optimal control system design of a nuclear reactor by generalized spectral factorization optimal feedback control system design of a nuclear power plant has usually been conducted in the time domain by solving the riccati equation in this paper the problem will be treated in the s domain by means of the macfarlane extension criterion mec the algorithm is based on generalized spectral factorization gsf and the mec is resolved by the newton raphson method featuring rapid convergence and high precision whether the plant is stable or unstable the initial matrix can be chosen effectively and a general computer code for finding the optimal feedback gain matrix of the multi input system is presented the control system design of a boiling water reactor bwr shows that the results obtained from the proposed method are consistent with those from solving the conventional riccati equation a satisfactory closed loop multivariable system with a prescribed degree of stability can also be designed in the s domain the methodology of this paper can also be generalized to treat similar control sys

optimal and self tuning deconvolution in time domain this paper is concerned with both the optimal minimum mean square error variance and self tuning deconvolution problems for discrete time systems when the signal model measurement model and noise statistics are known a novel approach for the design of the optimal deconvolution filter predictor and smoother is proposed based on projection theory and innovation analysis in the time domain the estimators are given in terms of an autoregressive moving average arma innovation model and one unilateral linear polynomial equation where the arma innovation model is obtained by performing one spectral factorization a self tuning scheme can be incorporated when the noise statistics the input model and or colored noise model are unknown the self tuning estimator is designed by identifying two arma innovation models

a reorganized innovation approach to linear estimation this note will address a linear minimum variance estimation of discrete time systems with instantaneous and delayed measurements although the problem may be approached via system augmentation and standard kalman filtering the computation of filter may be expensive when the dimension of the system is high and the measurement lag is significant in this note a new tool termed as reorganized innovation sequence is presented for deriving the optimal filter the optimal filter is given by two riccati difference equations rdes with the same dimension as that of the original system the approach is shown to induce saving of computational cost as compared to the system augmentation approach especially when the delay is large further it can be extended to solving the more complicated h sub spl infin fixed lag smoothing in krein space

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

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

matrix fraction construction of linear compensators a construction is given using polynomial matrix fractions of the compensator resulting from a combination of a linear feedback control law and estimator design

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

polynomial equations for the linear mmse state estimation the linear minimum mean square error mmse state estimation problem is solved via spectral factorization and a pair of bilateral diophantine equations detectability and or stability requirements in the riccati based solution context are expressed in terms of the stability of the greatest common right and left divisors of polynomial matrices

spectral factorization and lq optimal regulation for multivariable distributed systems a necessary and sufficient condition is proved for the existence of a bistable spectral factor with entries in the distributed proper stable transfer function algebra x1d49c in the context of distributed multivariable convolution systems with no delays a by product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system with entries in the algebra of fractions over x1d49c we next study semigroup state space systems sgb with bounded sensing and control having a transfer function with entries in and consider its standard lq optimal regulation problem having an optimal state feedback operator k0 for a system sgb a formula is given relating any spectral factor of a transfer function coprime fraction power spectral density to k0 a by product is the description of any normalized coprime fraction of the transfer function in terms of k0 finally we describe an alternative way of finding the solution operator k0 of the lq problem using spectral factor

modified doubly coprime fractional representations related to the reduced order observer modified doubly coprime fractional representations are introduced which are related to compensators based on reduced order observers from these representations the coprime compensator matrix fraction descriptions can directly be derived using standard software

mmse deconvolution via polynomial methods and its dual lqg regulation abstract the problem of linear minimum mean square error mmse multichannel deconvolution of sampled signals from noisy observations is approached via matrix polynomial equations the general solution is given in terms of a left spectral factorization and a pair of bilateral diophantine equations the first diophantine equation is obtained by imposing optimality of the deconvolution filter whereas the second ensures stability of the filter should the signal model be unstable the proposed solution encompasses classical wiener as well as stationary kalman filtering prediction and fixed lag smoothing the duality with the polynomial equations for lqg regulation is also discussed

a new method for optimal deconvolution using an innovation analysis method in the time domain the problem of optimal input estimation is considered two algorithms for calculating optimal deconvolution estimators are presented a new tool for obtaining the estimators is described it is based on the projection method and innovation theory the approach covers input prediction filtering and smoothing problems the solution is also applied to unstable linear systems disturbances or input models

robust filtering and feedforward control based on probabilistic descriptions of model errors abstract a new approach to robust estimation of signals prediction of time series and robust feedforward control is considered modelling errors are parametrized by random variables with known covariances a robust design is obtained by minimizing the squared estimation error averaged both with respect to model errors and the noise a polynomial equations approach based on averaged spectral factorizations and averaged diophantine equations is derived mild solvability conditions guarantee the existence of stable optimal filters and feedforward regulators the robust design turns out to be no more complicated than the design of an ordinary wiener filter or lqg regulator the proposed approach avoids two drawbacks of minimax design first probabilistic descriptions of model uncertainties may have soft bounds these are more readily obtainable in a noisy environment than the hard bounds required for minimax design furthermore not only the range of uncertainties but also their likelihood is taken into account common model deviations will have a greater impact on an estimator design than do very rare worst cases the conservativeness is thus reduced

the inverse problem of linear optimal control for constant disturbance this paper presents the solution to the inverse problem of linear optimal control systems to achieve pole placement and at the same time minimize the cost function and accommodate a constant but unknown disturbance the sufficient conditions for an optimal feedback law to have a positive r and positive semi definite q are found the relationships between the open loop poles and the closed loop poles that guarantee a positive r and q 0 are also obtained these relations offer a rule for selection of the appropriate closed loop poles which will guarantee the required feedback properties

lq optimal control of infinite dimensional systems by spectral factorization abstract we consider the standard lq optimal control of an exponentially stabilizable and detectable infinite dimensional semigroup state space system with bounded sensing and control it is reported that the reachable restriction of the lq optimal state feedback operator can be identified 1 by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper stable transfer function algebra and 2 by obtaining any constant solution of an operator diophantine equation over the properties of the restricted solution feedback operator are discussed it is shown in particular that the lq optimal state feedback operator and its reachable restriction coincide whenever the unreachable state components are unobservable these theoretical results are applied to a simple model of heat diffusion with collocated sensor and actuator leading to an approximation procedure converging exponentially fast to the lq optimal state feedback operator this procedure is based on approximate spectral factorization by symmetric extraction and on simple residue calculus

design of reduced order optimal estimators directly in the frequency domain the frequency domain design of optimal reduced order estimators caiman filters for continuous time linear time invariant systems containing 0 k m noise free output measurements is considered in a direct frequency domain approach to state feedback and estimation the states of a system do not appear explicitly and therefore we here focus our attention mainly on the frequency domain characteristics of the optimal filter by suitably modifying known time domain results a simple polynomial matrix equation can be derived from which the optimal filter parameters are obtained by spectral factorization the equivalence between the time and the frequency domain results is established with the aid of a non minimal representation of reduced order observers

strictly doubly coprime factorizations and all stabilizing compensators related to reduced order observers abstract doubly coprime factorizations dcf play an important role in the design of compensators for lumped linear time invariant systems they are defined as stable proper rational matrices and they not only constitute a starting point for the fractional approach to all stabilizing compensators but they are also closely related to the frequency domain design of optimal state feedback and estimation and of the resulting observer based compensators when defining dcfs related to reduced order observers some rational matrices become improper this can be prevented by the introduction of artificial stable dynamics the identity elements which cancel in the system and in the compensator transfer matrices such pole zero cancellations however are contrary to the usual notion of coprimeness it is shown here that these additional dynamics which have no meaning in an observer based compensator scheme are superfluous and that the parametrization of all stabilizing compensators is feasible on the basis of possibly nonproper factorizations not containing identity elements for such factorizations the new definition of strictly doubly coprime factorizations sdcf is proposed

flexible modelling of discrete failure time including time varying smooth effects discrete survival models have been extended in several ways more flexible models are obtained by including time varying coefficients and covariates which determine the hazard rate in an additive but not further specified form in this paper a general model is considered which comprises both types of covariate effects an additional extension is the incorporation of smooth interaction between time and covariates thus in the linear predictor smooth effects of covariates which may vary across time are allowed it is shown how simple duration models produce artefacts which may be avoided by flexible models for the general model which includes parametric terms time varying coefficients in parametric terms and time varying smooth effects estimation procedures are derived which are based on the regularized expansion of smooth effects in basis functions the approach is used to model the sojourn time in a psychiatric hospital it is demonstrated how initial conditions which have non linear influence are damped over time

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

fuzzy queries processing based on intuitionistic fuzzy social relational networks in this paper we propose fuzzy queries processing techniques based on the proposed intuitionistic fuzzy social relational network ifsrn model which contain positive relationships neutral relationships and negative relationships between actors where the degrees of relationship between actors are represented by intuitionistic fuzzy values ifvs the proposed fuzzy queries processing techniques based on the proposed ifsrn model are more flexible than the ones of yager s fuzzy social relational network fsrn model due to the fact that the system can get the degrees of truth and the degrees of false of fuzzy queries respectively whereas the fuzzy queries processing techniques based on yager s fuzzy social relational network fsrn model only can get the degrees of truth of fuzzy queries

a nonminimal representation of reduced order observers abstract a new nonminimal representation of reduced order observers of order n k in the time and in the frequency domain is introduced this reduced order observer is based on a full order plant model where the order reduction to n k results from an infinite gain feedback of k outputs this new representation is crucial for establishing the links between time and frequency domain design methods incorporating reduced order observers the main result are the doubly coprime fractional representations of a transfer matrix related to an observer of order n k

riccati equations for strongly stabilizable bounded linear systems we obtain necessary and sufficient conditions for the existence of strongly stabilizing solutions to riccati equations for infinite dimensional systems that are strongly but not exponentially stabilizable we apply the theory to derive a riccati criterion for the existence of j spectral factorizations and illustrate it by proving the strict positive real and bounded real lemmas for a class of strongly stable systems with collocated actuators and sensors