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Automatic Control, IEEE Transactions on

Issue 1 • Date January 1983

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Displaying Results 1 - 25 of 29
  • [Front cover and table of contents]

    Page(s): 0
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  • Comments on "Design of optimal dead-beat controllers"

    Page(s): 125 - 127
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    It is shown that the system considered in the numerical example of the above paper belongs to a class of systems (withnstates andrinputs) for which the set of all minimum-time dead-beat (MTDB) controllers is parameterized by an arbitrary matrix of order[(lambda + 1)r - n]x[n - lambda r]where λ is the greatest integer less than the ration/r. Since the example treats the case ofn = 3, r = 2, the MDTB controller is parameterized by a single scalar element. View full abstract»

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  • [Back cover]

    Page(s): 0
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    Freely Available from IEEE
  • Characterization of "Allowable perturbations" for robust stability

    Page(s): 107 - 109
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    The problem of determining stability for a closed-loop linear multivariable process in the presence of ill-defined process perturbations is considered. It is shown thatM-matrices may be used to characterize a class of allowable perturbations. View full abstract»

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  • Analysis of oscillations in systems with polynomial-type nonlinearities using describing functions

    Page(s): 31 - 41
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    Sufficient conditions for the existence of oscillations are obtained in the case of an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials. Both a graphical procedure and an algebraic technique are presented for use with describing function analysis, and a graphical procedure is given for use with multiple input describing functions. Graphing is done in a parameter space of the solution, rather than in the complex plane. View full abstract»

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  • Simultaneous identification and adaptive control of unknown systems over finite parameter sets

    Page(s): 68 - 76
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    The problem considered is one of simultaneously identifying an unknown system while adequately controlling it. The system can be any fairly general discrete-time system and the cost criterion can be either of a discounted type or of a long-term average type, the chief restriction being that the unknown parameter lies in a finite parameter set. For a previously introduced scheme of identification and control based on "biased" maximum likelihood estimates, it is shown that 1) every Cesaro-limit point of the parameter estimates is "closed-loop equivalent" to the unknown parameter; 2) for both the discounted and long-term average cost criteria, the adaptive control law Cesaro-converges to the set of optimal control laws; and 3) in the case of the long-term average cost criterion, the actual cost incurred by the use of the adaptive controller is optimal and cannot be bettered even if one knew the value of the unknown parameter at the start. View full abstract»

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  • On output-error methods for system identification

    Page(s): 12 - 23
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    In this paper are derived consistency and asymptotic normality results for the output-error method of system identification. The output-error estimator has the advantage over the prediction-error estimator of being more easily computable. However, it is shown that the output-error estimator can never be more efficient than the prediction-error estimator. The main result of the paper provides necessary and sufficient conditions for the output-error estimator and the prediction-error estimator to have the same efficiency, irrespective of the spectral density of the noise process. View full abstract»

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  • Equations for the angles of arrival and departure for multivariable root loci using frequency-domain methods

    Page(s): 118 - 121
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    Frequency-domain methods are used to study the angles of arrival and departure for multivariable root loci. Explicit equations are obtained. For a special class of poles and zeros, some simpler equations that are generalizations of the single-input-single-output equations are presented. View full abstract»

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  • Autoregressive model fitting and levinson algorithm in the multichannel degenerate case

    Page(s): 94 - 95
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    This note extends the autocorrelation method for fitting multichannel time series from the nondegenerate case to the general case. It shows that the AR model obtained by solving the normal equations is always stable even in the degenerate case. The multichannel Levinson algorithm for solving the normal equations is extended from the nondegenerate case to the general case. View full abstract»

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  • Hopf bifurcation via Volterra series

    Page(s): 42 - 53
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    The Hopf bifurcation theorem gives a method of predicting oscillations which appear in a nonlinear system when a parameter is varied. There are many different ways of proving the theorem and of using its results, but the way which is probably the most useful, to control and system theorists, uses Nyquist loci in much the same way as the describing function method does. The main advantages of this method are dimensionality reduction, which eases the calculation, and the ability to cope with higher-order approximations than are used in the original Hopf theorem. This paper shows how such an approach to the Hopf bifurcation follows naturally and easily from Volterra series methods. Such use of Volterra series in nonlinear oscillations appears to be new. In many problems, the calculations involved are simplified when the Volterra series approach is taken, so the approach has practical merits as well as theoretical ones. View full abstract»

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  • Bilinear systems with homogeneous input-output maps

    Page(s): 113 - 115
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    Minimal realizations of internally bilinear systems, whose input-output maps admit a Volterra representation homogeneous in the input of degreek, are examined. A new constructive algorithm establishes a special form of a minimal internally bilinear realization of ak-power. The method deals with the multiinput-multioutput case. View full abstract»

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  • Second-order convergence analysis of stochastic adaptive linear filtering

    Page(s): 76 - 85
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    The convergence of an adaptive filtering vector is studied, when it is governed by the mean-square-error gradient algorithm with constant step size. We consider the mean-square deviation between the optimal filter and the actual one during the steady state. This quantity is known to be essentially proportional to the step size of the algorithm. However, previous analyses were either heuristic, or based upon the assumption that successive observations were independent, which is far from being realistic. Actually, in most applications, two successive observation vectors share a large number of components and thus they are strongly correlated. In this work, we deal with the case of correlated observations and prove that the mean-square deviation is actually of the same order (or less) than the step size of the algorithm. This result is proved without any boundedness or barrier assumption for the algorithm, as it has been done previously in the literature to ensure the nondivergence. Our assumptions are reduced to the finite strong-memory assumption and the finite-moments assumption for the observation. They are satisfied in a very wide class of practical applications. View full abstract»

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  • Convergence in distribution of LMS-type adaptive parameter estimates

    Page(s): 54 - 60
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    We study the asymptotic behavior of parameter estimates generated by LMS (least mean-square)-adaptive estimation algorithms in stationary dependent random situations. We show that, subject to mild, practically reasonable conditions, the estimates converge in distribution. Further, we extend this result to prove a more explicit type of convergence in distribution which explains other observed properties. We then estimate the moments of this limiting distribution and discuss how this relates to the work of others. View full abstract»

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  • On computing output-error estimates

    Page(s): 99 - 101
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    In this note, we consider a system with rational transfer function from input to output where this transfer function haspparameters. It is also supposed that the input has a spectrum consisting ofpdistinct points (equivalently, we suppose that the design index =p/2). As proved in [2], this implies that the output-error estimator has the same efficiency as the prediction-error estimator. We present a very convenient algorithm for computing the output-error estimate of the transfer function from input to output. View full abstract»

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  • Simultaneous stabilization with fixed closed-loop characteristic polynomial

    Page(s): 103 - 104
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    A solution is given to the problem of simultaneously stabilizingmsingle-input-single-output plants by one dynamic compensator with the constraint that each closed-loop system has the same characteristic polynomial. View full abstract»

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  • On variance neutrality of systems within general random parameters

    Page(s): 101 - 103
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    A necessary condition for variance neutrality of discrete-time linear systems within general random parameters and with arbitrary observations is established. It is proved that this condition is sufficient as well if the observations are linear. This result is of importance in connection with separability, of optimal control and state estimation. View full abstract»

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  • Persistence of excitation in extended least squares

    Page(s): 60 - 68
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    In least-squares parameter estimation schemes, "persistency of excitation" conditions on the plant states are required for consistent estimation. In the case of extended least squares, the persistency conditions are on the state estimates. Here, these "persistency of excitation" conditions are translated into "sufficiently rich" conditions on the plant noise and inputs. In the case of adaptive minimum variance control schemes, the "sufficiently rich" conditions are on the noise and specified output trajectory. With sufficiently rich input signals, guaranteed convergence rates of prediction errors improve, and it is conjectured that the algorithms are consequently more robust. View full abstract»

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  • Design of linear systems with saturating linear control and bounded states

    Page(s): 121 - 124
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    A theorem is developed, based on the circle criterion, which gives sufficient conditions for the stability of a saturating linear control for a linear system with bounded states. This theorem can be applied to determine a range of gains for the linear control which ensures stability. It is shown by example that this approach results in an increased speed of response over that obtained by previous methods which do not account for state bounds. View full abstract»

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  • A Stackelberg solution of dynamic games

    Page(s): 85 - 93
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    The paper proposes a formulation of ε-Stackelberg and Stackelberg strategies for a large class of dynamic closed-loop games, discusses the interpretation of the leader's strategy as the formalization of the intuitive notion of incentives or threats, and considers limitations of the Stackelberg solution concept which, within the dynamic context, are applicable only in situations where the realization of a leader's strategy is ensured by a binding contract. The solution method is based on the idea of discontinuous strategies assuming that the leader punishes the follower by minimizing his payoff if the latter does not comply with the policy selected for him by the leader. View full abstract»

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  • Efficient computation of the covariance sequence of an autoregressive process

    Page(s): 97 - 99
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    An efficient algorithm is presented for computing the covariance sequence of a multichannel autoregressive process represented by a set of reflection coefficients. The covariance sequence is shown to be the impulse response of a certain lattice filter related to the optimal predictor. View full abstract»

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  • Routh-Hurwitz test under vanishing leading array elements

    Page(s): 104 - 106
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    A slight modification to construct Routh's array is presented to cope with the special case of vanishing leading array elements. By means of the modified array, root locations of a polynomial can readily be determined through counting first-column sign changes, as is with the normal Routh's test, without the necessity, of adopting the ε-approach. View full abstract»

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  • Smith forms over R[z_{1},z_{2}]

    Page(s): 115 - 118
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    Relationships between a polynomial matrix and its Smith forms are explored. It is shown, for example, that a matrix overR[z_{1}, z_{2}]is equivalent to its Smith form overR[z_{1}, z_{2}]if and only if a certain system of linear polynomial equations has a solution. View full abstract»

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  • Strictly Hurwitz property invariance of quartics under coefficient perturbation

    Page(s): 106 - 107
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    In this note, it is shown how the maximum interval, centered around each of the coefficients of a prescribed fourth-degree strictly Hurwitz polynomial, may be determined so that the strictly Hurwitz property remains invariant when each coefficient might be perturbed to any arbitrary value within its permissible interval. View full abstract»

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  • Uniqueness of weakly minimal analytic realizations

    Page(s): 111 - 113
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    After Crouch [2], we clarify the relation between minimal realizations Sussmann [7]-[11] and weakly minimal realizations Hermann and Krener [3] of a given input-output mapping in the analytic case. For a given input-output mapping, all the weakly minimal analytic realizations are classified. Our result, applied to realization theory, is exactly Crouch's one, and can be derived from Sussmann's paper [8]. Otherwise, it is closely related to other works of Krener [4] and Hermann and Krener [3]. Our contribution is essentially a presentation of the above-mentioned results in a general unified manner. View full abstract»

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Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame