally tuned sor scheme

exact and inexact lqg model matching problems the design of discrete time lqg linear quadratic gaussian controllers that yield closed loop systems that match a provided model is addressed the solution is in the form of a two degree of freedom controller having feedback and feedforward paths that independently provide the optimal actions for disturbance rejection and model matching exact and approximate model matching cases are discussed in a unified fashion

convergence studies on iterative algorithms for image reconstruction we introduce a general iterative scheme for image reconstruction based on landweber s method in our configuration a sequential block iterative seqbi version can be readily formulated from a simultaneous block iterative simbi version and vice versa this provides a mechanism to derive new algorithms from known ones it is shown that some widely used iterative algorithms such as the algebraic reconstruction technique art simultaneous art sart cimmino s and the recently designed diagonal weighting and component averaging algorithms are special examples of the general scheme we prove convergence of the general scheme under conditions more general than assumed in earlier studies for its seqbi and simbi versions in the consistent and inconsistent cases respectively our results suggest automatic relaxation strategies for the seqbi and simbi versions and characterize the dependence of the limit image on the initial guess it is found that in all cases the limit is the sum of the minimum norm solution of a weighted least squares problem and an oblique projection of the initial image onto the null space of the system matrix

robustness of multipredictor adaptive regulators musmar abstract effects of multipredictor information in adaptive control are studied particularly from the standpoint of plant structural uncertainties and unmodelled dynamics by an ode analysis it is shown that for an armax plant the equilibria of a multipredictor based lq self tuning regulator namely the musmar algorithm are the extrema of a receding horizon variant of the cost further if the control horizon is large enough the musmar possible convergence points tightly approximate the local minima of the unconditional quadratic cost constrained to the chosen regulator regressor

component averaged row projections a robust block parallel scheme for sparse linear systems a new method for the parallel solution of large sparse linear systems is introduced it proceeds by dividing the equations into blocks and operating in block parallel iterative mode i e all the blocks are processed in parallel and the partial results are merged to form the next iterate the new scheme performs kaczmarz row projections within the blocks and merges the results by certain component averaging operations hence it is called component averaged row projections or carp the system matrix can be general nonsymmetric and ill conditioned and the division into blocks is unrestricted for partial differential equations pdes if the blocks are domain based then only variables at the boundaries between domains are averaged thereby minimizing data transfer between processors carp is very robust its application to test cases of linear systems derived from pdes shows that it converges in difficult cases where state of the art methods fail it is also very memory efficient and exhibits an almost linear speedup ratio with efficiency greater than unity in some cases a formal proof of convergence is presented it is shown that the component averaging operations are equivalent to row projections in a certain superspace so the convergence properties of carp are identical to those of kaczmarz s algorithm in the superspace carp and its convergence proof also apply to the consistent convex feasibility problem

convergence studies on block iterative algorithms for image reconstruction the sequential block iterative scheme based on landweber s method is a general iterative one for image reconstruction in this paper we give the finite termination convergence for this scheme which provides an approach to choose relaxation coefficients furthermore sufficient and necessary convergence conditions are also established for the sequential block iterative scheme case

a novel derivation methodology for polynomial lq controller design a simple derivation method for optimization of linear quadratic lq controllers is presented in the discrete time polynomial systems framework a control law variation regarded as a potential feedforward from the innovations is used orthogonality is evaluated in the frequency domain by collectively cancelling unstable poles by zeros the suggested method summarized as a three step scheme is exemplified on a disturbance measurement feedforward and an output feedback problem it is a simple more direct alternative to the completing the squares approach

some unitary similarity invariant sets preservers of skew lie products abstract let h and k be complex separable hilbert spaces with dimensions at least three and b h the banach algebra of all bounded linear operators on h let denote w or e where for a w a stands for the numerical range of a b h and e a the e pseudospectrum of a it is shown that a bijective map no algebraic structure assumed b h b k satisfies that a b b a a b b a for all a b b h if and only if there exists a unitary operator u b h k such that a u a u for all a b h where 1 1 if w then the injectivity assumption on can be omitted

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

a condition for a subspace of b h to be an ideal abstract let h be a real or complex hilbert space with dim h 1 the subspace a b h is an ideal if and only if ta at a for every t b h a a every element of b h is the finite sum of ta at type operators

multivariable self tuning regulator with generalized cost function abstract the control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed a strategy using a generalized cost function is first presented a multivariable self tuning regulator based on this generalized minimum variance strategy is then proposed it uses a recursive multiple least squares estimator and a linear matrix controller obtained directly from the estimates the algorithm can be considered as a multivariable generalization of clarke s self tuning controller

optimal multivariable lqg control using a single diophantine equation the general solution of the optimal lqg problem using the polynomial equation approach involves the solution of a couple of two sided matrix polynomial equations the conditions under which a single one sided equation which is related to the original two the implied diophantine equation yields the unique optimal controller are derived in this paper the result has considerable relevance to aspects such as computation and self tuning control applications

regularization of inverse problems by two point gradient methods in banach spaces in this paper we propose and analyze a two point gradient method for solving inverse problems in banach spaces which is based on the landweber iteration and an extrapolation strategy the method allows to use non smooth penalty terms including the l 1 like and the total variation like penalty functionals which are significant in reconstructing special features of solutions such as sparsity and piecewise constancy in practical applications the design of the method involves the choices of the step sizes and the combination parameters which are carefully discussed numerical simulations are presented to illustrate the effectiveness of the proposed method

graph cut based discrete valued image reconstruction efficient graph cut methods have been used with great success for labeling and denoising problems occurring in computer vision unfortunately the presence of linear image mappings has prevented the use of these techniques in most discrete amplitude image reconstruction problems in this paper we develop a graph cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations we first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator we then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph cut frameworks we use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems we first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter then we focus on nonlocal tomographic examples where we consider limited angle data problems we compare our technique with state of the art discrete and continuous image reconstruction techniques experiments show that the proposed method outperforms state of the art techniques in challenging scenarios involving discrete valued unknowns

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

further results on implicit models with application to lq adaptive optimization abstract the theory of implicit models was defined by the authors in a previous work and is extended in this brief paper to include the possibility that an external dither signal may affect the regulator action the presence of this dither signal permits the existence of a broader class of implicit models as a consequence it is possible to develop an adaptive control algorithm based on finite and infinite horizon quadratic optimization criteria

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

polynomial design of stochastic tracking systems a new technique to design optimal stochastic tracking systems is presented for single input output plants described by rational transfer functions the optimal controller is shown to consist of feedback and feedforward parts and it is designed by solving two couples of linear polynomial equations whose coefficients are obtained by spectral factorization

minimax lq stochastic tracking and servo problems it is proved that the separation between feedback and feedforward of the two degree of freedom linear quadratic lq stochastic controller reported by e mosca and g zappa ibid vol 34 p 240 2 1989 can be suitably extended when a linear controller is postulated to the minimax lq stochastic tracking and servo problems besides the relevance of the results the authors show that in some problems the wiener and the h sub infinity approaches can play a fruitful complementary role

noise representation in residuals of lsqr lsmr and craig regularization abstract golub kahan iterative bidiagonalization represents the core algorithm in several regularization methods for solving large linear noise polluted ill posed problems we consider a general noise setting and derive explicit relations between noise contaminated bidiagonalization vectors and the residuals of bidiagonalization based regularization methods lsqr lsmr and craig for lsqr and lsmr residuals we prove that the coefficients of the linear combination of the computed bidiagonalization vectors reflect the amount of propagated noise in each of these vectors for craig the residual is only a multiple of a particular bidiagonalization vector we show how its size indicates the regularization effect in each iteration by expressing the craig solution as the exact solution to a modified compatible problem validity of the results for larger two dimensional problems and influence of the loss of orthogonality is also discussed

optimal h2 and h lq stochastic feedforward control this paper deals with the solution of the discrete time lq stochastic tracking and servo problems for a general system configuration it is shown that the resultant solution is in the form of a three degree of freedom controller when the vector of the exogeneous signal is extended to include accessible disturbances in particular it is shown that a separation property between feedback reference and accessible disturbance feedforward actions proved for a two degree of freedom optimal lq stochastic control scheme also holds true for the general system configuration here addressed further this separation property can be suitably extended when a linear control law is assumed to the minimax lq stochastic tracking and servo problems

model reference predictive lqg optimal control law for simo systems the design of linear quadratic gaussian lqg controllers for single input multiple output simo systems is considered this includes the class of multiloop control problems which are often solved using a classical nested loop structure many simplifications can be achieved over the more general multivariate problem which is important in self tuning control applications for example the tracking problem allows a model following capability to be introduced a predictive control feature is also available which enables the future values of the set point to be taken into account as in preprogrammed robot control

on implicit modelling theory basic concepts and application to adaptive control abstract the paper aims at presenting a unifying theory regarding the so called implicit models in adaptive control theory this term commonly indicates system models which do not correspond to the true one although they convey all the necessary information for the synthesis of the optimal controller and are simpler to be identified in the paper arx implicit models are considered and their possible use in adaptive control algorithms based on lq or pole assignment control criteria is discussed

on the h 2 two sided model matching problem with preview the h2 optimization problem with preview and asymptotic behavior constraints is considered in a general two sided model matching setting the solution is obtained in terms of two constrained sylvester equations associated with asymptotic behavior and stabilizing solutions of two algebraic riccati equations the riccati equations do not depend on the preview length yet are affected by asymptotic behavior constraints and are thus different from the standard h2 riccati equations arising in problems with no steady state requirements or in one sided problems

on the regularizing behavior of the sda and sdc gradient methods in the solution of linear ill posed problems we analyze the regularization properties of two recently proposed gradient methods sda and sdc applied to discrete linear inverse problems by studying their filter factors we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution thus yielding a useful filtering effect this behavior is confirmed by numerical experiments performed on some image restoration problems furthermore the experiments show that for severely ill conditioned problems and high noise levels the sda and sdc methods can be competitive with the conjugate gradient cg method since they are slightly slower than cg but exhibit a better semiconvergence behavior

on maps preserving zeros of the polynomial xy yx abstract let a m n f be the matrix algebra over a field f with an involution where n 20 suppose that a a is a bijective linear map such that x y y x for all x y a such that xy yx we show that is of the form x uxu 1 for x a where is a nonzero symmetric scalar and u is a normal matrix such that uu is a nonzero scalar

maps preserving product xy yx on factor von neumann algebras abstract let a and b be two factor von neumann algebras for a b a define by a b ab ba the new product of a and b in this paper we prove that a nonlinear bijective map a b satisfies a b a b for all a b a if and only if is a ring isomorphism in particular if the von neumann algebras a and b are type i factors then is a unitary isomorphism or a conjugate unitary isomorphism

notes on flexible sequential block iterative methods abstract we consider a flexible sequential block iterative method for the solution of consistent linear systems of equations and give its convergence analysis the method is able to use weight matrices and relaxation parameters which can be updated in each iteration whereas the most of previous studies on sequential block iterative methods considered a finite number of weight matrices furthermore we consider the constraint version of the method and give its convergence analysis for the special case of relaxation parameters and weight matrices we report on some numerical tests with examples taken from the field of image reconstruction from projections our numerical results show considerable improvement specially on noisy data compared to the other methods which use finite number of weight matrices

strong skew commutativity preserving maps on von neumann algebras abstract let m be a von neumann algebra without central summands of type i 1 assume that m m is a surjective map it is shown that is strong skew commutativity preserving that is satisfies a b b a a b b a for all a b m if and only if there exists some self adjoint element z in the center of m with z 2 i such that a z a for all a m the strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized

minimum variance control of linear time varying systems we study the problem of minimum variance control of linear time varying discrete time systems we consider the standard time varying controlled autoregressive moving average model and develop a time varying controller that guarantees both closed loop stability and minimum variance output control for a large class of linear time varying systems the controller is based on our previous results on minimum variance prediction for linear time varying systems we also show that the standard minimum variance controller cannot in general guarantee closed loop stability when applied to linear time varying systems however a simple modification can make the closed loop stable

extensions to generalized lqg and h multivariable controllers a particular form of the yjbk parametrization is used to address the generalized h control problem it consists of using as an intermediate stabilizing controller the solution of an underlying generalized lqg control problem this provides a direct link between the two solutions in fact when the yjbk free parameter falls to zero the two controllers become identical

pseudospectra of special operators and pseudospectrum preservers abstract denote by b h the banach algebra of all bounded linear operators on a complex hilbert space h let a b h and denote by a the spectrum of a for e 0 define the e pseudospectrum e a of a as e a z a e e b h e e in this paper the pseudospectra of several special classes of operators are characterized as an application complete descriptions are given of the maps of b h leaving invariant the pseudospectra of a b for different kinds of binary operations on operators such as the difference a b the operator product ab and the jordan product a b b a

a parallel subgradient projections method for the convex feasibility problem abstract an iterative method to solve the convex feasibility problem for a finite family of convex sets is presented the algorithm consists in the application of a generalization of an acceleration procedure introduced by de pierro in a parallel version of the subgradient projections method proposed by censor and lent the generated sequence is shown to converge for any starting point some numerical results are presented

necessary and sufficient convergence conditions for algebraic image reconstruction algorithms the landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases the convergence of the landweber scheme is of both theoretical and practical importance using the singular value decomposition svd we derive an iterative representation formula for the landweber scheme and consequently establish the necessary and sufficient conditions for its convergence in addition to verifying the necessity and sufficiency of known convergent conditions we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results moreover it is found that the landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values furthermore the limits of the landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least squares problem and an oblique projection of the initial image onto the null space of the system matrix

convergence of the simultaneous algebraic reconstruction technique sart computed tomography ct has been extensively studied for years and widely used in the modern society although the filtered back projection algorithm is the method of choice by manufacturers efforts are being made to revisit iterative methods due to their unique advantages such as superior performance with incomplete noisy data in 1984 the simultaneous algebraic reconstruction technique sart was developed as a major refinement of the algebraic reconstruction technique art however the convergence of the sart has never been established since then in this paper the convergence is proved under the condition that coefficients of the linear imaging system are nonnegative it is shown that from any initial guess the sequence generated by the sart converges to a weighted least square solution

projected randomized kaczmarz methods abstract for a constrained linear ill posed problems the projected algebra reconstruction technique part usually has a faster convergence rate than the projected simultaneous iterative reconstruction technique psirt but can not be applied to the inconsistent case in this work we propose the projected randomized kaczmarz method prk to further accelerate the convergence of part and analyze its convergence with the noise free right hand side we show that the prk method can converge exponentially in expectation to the solution for the consistent system with the noisy right hand side we present some insights into the semiconvergence property of the prk method and propose an extended version of prk prek method to seek the least squares solution we prove that the prek method can converge exponentially in expectation to the least squares solution for the inconsistent systems

paper implicit and explicit lqg self tuning controllers the design of optimal controllers for use in self tuning systems is considered linear quadratic gaussian lqg controllers are widely used elsewhere but have not until recently been applied in self tuning systems except in minimum output variance forms the lqg controllers offer a guarantee of stability when the plant parameters are known which is particularly useful for nonminimum phase systems the explicit lqg self tuning controllers introduced in the following are relatively simple to implement the first version of an implicit lqg self tuning controller is also introduced the magnitude of the transport delay terms need not be known a priori and integral action may be introduced easily if required the desired closed loop poles of the system can be prespecified

adaptive projection selection for computed tomography the number of projections is a critical factor in tomographic imaging the larger the number the better the quality of the reconstructed image however it increases the radiation dose delivered to the patient therefore it is important to keep the number of projections as small as possible traditionally the projections are taken by moving the x ray source around the patient at uniform angular steps taking projections at nonuniform steps may result in better images as compared with that obtained using uniform projections this paper describes two different approaches that adjust the step size to adaptively select the angle of projections the first one is based on the spectral richness of the acquired projections and the second relies on the amount of new information added by successive projections the superior performance of the two proposed methods over the uniform projection scheme is demonstrated through simulation results using both phantom and real images

two degrees of freedom feedback and feedforward optimal control of multivariable stochastic systems abstract a polynomial matrix solution is obtained to the optimal lqg output regulator problem for a system with both input and output disturbances dynamic feedback element and a cost function with dynamic weighting terms the cost function can include both the usual lqg output and control terms and sensitivity complementary sensitivity terms the solution of this regulating problem is also shown to provide a two degrees of freedom controller when a reference input is used for a tracking problem similarly a feedforward controller can also be derived from the results when a disturbance is measurable since in practice disturbances cannot usually be measured accurately provision is made for corrupting the measured spectrum and allowance is made for a measurement noise on this signal the results are obtained for a general multivariable plant

on diagonally relaxed orthogonal projection methods we propose and study a block iterative projection method for solving linear equations and or inequalities the method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system and is thus called diagonally relaxed orthogonal projections drop diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block iterative projection algorithms but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections drop has been used by practitioners and in this paper a contribution to its convergence theory is provided the mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of drop

iterative algorithms for large partitioned linear systems with applications to image reconstruction abstract we present a unifying framework for a wide class of iterative methods in numerical linear algebra in particular the class of algorithms contains kaczmarz s and richardson s methods for the regularized weighted least squares problem with weighted norm the convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for kaczmarz s and richardson s methods the algorithms in the class may be characterized as being group iterative and incorporate relaxation matrices as opposed to a single relaxation parameter we show that some well known iterative methods of image reconstruction fall into the class of algorithms under consideration and are thus covered by the convergence theory we also describe a novel application to truly three dimensional image reconstruction

implied polynomial matrix equations in multivariable stochastic optimal control abstract this paper reports recent work in the theoretical development of the polynomial equation approach to the optimization of multivariable control systems the algebraic properties of the polynomial matrix equations which define the optimal controller are investigated and new results concerned with the numerical solvability of the equations are derived

acceleration and filtering in the generalized landweber iteration using a variable shaping matrix the generalized landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography the method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized landweber iteration this component will still stay within in during subsequent iterations with a different shaping matrix as long as this shaping matrix satisfies the convergence criterion for the component two different shaping matrices are used the first recovers low frequency image components and the second may be used either to accelerate the reconstruction of high frequency image components or to attenuate these components to filter the image the variable shaping matrix gives results similar to truncated inverse filtering but requires much less computation and memory since it does not rely on the singular value decomposition

semiconvergence and relaxation parameters for projected sirt algorithms we give a detailed study of the semiconvergence behavior of projected nonstationary simultaneous iterative reconstruction technique sirt algorithms including the projected landweber algorithm we also consider the use of a relaxation parameter strategy proposed recently for the standard algorithms for controlling the semiconvergence of the projected algorithms we demonstrate the semiconvergence and the performance of our strategies by examples taken from tomographic imaging

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

an adaptive lq controller for non minimum phase systems abstract the paper studied the problem of the adaptive tracking of a reference signal by the output of any deterministic discrete siso linear system with unknown parameters an adaptive control scheme based on the lq control solution is proposed the stability of the resulting adaptively controlled system and conditions for a good tracking are studied several simulations illustrate the proposal

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

matrix fraction solution to the discrete time lq stochastic tracking and servo problems a novel matrix fraction solution to the discrete time lq linear quadratic stochastic tracking and servo problems is presented the resulting control law is based on the knowledge at time t of the output reference up to time t gamma if gamma is positive and large enough the optimal feedforward input can be tightly approximated without requiring any stochastic model for the reference if the latter is known the optimal feedforward input is obtained by solving a bilateral diophantine equation

implicit predictive adaptive control with stochastic gradient identifiers the replacement in an implicit predictive adaptive controller of recursive least squares rls identifiers with stochastic gradient sg identifiers is considered by an ordinary differential equation analysis local convergence properties of the new algorithm are investigated the conclusions supported by simulation results are that in contrast with the one step ahead self tuning regulator the convergence properties of the resulting adaptive controller deteriorate if rls identifiers are replaced with sg identifiers

tomographic image reconstruction using training images abstract we describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images we first construct a non negative dictionary based on prototype elements from the training images this problem is formulated within the framework of sparse learning as a regularized non negative matrix factorization incorporating the dictionary as a prior in a convex reconstruction problem we then find an approximate solution with a sparse representation in the dictionary the dictionary is applied to non overlapping patches of the image which reduces the computational complexity compared to previous formulations computational experiments clarify the choice and interplay of the model parameters and the regularization parameters and we show that in few projection low dose settings our algorithm is competitive with total variation regularization and tends to include more texture and more correct edges

arx modeling of controlled armax plants and lq adaptive controllers conditions under which controlled armax autoregressive moving average models with auxiliary inputs plants can be described by arx autoregressive models with auxiliary inputs models are studied among all possible arx models the ones that can be correctly used in long range lq linear quadratic adaptive control are characterized within this framework lq adaptive controllers embodying standard recursive least squares identifiers are singled out and shown to have equilibrium points solving related underlying lq control problems for the true armax plant

schultz matrix iteration based method for stable solution of discrete ill posed problems abstract in this paper we propose an iterative method for solving discrete ill posed problems based on matrix iterations generated by schultz method and known to converge to the moore penrose pseudoinverse of a matrix practically letting the schultz matrix iteration be x k we construct the vector x k x k b where b is a data vector hence by construction the iterates converge to the minimum 2 norm solution of a least squares problem with coefficient matrix a and data vector b we derive theoretical properties of the sequence x k and show that it is quadratically convergent in the case of corrupted data we analyze the semi convergence behavior of the iterates and conclude that the iteration must be truncated to control the propagation of the noise error as a result we derive an error estimate for the case where the truncation parameter is chosen by the discrepancy principle in addition combining a projected approach with the new method we propose variants of the method that are well suited for large scale problems several numerical results are presented to illustrate the effectiveness of the method on well known test problems

a semi infinite horizon lq self tuning regulator for armax plants based on rls so far no extension of the celebrated self tuning property of the rls gmv adaptive controller is available for the steady state lq stochastic control the above extension is addressed in the paper namely we pose the question is it possible to adaptively get the semi infinite horizon lq stochastic control for any armax plant by using a finite number of predictors whose parameters are estimated by standard rls an adaptive control algorithm solving an underlying control problem that coincides with the semi infinite lq stochastic feedback is developed it embodies a standard rls separate identification of the parameters of t n 1 predictors of the joint i o process n being the order of the armax plant together with an appropriate control synthesis rule the proposed algorithm turns out to be a slightly modified version of musmar with the capability of turning itself to the semi infinite horizon lq stochastic regulator

online identification of continuous time systems with unknown time delay in this note we present a recursive algorithm for online identification of systems with unknown time delay the proposed algorithm can be interpreted as an approximate nonlinear least squares corresponding to modified normalized or un normalized least squares when the normalizing factor spl gamma 0 or spl gamma 0 respectively both algorithms are essentially extensions to general least squares methodology simulation studies demonstrate the characteristics and performance of these algorithms

paper self tuning leader follower games the optimization of a class of linear discrete time stochastic systems with unknown parameters and multiple decision makers or controllers each having his own single stage quadratic objective is considered based on a centralized information pattern a steady state solution is obtained for the stochastic adaptive leader follower game problem it is shown that this class of leader follower game problems can be transformed to an equivalent class of multiple input multiple output self tuning control problems with a single decision maker the convergence of the multiple input multiple output self tuning controller is established and applied to the leader follower game a numerical simulation illustrates the proposed self tuning algorithm for an adaptive leader follower strategy

optimal preview control of markovian jump linear systems in this technical note we investigate the design of controllers for discrete time markovian jump linear systems that achieve optimal reference tracking in the presence of preview reference look ahead for a quadratic cost and given a reference sequence we obtain the optimal solution for the full information case the optimal control policy consists of the additive contribution of two terms a feedforward term and a feedback term we show that the feedback term is identical to the standard optimal linear quadratic regulator for markovian jump linear systems we provide explicit formulas for computing the feedforward term including an analysis of convergence

a polynomial approach to the mimo lq servo and disturbance rejection problems abstract a novel matrix fraction solution to the discrete time lq stochastic tracking and servo problems is extended to the disturbance rejection problem unlike recent contributions here the resulting control law at time t is given in terms of an expectation conditioned to the accessible disturbance given up to time t k if k is positive and large enough the optimal feedforward input can be tightly approximated without requiring any stochastic model for the disturbance if the latter is known also for recurrent or predictable disturbance the optimal feedforward input is obtained by solving a single bilateral diophatine equation

lqg predictive optimal control for adaptive applications abstract the lqg optimal control philosophy is extended so that use may be made of future set point or reference signal information the tracking error is defined in terms of an ideal response model so that a model following capability may be introduced the cost function may also be augmented by the addition of prediction error terms the controller was derived for adaptive control applications and has many of the desirable features of the new predictive control philosophy however there are fewer variables to choose and guaranteed stability properties are obtained for all weightings or prediction intervals the self tuning controller briefly described is almost as simple as existing lqg industrial self tuners

image reconstruction and restoration using the simplified topological e algorithm in order to compute meaningful approximations of the solutions of large scale linear inverse ill posed problems some form of regularization should be employed cimmino and landweber methods are well known iterative regularization methods that can be quite successfully applied for tomographic reconstruction and image restoration problems despite their usually slow convergence the goal of this paper is to explore the performance of a recent extrapolation algorithm when applied to accelerate the convergence of these iterative regularization methods in particular we provide insight and algorithmic details about the simplified topological e algorithm applied to slow converging iterative regularization methods the results of many numerical experiments and comparisons with other methods are also displayed

deterministic lq preview tracking design in this note the discrete time linear quadratic tracking problem with previewed feedforward action is considered it is assumed that the initial plant state is arbitrary and the whole reference sequence on 0 spl infin is known in advance the controller solving the problem is in a two degrees of freedom form whose feedback part equals the solution to the standard lq pure regulation problem whereas the feedforward part consists of an anticipative dynamic action whose calculation does not require a dynamic reference model an example is presented to show the use of the theory

lqg multivariable controllers minimum variance interpretation for use in self tuning systems it is first demonstrated that every lqg optimal control problem can be rewritten as a minimum output variance control problem for a related system model this system may be defined in either minimum or non minimum phase forms the optimal controller derived from the equivalent minimum variance problem is identical to the lqg optimal controller during the solution of the equivalent problem an equation is derived which is similar to the implicit relationships used in direct self tuning control schemes this enables the problems in constructing a multivariable implicit lqg self tuning controller using polynomial matrix methods to be explored the inherent difficulties become clear but a possible strategy is evident finally the results are specialized to the scalar case and a very simple implicit lqg self tuning algorithm is described