# Showing papers in "International Journal of Control in 1973"

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TL;DR: In this paper, observers which approximately reconstruct state variables of classes of nonlinear systems are presented, and the question of convergence of the reconstruction error is examined for special cases, and simulation results of the performance of some non-linear observers are also included.

Abstract: In this paper observers which approximately reconstruct state variables of classes of nonlinear systems are presented. The question of convergence of the reconstruction error is examined for special cases. Simulation results of the performance of some non-linear observers are also included.

735 citations

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Yale University

^{1}TL;DR: In this article, an adaptive scheme is synthesized to estimate the state vector and identify all the parameters of a single-input single-output nth order linear system, from only the input-output data.

Abstract: An adaptive scheme is synthesized to estimate the state vector and identify all the parameters of a Single-input single-output nth order linear system, from only the input—output data. The scheme is proved to be asymptotically stable in the whole, thus ensuring the convergence of the identification process.

136 citations

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TL;DR: In this paper, the authors studied the effect of measurement locations on the observability of a class of linear distributed parameter systems whose solutions can be represented by eigenfunction expansions (the so-called modal form).

Abstract: Observability and the optimal location of measurements are developed for a class of linear distributed parameter systems whose solutions can be represented by eigen-function expansions (the so-called modal form). A key question studied is the effect of measurement locations on the observability of this class of systems. Since observability is realty a prerequisite to state estimation, an algorithm is developed to determine a set of measurement locations which, in some sense, lead to the beat state estimates. This is accomplished by minimizing the trace of the steady-state covariance matrix of the state estimates.

119 citations

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TL;DR: In this paper, the authors extended the classical Smith Predictor method for single variable systems to a class of linear multivariable systems, and proposed a multivariable Smith predictor for both continuous-time and discrete-time systems.

Abstract: The classical Smith Predictor method for single variable systems is extended to a class of linear multivariable systems. Derivations of the multivariable Smith Predictor are presented for both continuous-time and discrete-time systems which contain time delays in the control variables and/or output variables. As in the classical method, use of the multivariable Smith Predictor eliminates the time delays from the characteristic equation of the closed-loop system

115 citations

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TL;DR: The fast Fourier transform is employed in the most efficient measurement of the Wiener kernels of a non-linear system so far discovered.

Abstract: A new method is presented for the measurement of the Wiener kernels of a non-linear system. The method uses the complex exponential functions as a set of orthogonal functions with which to expand the kernels. The fast Fourier transform is then employed in the most efficient measurement of the kernels so far discovered.

105 citations

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TL;DR: In this article, a method for finding a system S ∗ with a proper rational transfer function of small denominator degree, such that the step response of S∗ is, in an appropriate sense, the baat approximant to the stepresponse of S, is presented.

Abstract: Given a system S characterized by a transfer function, a practical method is developed for finding a system S∗ with proper rational transfer function of small denominator degree, such that the step response of S∗ is, in an appropriate sense, the baat approximant to the step response of S. The method is extended to multivariable systems. Various relations between moment and Pade approximants are derived.

95 citations

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TL;DR: In this paper, the singular pencil theory is applied to multivariable systems in state-space form and the minimal indices and divisors that characterize the theory are related to the system transfer function matrix through a new canonical form.

Abstract: Kronecker's theory of singular pencils ia applied to multivariable systems in state-space form. The minimal indices and divisors that characterize the theory are related to the system transfer-function matrix through a new canonical form. A new minimal realization procedure based on the infinite divisors of the pencil is given. The concept- of strictly equivalent pencils is used to provide an alternative solution to a model matching problem.

94 citations

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TL;DR: In this paper, a definition of the zero of a system has been given and the properties of these zeros are considered, and a definition is given and properties of zero properties are considered.

Abstract: Zeros of a system have not previously been defined. A definition is given and the properties of these zeros are considered.

92 citations

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TL;DR: In this article, the sensitivity specification is formulated in terms of bounds on the acceptable value of the loop transfer function L(s=σ+jω) on the imaginary axis jω, for each ω.

Abstract: In the single-loop, linear, time-invariant feedback control system with parameter ignorance and/or unwanted disturbances, the sensitivity specification may be formulated in terms of bounds on the acceptable value of the loop transfer function L(s=σ+jω) on the imaginary axis jω, for each ω. Due to the ever-present noise in the feedback return path, it is highly important to satisfy these bounds with an L(jω) whose magnitude is as small as possible at large id. Such an optimum exists, is unique and lies on the associated boundary at each value of ω

87 citations

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TL;DR: A survey of the literature devoted to the synthesis of model-tracking adaptive systems based on application of Liapunov's second method is given in this article, where the basic synthesis procedure is introduced and a critical review of extensions made to the theory since 1966 is made.

Abstract: A survey was made of the literature devoted to the synthesis of model-tracking adaptive systems based on application of Liapunov's second method. The basic synthesis procedure is introduced and a critical review of extensions made to the theory since 1966 is made. The extensions relate to design for relative stability, reduction of order techniques, design with disturbance, design with time variable parameters, multivariable systems, identification, and an adaptive observer.

72 citations

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TL;DR: In this article, the decoupling problem for an m-input m-output linear time-invariant system with multiple delays in the state and/or the control is solved.

Abstract: The decoupling problem is solved for an m-input m-output linear time-invariant system with multiple delays in the state and/or the control. The conditions under which such a system can be decoupled are found and the class of the feedback decoupling operators is given. These operators are realized by means of digital filters. Then, the more general linear model in which the input effects directly the output is considered which, upon the introduction of both feedback and feedforward, is shown to be decoupled, Two illustrative examples are included to support the theoretical results.

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TL;DR: In this paper, a new approach for analysing some important structural properties of linear systems, such as unknown-input observability, invertibility and functional controllability, is presented.

Abstract: A new approach for analysing some important structural properties of linear systems as unknown-input observability, invertibility and functional controllability, is presented. It is based on the concepts of ‘ controlled ’ and ‘ conditioned ’ invariance which have recently been developed and applied by the authors for a schematic and unitary treatment of many topics related to analysis and synthesis problems in linear system theory. The necessary and sufficient conditions herein derived are simple in their statement, can be quickly cheeked by means of a digital machine and have a geometrical meaning which tends to be very helpful for understanding their connection with other structural properties and for devising effective synthesis procedures.

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TL;DR: In this article, a recursive form of the Bryson-Frazier smoothing equations for a linear continuous dynamic system with linear discrete measurements is presented, which exhibits a duality with the Kalman filtering equations.

Abstract: A recursive form of the Bryson-Frazier (1963) smoothing equations for a linear continuous dynamic system with linear discrete measurements is presented. The now algorithm exhibits a duality with the Kalman filtering equations. As a result of this duality it is possible to convert existing Kalman filtering programmes into smoothing programmes by redefining variables. Storage and computational requirements for the new algorithm are less than that for the Rauch-Tung-Streibel (1965) continuous smoother or the Fraser (1067) two-filter continuous smoother

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TL;DR: In this article, a computer-oriented procedure for simplification of a z -transfer function is presented, which consists of transformation of the z-transfer function into the w domain by the bilinear transformation, w=(z− l)/)z+ 1), and continued fraction expansion of the w -transfer functions into the Cauer second form, keeping the first several quotients and discarding others, converting the truncated continued fraction into ztransfer functions of low order.

Abstract: A computer-oriented procedure for the simplification of a z -transfer function is presented. The method consists of (1) transformation of the z-transfer function into the w domain by the bilinear transformation, w=(z− l)/)z+ 1), (2) continued fraction expansion of the w -transfer function into the Cauer second form, (3) keeping the first several quotients and discarding others, (4) converting the truncated continued fraction into z-transfer function of low order. An example is used to illustrate the rapid rate of convergence.

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TL;DR: In this paper, a class of non-linear non-autonomous systems with multiple nonlinearities is considered and sufficient conditions are developed for a type of practical stability with specified settling time.

Abstract: In this paper, a class of non-linear non-autonomous systems with multiple non-linearities is considered. Sufficient conditions are developed for a type of practical stability with specified settling time. The conditions are independent of the actual Form of the non-linear characteristics so that they can be interpreted as conditions for ‘absolute’ practical stability. The stability test is reduced to verification of the Hurwitz property of a constant matrix. This makes the stability analysis of the considered class of non-linear systems convenient for machine computations The proposed practical stability analysis is applied to a third-order system with several non-linearities.

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TL;DR: In this paper, a linear system is proposed and a quadratic criterion is optimized over an infinite interval to obtain time-invariant laws for the control of systems having time-delays in their control paths.

Abstract: The control of systems having time-delays in their control paths is considered and feedback laws are developed. A linear system is proposed and a quadratic criterion is optimized over an infinite interval to obtain time-invariant laws. A particularly simple law obtained by the solution of a non-delayed problem can be developed when all controls are delayed by the same amount, but when each control is delayed by a different amount the solution becomes quite complicated. Nevertheless this paper shows how solutions can be obtained by solving a sequence of tracking problems. In contrast to the state-delayed problem, where non-linear partial differential equations need be solved, only ordinary differential equations with single-point boundary values need be solved for the control-delayed problem. The time-invariant feedback law obtained involves a knowledge of the time-delay storages and performs a linear operation on these. The kernels of this operation cannot in general be derived as impulse responses of lum...

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TL;DR: In this article, the effect of plant parameter variations on systems with nominally time-optimal feedback controllers is investigated, assuming that the plant parameter remains constant and that the timeoptimal controller calculated for the nominal plant parameter is used.

Abstract: The effect of plant parameter variations on systems with nominally time-optimal feedback controllers is investigated. It is assumed that the plant parameter remains constant and that the time-optimal controller calculated for the nominal plant parameter is used. For higher-order systems remarkably small deviations of the plant parameter from its nominal value are found to yield instability. A sub-optimal controller design which results in sliding motion ensures stability and yields acceptable settling time for moderato parameter variations

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TL;DR: It is shown that the above problem constitutes a class of non-linear mean-square estimation problems and closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification by utilizing the adaptive approach.

Abstract: The recent results of Lainiotis (1971 a, b, 1971) on single-shot, as well as multishot, joint detection, estimation and system identification for continuous data and dynamics are extended to multishot, discrete data and discrete dynamical systems. The results are given for the signals generated by the linear dynamical systems with unknown parameter vectors and driven by white gaussian sequences, where the observation contains additive white gaussian noise. Specifically, it is shown that the above problem constitutes a class of non-linear mean-square estimation problems. By utilizing the adaptive approach, closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification. In addition, several approximate algorithms that utilize linear Kalman estimators are presented to limit the storage requirement to finite size and reduce computational requirements. The results presented in this paper are applicable to both independent and Markov signalling sources

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TL;DR: In this paper, it was shown that p closed loop poles of a linear time invariant multivariable system can be assigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable and observable.

Abstract: Given a linear time invariant multivariable system with m inputs and p outputs, it was shown that p closed loop poles of the system can be preassigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable. These data show that if (A circumflex, B circumflex, C circumflex) is controllable and observable, and Rank B circumflex = m, Rank C circumflex = p, then max (m,p) poles of the system can be assigned arbitarily using constant gain output feedback. Further, it is shown that in some cases more than max (m,p) poles can be arbitrarily assigned. A least square design technique is outlined to approximate the desired pole locations when it is not possible to place all the poles.

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TL;DR: In this article, a prior knowledge of the approximate system and noise model parameters is used to design a test signal which will minimize the variance of the parameter estimates in linear S.I.O. systems.

Abstract: A sufficient condition for consistent estimates of parametera in linear S.I.S.O. system identification is that the input signal should be ‘ persistently exciting ’, However,. in practice the exact nature of the test signal has a direct bearing upon the identification accuracy. This paper shows how a-priori knowledge of the approximate system and noise model parameters may be used to design a test signal which will minimize the variance of the parameter estimates. The design procedure is computationally efficient as full advantage is taken of the special structure of linear S.I.S.O. systems. The optimal test signals are shown to result in a significant reduction in the parameter variances. This is of considerable practical importance as either the experiment time may be reduced for the same model accuracy or for fixed experiment time a model of much higher accuracy may be obtained.

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TL;DR: In this article, the optimal output decentralized and global control of a power system consisting of three interconnected synchronous machines is considered and a computational method is introduced to find the optimal control (either global or local) of a complete system.

Abstract: The optimal output decentralized (i.e. local) and global control of a power system consisting of three interconnected synchronous machines is considered in this paper. A computational method is introduced which enables the optimal output control (either global or local) of a complete system to be found, thereby allowing realistic control configurations to be studied.

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TL;DR: In this article, a new formulation for the problem of system reliability optimization when constrained by some linear constraints is presented, which is easily adaptable to geometric programming form and is further reduced to that of an optimization of an unconstrained objective function with variables one less than the number of constraints, when its dual is defined.

Abstract: A new formulation for the problem of system reliability optimization when constrained by some linear constraints is presented in this paper. The formulation provided is easily adaptable to geometric programming form. The problem is further reduced to that of an optimization of an unconstrained objective function with variables one less than the number of constraints, when its dual is defined. It is amply demonstrated through this paper that the formulation and approach of this paper are simpler than earlier attempts described elsewhere. An example is also given.

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TL;DR: In this article, it was shown that the existence of first integrals of Pontryagin's maximum principle equations depend on solutions of a system of partial differential equations (generalized Killing's equations) for optimum control systems.

Abstract: In this paper Noether's theorem of classical mechanics and the variational calculus is developed for optimum control systems. Also, it is shown that the existence of first integrals of Pontryagin's maximum principle equations depend on the existence of solutions of a system of partial differential equations—generalized Killing's equations —for optimum control systems.

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TL;DR: The so-called ‘ iterative ’ or ‘ reprocessed ’ smoothing scheme, used extensively as a data reduction process in the Apollo Space Programme, is studied using the ‘ partition smoothing ’ algorithm, and its computational and analytical advantages studied.

Abstract: Recently, Lainiotia (1971 c), using the so-called ‘ partition theorem ’, has obtained an optimal linear smoothing algorithm in explicit, closed-form expressions that are attractive, both from a computational and an analysis point of view. Lainiotis (1971c( ‘partition smoothing’ algorithm is re-examined herein, and its computational and analytical advantages studied. It is compared to the previously established two-filter smoothing algorithm of Mayne (1966), Fraser (1967), and Mehra (1968), as well as to the ‘ innovation smoothing ’ algorithm of Kailath and Frost (1968) Subsequently, the so-called ‘ iterative ’ or ‘ reprocessed ’ smoothing scheme, used extensively as a data reduction process in the Apollo Space Programme, is studied using the ‘ partition smoothing ’ algorithm. The resulting explicit and closed-form expressions are readily amenable to interpretation and optimization, and are, moreover, both theoretically interesting as well as practically useful. The statistical and limiting properties of t...

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TL;DR: In this paper, a simple test is given in analytic (matrix) terms which provides both necessary and sufficient conditions for arbitrary assignment of all of the system poles using only constant output feedback.

Abstract: A simple test is given in analytic (matrix) terms which provides both necessary and sufficient conditions for arbitrary assignment of all of the system poles using only constant output feedback A formula to determine the required output compensator is presented, and the whole procedure is illustrated by an example

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TL;DR: In this paper, the first-passage time problem for envelope crossing for a linear oscillator subject to stationary wide-band random excitation is investigated, and the amplitude of the response is approximated by a one-dimensional Markov process, and differential equations governing the moments of the first passage time are derived.

Abstract: The first-passage time problem for envelope crossing for a linear oscillator subject to stationary wide-band random excitation is investigated. The amplitude of the response is approximated by a one-dimensional Markov process, and differential equations governing the moments of the first-passage time are derived. Analytical solutions are obtained for the mean and the variance

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TL;DR: These equations are shown to imply that in principle a modified B. L. Ho algorithm can be used to find the approximation of a system of lower dimension which optimally approximates the given system with respect to the sum of squared output errors of the impulse response.

Abstract: Given a multi–input, multi–output linear time–invariant discrete–time system or its weighting matrices, equations are derived to characterize a system of lower dimension which optimally approximates the given system with respect to the sum of squared output errors of the impulse response. These equations are shown to imply that in principle a modified B. L. Ho algorithm can be used to find the approximation. The connection with projection methods of approximation is demonstrated, Some comments on computational difficulties are included.

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TL;DR: In this paper, the problem of designing an optimal (n − m)-order Luenberger observer for an nth-order time-invariant linear system with m (m

Abstract: The problem of designing an optimal (n — m)-order Luenberger observer for an nth-order time-invariant linear system with m (m

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TL;DR: In this article, two methods of approximating such transfer function models by lower order models, the continued fraction expansion of Chen and Shieh and the moments matching method of Gibilaro and Lees, are compared.

Abstract: A widely used form of transfer function model is $ Two methods of approximating such transfer function models by lower order models, the continued fraction expansion of Chen and Shieh and the moments matching method of Gibilaro and Lees, are compared. It is demonstrated that these two methods can give identical results. An efficient computational procedure for the moments matching method is described and the results of computation for the reduction of a seventh-order model are given.

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TL;DR: In this article, a simplified method for solving the asymmetric, coupled, Riccati-type matrix differential equations occurring in the solution of open-loop Nash controls in linear quadratic differential games is discussed.

Abstract: A simplified method for solving the asymmetric, coupled, Riccati-type matrix differential equations occurring in the solution of open-loop Nash controls in linear quadratic differential games is discussed m this paper. This method offers considerable savings in the computational requirements of the sampled-data Nash solution in time-invariant linear quadratic differential games where the open-loop Nash Riccati equations must be solved repeatedly several times for different boundary conditions. A simple example is presented to illustrate the results