Showing papers in "IEEE Transactions on Automatic Control in 1974"
TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
47,133 citations
2,140 citations
TL;DR: This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.
Abstract: This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.
1,623 citations
Journal Article•
TL;DR: In this paper, the authors defined the concepts of structural and structural controllability for a linear time-invariant control system (described by a pair (A,b )) and studied the physical justification of these concepts and examples.
Abstract: The new concepts of "structure" and "structural controllability" for a linear time-invariant control system (described by a pair ( A,b )) are defined and studied. The physical justification of these concepts and examples are also given. The graph of a pair ( A,b ) is also defined. This gives another way of describing the structure of this pair. The property of structural controllability is reduced to a property of the graph of the pair ( A,b ). To do this, the basic concept of a "cactus" and the related concept of a "precactus" are introduced. The main result of this paper states that the pair ( A,b ) is structurally controllable if an only if the graph of ( A,b ) is "spanned by a cactus." The result is also expressed in a more conventional way, in terms of some properties of the pair ( A,b ).
1,276 citations
TL;DR: This paper surveys the field of optimal input design for parameter estimation as it has developed over the last two decades, with a derivation of the Fisher information matrix for multiinput multioutput systems with process noise.
Abstract: This paper surveys the field of optimal input design for parameter estimation as it has developed over the last two decades. Many of the developments covered are only recent and have not appeared in the open literature elsewhere. After a brief introduction, the paper discusses the historical background of the subject both in the engineering and in the statistical literature. The concepts of optimality and input design are then discussed, followed by a derivation of the Fisher information matrix for multiinput multioutput systems with process noise. The design procedures are divided into the categories of time-domain methods and frequency-domain methods, with the former being more general, but also more time consuming (computationally). Several extensions to state constraints, continuous-time systems, etc., are discussed. A number of examples are given to illustrate the nature of optimal inputs. The results on time-domain synthesis with state constraints and their relationship to "dual control" are new.
568 citations
TL;DR: It is shown how globally stable model reference adaptive control systems may be designed when one has access to only the plant's input and output signals.
Abstract: It is shown how globally stable model reference adaptive control systems may be designed when one has access to only the plant's input and output signals Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Lyapunov's direct method and the Meyer-Kalman-Yacubovich lemma Derivatives of the plant output are not required, but are replaced by filtered derivative signals An augmented error signal replaces the error normally used, which is defined as the difference between the model and plant outputs However, global stability is assured in the sense that the normally used error signal approaches zero asymptotically
497 citations
TL;DR: This work is intended to motivate the interest of bilinear systems and to present the current state of research in its various aspects.
Abstract: Recently, attention has been focused on the class of bilinear systems, both for its applicative interest and intrinsic simplicity. In fact, it appears that many important processes, not only in engineering, but also in biology, socio-economics, and ecology, may be modeled by bilinear systems. Moreover, since their nonlinearity is due to products between input and state variables, this class frequently may be studied by techniques similar to those employed for linear systems. This work is intended to motivate the interest of bilinear systems and to present the current state of research in its various aspects. After an introductory section, in which theoretical and applicative aspects of bilinear systems are enlightened, four other sections follow, respectively, devoted to structural properties, mathematical models, identification and optimization. In a final section, some concluding remarks are made on still open problems and possible trends for future research.
495 citations
TL;DR: In this paper, the difference between the feedback and closed-loop policies is discussed, and it is shown how the closed loop policy has the important property that it can be actively adaptive, while the feedback policy can only be passively adaptive.
Abstract: In this paper the various policies in fixed end-time stochastic control are discussed first. The emphasis is on the difference between the feedback and closed-loop policies. It is shown how the closed-loop policy has the important property that it can be actively adaptive, while the feedback policy can only be passively adaptive. The feature of being actively adaptive is possible when the control has a dual effect, i.e., in addition to its effect on the state it affects the state uncertainty. The intimate connection between the neutrality (lack of dual effect) and certainty equivalence properties for a class of problems is proved. This new result is then used to widen the class of problems for which it was previously known that the certainty equivalence property holds.
394 citations
TL;DR: In this article, it is shown that a natural representation of a state space is given by the predictor space, the linear space spanned by the predictors when the system is driven by a Gaussian white noise input with unit covariance matrix.
Abstract: In this paper it is shown that a natural representation of a state space is given by the predictor space, the linear space spanned by the predictors when the system is driven by a Gaussian white noise input with unit covariance matrix. A minimal realization corresponds to a selection of a basis of this predictor space. Based on this interpretation, a unifying view of hitherto proposed algorithmically defined minimal realizations is developed. A natural minimal partial realization is also obtained with the aid of this interpretation.
389 citations
TL;DR: In this article, the authors describe some of the important concepts and techniques which seem to help provide a solution of the stationary time series problem (prediction and model identification), and introduce a criterion for selecting the Order of an autoregressive estimator which can be regarded as determining the order of an AR scheme when in fact the time series is generated by an AR of finite order.
Abstract: The aim of this paper is to describe some of the important concepts and techniques which seem to help provide a solution of the stationary time series problem (prediction and model identification). Section I reviews models. Section II reviews prediction theory and develops criteria of closeness of a "fitted" model to a "true" model. The central role of the infinite autoregressive transfer function g_{\infty} is developed, and the time series modeling problem is defined to be the estimation of g_{\infty} . Section III reviews estimation theory. Section IV describes autoregressive estimators of g_{\infty} . It introduces a criterion for selecting the Order of an autoregressive estimator which can be regarded as determining the order of an AR scheme when in fact the time series is generated by an AR scheme of finite order.
340 citations
TL;DR: In this paper, the authors propose a concrete-concrete approach to the problem of concretization.Concrete-convex, concrete, and concrete-decrease.
Abstract: Concrete
TL;DR: Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined and new results on the calculation of state sensitivity functions via reduced order models are given.
Abstract: This paper discusses numerical aspects of computing maximum likelihood estimates for linear dynamical systems in state-vector form. Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined. The problems due to singular Hessian or singular information matrix that are common in practice are discussed in detail and methods for their solution are proposed. New results on the calculation of state sensitivity functions via reduced order models are given. Several methods for speeding convergence and reducing computation time are also discussed.
TL;DR: In this paper, the identification problem of linear dynamical systems is considered and the identiability of such an arbitrary parametrization is considered in several situations, assuming that the transfer function can be identified asymptotically, conditions are derived for local and global identifiability.
Abstract: We consider the problem of what parametrizations of linear dynamical systems are appropriate for identification (i.e., so that the identification problem has a unique solution, and all systems of a particular class can be represented). Canonical forms for controllable linear systems under similarity transformation are considered and it is shown that their use in identification may cause numerical difficulties, and an alternate approach is proposed which avoids these difficulties. Then it is assumed that the system matrices are parametrized by some unknown parameters from a priori system knowledge. The identiability of such an arbitrary parametrization is then considered in several situations. Assuming that the system transfer function can be identified asymptotically, conditions are derived for local and global identifiability. Finally, conditions for identifiability from the output spectral density are given for a system driven by unobserved white noise.
TL;DR: In this paper, an algorithm is introduced which ensures that the reduced-order model derived by equating time-moments and by continued fraction synthesis will be stable, assuming the high-order system is stable.
Abstract: An algorithm is introduced which ensures that the reduced-order model derived by equating time-moments and by continued fraction synthesis will be stable, assuming the high-order system is stable.
TL;DR: In this article, it is shown that string stability can be achieved only by using both forward and rearward intervehicle separation measurements, which can be obtained by using a moving-cell position reference for each vehicle.
Abstract: An important performance criterion for moving vehicle longitudinal control systems is string stability in the face of perturbations in the motion of individual vehicles. Systems employing a moving-cell reference for each vehicle always exhibit string stability since there is no vehicle interaction within the string. This correspondence investigates the string stability for a class of relative-motion systems where a moving-cell position reference is not available. It is shown that string stability can be achieved only by using both forward and rearward intervehicle separation measurements.
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Abstract: Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.
TL;DR: In this article, the linearity of the optimal control laws for the one-step delay linear quadratic Gaussian (LQG) stochastic control problem is established, and explicit formulae are presented.
Abstract: This paper considers stochastic problems in team theory. In particular, the linearity of the optimal control laws for the one-step delay linear quadratic Gaussian (LQG) stochastic control problem is established, and explicit formulae are presented. In addition, the control sharing, nonstatic, nonclassical LQG problem is solved.
TL;DR: In this article, a variant of Ho's algorithm that generates approximate realizations of specified dimension from approximate data is discussed. But it is not shown how to apply it to the problem of finite-dimensional linear systems.
Abstract: Ho's Algorithm generates exact realizations of finite-dimensional linear systems, given exact data. We discuss here a variant of the algorithm that generates approximate realizations of specified dimension from approximate data.
TL;DR: In this paper, conditions for the existence of a unique global and local minimum are given for a mixed autoregressive moving average (MAMA) model with respect to both local and global extrema.
Abstract: Estimation of the parameters in a mixed autoregressive moving average process leads to a nonlinear optimization problem. The negative logarithm of the likelihood function, suitably normalized, converges to a deterministic function as the sample length increases. The local and global extrema of this function are investigated. Conditions for the existence of a unique global and local minimum are given.
TL;DR: In this paper, the authors considered the design of optimal inputs for identifying parameters in linear dynamic systems and showed that the optimal energy constrained input is an eigenfunction of a positive self-adjoint operator corresponding to its largest eigenvalue.
Abstract: This paper considers the design of optimal inputs for identifying parameters in linear dynamic systems. The criterion used for optimization is the sensitivity of the system output to the unknown parameters as expressed by the weighted trace of the Fisher information matrix. It is shown that the optimal energy constrained input is an eigenfunction of a positive self-adjoint operator corresponding to its largest eigenvalue. Several different representations of the optimal input and several methods for its numerical computation are considered. The results are extended to systems with process noise, and the relationship to other criteria for input design are brought out. Three analytical examples are solved in closed form which show that the optimal input is a sum of sine and cosine functions at appropriate frequencies. Optimal elevator deflections for identifying the short period parameters of C-8 aircraft are computed numerically and compared with the doublet input currently in use.
TL;DR: In this paper, a connection between the input-output property of passivity and a set of constraints on the state equations of the system is established, and these constraints are then interpreted in terms of the stored energy and dissipation of a passive system.
Abstract: For a broad class of nonlinear systems, a connection is established between the input-output property of passivity and a set of constraints on the state equations of the system. These constraints are then interpreted in terms of the stored energy and dissipation of a passive system. Applications are given in two problems of optimal control theory, and a generalized form of the circle criterion is also derived.
TL;DR: In this article, the expected value of a multiplicative performance criterion, represented by the exponential of a quadratic function of the state and control variables, is minimized subject to a discrete stochastic linear system with additive Gaussian measurement and process noise.
Abstract: The expected value of a multiplicative performance criterion, represented by the exponential of a quadratic function of the state and control variables, is minimized subject to a discrete stochastic linear system with additive Gaussian measurement and process noise. This cost function, which is a generalization of the mean quadratic cost criterion, allows a degree of shaping of the probability density function of the quadratic cost criterion. In general, the control law depends upon a gain matrix which operates linearly on the smoothed history of the state vector from the initial to the current time. This gain matrix explicitly includes the covariance of the estimation errors of the entire state history. The separation theorem holds although the certainty equivalence principle does not. Two special cases are of importance. The first occurs when only the terminal state is costed. A feedback control law, linear in the current estimate of the state, results where the feedback gains are functionally dependent upon the error covariance of the current state estimate. The second occurs if all the intermediate states are costed but there is no process noise except for an initial condition uncertainty. A feedback law results which depends not only upon the current dynamical state estimate but also on an additional vector which is path dependent.
TL;DR: In this paper, the possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed and concepts that are useful for a systematic treatment of the problem are introduced.
Abstract: The possibility of estimating process parameters using input-output data collected when the system operates in closed loop is discussed in this paper. Concepts that are useful for a systematic treatment of the problem are introduced. The results refer to the case where the regulator is a linear feedback law or alternates between several such laws. It is shown that a straightforwardly applied identification scheme has the same identifiability properties as the more complex method in which the parameters of the closed-loop system are estimated first. It is also shown that it is always possible to achieve the same identifiability properties as for open-loop systems by shifting between different linear regulators. The required number of regulators depends only on the number of inputs and outputs. The results obtained are illustrated by a numerical example.
TL;DR: In this article, it was shown that even if the eigenvalues of the system A -matrix A(t) of a linear time-varying system are independent of t and some of them have positive real parts, the system is asymptotically stable.
Abstract: An example is given to show that even if the eigenvalues of the system A -matrix A(t) of a linear time-varying system \dot{x}(t) = A(t)x(t) are independent of t and some of them have positive real parts, the system is asymptotically stable.
TL;DR: In this article, several sets of canonical forms are described for state space models of deterministic multivariable linear systems; the members of these sets having therefore the required uniqueness property within the equivalence classes of minimal realizations of the system.
Abstract: The advantage of using a unique parameterization in a numerical procedure for the identification of a system from operating records has been well established. In this paper several sets of canonical forms are described for state space models of deterministic multivariable linear systems; the members of these sets having therefore the required uniqueness property within the equivalence classes of minimal realizations of the system. In the identification of a stochastic system, it is shown how the problem depends also upon determining a unique factorization of the spectral density matrix of the system, and the sets of canonical forms obtained for the deterministic system are extended to this case.
TL;DR: In this paper, the authors developed two new mathematical models of driver behavior in single-lane cars following situations and obtained the optimum parameter values in each of these models using standard parameter identification algorithms.
Abstract: This paper presents the development of two new mathematical models of driver behavior in single-lane car following situations. Optimum parameter values in each of these models were obtained using standard parameter identification algorithms. The basic approach to model development was to derive the model structure using optimal control theory. The problem was formulated as a model-tracking problem and a quadratic cost function was minimized. Model parameters were optimized by comparing model behavior with freeway data obtained on Interstate 71 in Ohio by Clear and Treiterer. The results indicate that the models fit the data very well during acceleration and deceleration phases, but not during constant velocity regions. To obtain a better fit during transitions between acceleration and deceleration phases, a second model was postulated based on the hypothesis that the driver tracks not only the car directly in front of him, but also cars directly ahead of the lead car. An adaptive controller structure with a mode switching algorithm has been derived and its parameters optimized.
TL;DR: In this paper, a new canonical form for an adaptive observer is presented which estimates the state and identifies the parameters of an unknown n th order linear time-invariant system.
Abstract: A new canonical form for an adaptive observer is presented which estimates the state and identifies the parameters of an unknown n th order linear time-invariant system. This is the simplest adaptive observer presented so far in the literature. The adaptive scheme is shown to be globally asymptotically stable, thus guaranteeing the convergence of the identification process.
TL;DR: The important case of autoregressive processes is studied and it is shown how the Chandrasekhar-type equations can be used to obtain and generalize the well known Levinson-Wiggins-Robinson (LWR) recursion for estimation of stationary autore progressive processes.
Abstract: Several results exposing the interrelations between state-space and frequency-domain descriptions of multivariable linear systems are presented. Three canonical forms for constant parameter autoregressive-moving average (ARMA) models for input-output relations are described and shown to corrrespond to three particular canonical forms for the state variable realization of the model. Invariant parameters for the partial realization problem are characterized. For stochastic processes, it is shown how to construct an ARMA model, driven by white noise, whose output has a specified covariance. A two-step procedure is given, based on minimal realization and Cholesky-factorization algorithms. Though the goal is an ARMA model, it proves useful to introduce an artificial state model and to employ the recently developed Chandrasekhar-type equations for state estimation. The important case of autoregressive processes is studied and it is shown how the Chandrasekhar-type equations can be used to obtain and generalize the well known Levinson-Wiggins-Robinson (LWR) recursion for estimation of stationary autoregressive processes.