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Automatic Control, IEEE Transactions on

Issue 11 • Date Nov. 2002

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Displaying Results 1 - 25 of 30
  • Scanning the issue

    Publication Year: 2002 , Page(s): 1785
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    Freely Available from IEEE
  • Quasi-deadbeat minimax filters for deterministic state~space models

    Publication Year: 2002 , Page(s): 1904 - 1908
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    In this note, a quasi-deadbeat property is introduced and a quasi-deadbeat minimax filter (DMF) is proposed as a new class of filters for deterministic discrete-time state??space models. Constraints such as linearity, quasi-deadbeat property, and independence of the initial-state information will be required in advance, in addition to a new performance index of the worst-case gain between the disturbance and the current estimation error. The proposed DMF is obtained by directly minimizing the new performance index with above constraints. Finite impulse response (FIR) and infinite impulse response (IIR) structures are suggested with emphasis on the FIR structure. The proposed DMF is represented first, in a standard batch form and then in an iterative form. It is shown that the DMF with FIR and IIR structures for deterministic systems are similar in form to the existing receding horizon unbiased FIR filter (RHUFF) and the Kalman filter, respectively, for stochastic systems. View full abstract»

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  • Comment on "Order-recursive factorization of the pseudoinverse of a covariance matrix" [with reply]

    Publication Year: 2002 , Page(s): 1952 - 1957
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB) |  | HTML iconHTML  

    Numerical counterexamples and theoretical analysis of the aforementioned paper are presented, and they show that the main result, Theorem 2, in the paper is incorrect. The original author's reply is also provided. The comment gives a counterexample to the previous paper, with which this author agrees. In this correction to that paper, it is shown that replacing "the pseudoinverse" with "a generalized inverse" and replacing Section II: Factor of a pseudoinverse of a covariance matrix with the new Section II as follows, corrects the problem and establishes a rigorous theory. Some examples are give to illustrate the theory and practice of the order-recursive procedure using g-inverses. View full abstract»

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  • Author's reply

    Publication Year: 2002 , Page(s): 1953 - 1957
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (319 KB) |  | HTML iconHTML  

    First Page of the Article
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  • Correction to "A new parameterization of stable polynomials"

    Publication Year: 2002 , Page(s): 1957
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (142 KB) |  | HTML iconHTML  

    First Page of the Article
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  • Book review

    Publication Year: 2002 , Page(s): 1958
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  • Robustness of periodic trajectories

    Publication Year: 2002 , Page(s): 1842 - 1856
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1261 KB) |  | HTML iconHTML  

    A robustness problem for periodic trajectories is considered. A nonautonomous system with a periodic solution is given. The problem is to decide whether a stable periodic solution remains in a neighborhood of the nominal periodic solution when the dynamics of the system is perturbed. The case with a structured dynamic perturbation is considered. This makes the problem a nontrivial generalization of a classical problem in the theory of dynamical systems. A solution to the robustness problem will be obtained by using a variational system obtained by linearizing the system dynamics along a trajectory, which is uncertain but within the prespecified neighborhood of the nominal trajectory. This gives rise to robustness conditions that can be solved using integral quadratic constraints for linear time periodic systems. View full abstract»

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  • H control for nonlinear descriptor systems

    Publication Year: 2002 , Page(s): 1919 - 1925
    Cited by:  Papers (39)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (427 KB) |  | HTML iconHTML  

    In this paper, we study the H control problem for nonlinear descriptor systems governed by a set of differential-algebraic equations (DAEs) of the form Ex˙ = F(x, w, u), z = Z(x, w, u), y = Y(x, w, u), where E is, in general, a singular matrix. Necessary and sufficient conditions are derived for the existence of a controller solving the problem. We first give various sufficient conditions for the solvability of H control problem for DAEs. Both state-feedback and output-feedback cases are considered. Then, necessary conditions for the output feedback control problem to be solvable are obtained in terms of two Hamilton-Jacobi inequalities plus a weak coupling condition. Moreover, a parameterization of a family of output feedback controllers solving the problem is also provided. View full abstract»

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  • On the numerical computation of a structural decomposition in systems and control

    Publication Year: 2002 , Page(s): 1786 - 1799
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (888 KB) |  | HTML iconHTML  

    In this paper, we develop a new numerical method for a special coordinate basis of a linear time invariant system. Such a special coordinate basis is essentially a structural decomposition which explicitly displays the finite and infinite zero structures, as well as the invertibility structures of the given system. The technique is playing important roles in numerous topics in system and control theory, such as robust control, H and H2 optimal control almost disturbance decoupling, and zero placement of linear systems, just to name a few. Our method consists of three steps: reduction by orthogonal transformations, reduction by generalized Sylvester equations, and extraction of infinite zero structure. The performance of our method is illustrated by some numerical examples. View full abstract»

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  • On the Lyapunov theorem for singular systems

    Publication Year: 2002 , Page(s): 1926 - 1930
    Cited by:  Papers (77)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (293 KB) |  | HTML iconHTML  

    In this paper, we revisit the Lyapunov theory for singular systems. There are basically two well-known generalized Lyapunov equations used to characterize stability for singular systems. We start with the Lyapunov theorem of the work by Lewis. We show that the Lyapunov equation of that theorem can lead to incorrect conclusion about stability. Some cases where that equation can be used are clarified. We also show that an attempt to correct that theorem with a generalized Lyapunov equation similar to the original one leads naturally to the generalized equation of Takaba et al. View full abstract»

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  • Stochastic approximation in nonparametric identification of Hammerstein systems

    Publication Year: 2002 , Page(s): 1800 - 1810
    Cited by:  Papers (39)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (864 KB) |  | HTML iconHTML  

    Derived from the idea of stochastic approximation, recursive algorithms to identify a Hammerstein system are presented. Two of them recover the characteristic of the nonlinear memoryless subsystem, while the third one estimates the impulse response of the linear dynamic part. The a priori information about both subsystems is nonparametric. Consistency in quadratic mean is shown, and the convergence rate is examined. Results of numerical simulation are also presented. View full abstract»

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  • Guaranteed robust nonlinear minimax estimation

    Publication Year: 2002 , Page(s): 1857 - 1864
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (659 KB) |  | HTML iconHTML  

    Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs. It is well known, however, to be extremely sensitive to outliers in the data resulting, e.g., of sensor failures. In this paper, a new method is proposed to robustify minimax estimation by allowing a prespecified number of absolute deviations to become arbitrarily large without modifying the estimates. By combining tools of interval analysis and constraint propagation, it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way, even when the model output is nonlinear in its parameters. The method is illustrated on a problem where the parameters are not globally identifiable, which demonstrates its ability to deal with the case where the minimax solution is not unique. View full abstract»

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  • An improved stabilization method for linear time-delay systems

    Publication Year: 2002 , Page(s): 1931 - 1937
    Cited by:  Papers (343)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (392 KB) |  | HTML iconHTML  

    In this paper, we combine a new approach for linear time delay systems based on a descriptor representation with a recent result on bounding of cross products of vectors. A delay-dependent criterion for determining the stability of systems with time-varying delays is obtained. This criterion is used to derive an efficient stabilizing state-feedback design method for systems with parameter uncertainty, of either the polytopic or the norm-bounded types. View full abstract»

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  • Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parametrization

    Publication Year: 2002 , Page(s): 1811 - 1823
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (925 KB) |  | HTML iconHTML  

    Input spectra, which are consistent with a given state covariance of a linear filter, correspond to solutions of an analytic interpolation problem. We derive an explicit formula for the power spectrum with maximal entropy, and provide a linear fraction parametrization of all solutions. View full abstract»

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  • Algebraic properties of singular systems subject to decentralized output feedback

    Publication Year: 2002 , Page(s): 1898 - 1903
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB) |  | HTML iconHTML  

    This paper investigates algebraic properties of decentralized singular systems (DSSs) under local static output feedback. New concepts of the geometric multiplicity (GM) of the finite decentralized fixed mode (DFM), the decentralized output feedback variable polynomial (DVP), and the finite decentralized output feedback cycle index (DCI) of the DSS are defined. The formulas for determining the GM and the DCI are given in terms of the DFM and the system matrices. It is shown that almost any decentralized output feedback can make the zeros of the DVP (i.e., the closed-loop poles that are variable) distinct and away from any given finite set in the complex plane. It is also shown that the finite DFM of the DSS are those uncontrollable and/or observable finite modes of the closed-loop DSS through any single channel. Finally, the minimal number of the inputs and outputs that guarantee the finite modes of the closed-loop DSS controllable and observable is shown to be the finite DCI of the DSS. An illustrative example is provided. View full abstract»

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  • Control of systems with I/O delay via reduction to a one-block problem

    Publication Year: 2002 , Page(s): 1890 - 1895
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (367 KB) |  | HTML iconHTML  

    In this paper, the standard (four-block) H control problem for systems with a single delay in the feedback loop is studied. A simple procedure of the reduction of the problem to an equivalent one-block problem having particularly simple structure is proposed. The one-block problem is then solved by the J-spectral factorization approach, resulting in the so-called dead-time compensator (DTC) form of the controller. The advantages of the proposed procedure are its simplicity, intuitively clear derivation of the DTC form of the H controller, and extensibility to the multiple delay case. View full abstract»

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  • Optimal control of discrete-time uncertain systems with imperfect measurement

    Publication Year: 2002 , Page(s): 1909 - 1914
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (431 KB) |  | HTML iconHTML  

    We consider a discrete-time optimal control problem in the presence of uncertainties in the dynamics and in the measurement. An optimal (in min-max sense) output-feedback controller is derived from a discrete Bellman equation. We propose a formulation of the last equation in the estimation space, which allows approximation by a reduced-order equation corresponding to a prescribed collection of estimation sets. The approach is illustrated up to numerical experiments by a pursuit-evasion game on the plane, with incomplete information of the current state of the evader. View full abstract»

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  • Robust continuous-time smoothers without two-sided stochastic integrals

    Publication Year: 2002 , Page(s): 1824 - 1841
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1449 KB) |  | HTML iconHTML  

    We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two-sided stochastic calculus. The main contribution of the paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are nonstochastic parabolic partial differential equations (with random coefficients) and, hence, the technical machinery associated with two sided stochastic calculus is not required. Furthermore, the robust smoothed state estimates are locally Lipschitz in the observations, which is useful for numerical simulation. As examples, finite dimensional robust versions of the Benes and hidden Markov model smoothers and smoothers for piecewise linear dynamics are derived; these finite-dimensional smoothers do not involve stochastic integrals. View full abstract»

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  • Inner-outer factorization for strictly proper transfer matrices

    Publication Year: 2002 , Page(s): 1915 - 1919
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (318 KB) |  | HTML iconHTML  

    Considers inner-outer factorization for strictly proper transfer matrices. We provide characterizations to the solution of this particular factorization problem, and develop a computational algorithm to solve it. A numerical example is used to illustrate the proposed theory and algorithm. View full abstract»

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  • BIBO stability of linear switching systems

    Publication Year: 2002 , Page(s): 1895 - 1898
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (262 KB) |  | HTML iconHTML  

    In this paper, we show that for linear switching systems of the form xn+1 = Anxn+un+1, where the matrices An are chosen arbitrarily from a given set of matrices, bounded-input-bounded-output stability implies uniform exponential stability. View full abstract»

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  • Limitations of the describing function for limit cycle prediction

    Publication Year: 2002 , Page(s): 1887 - 1890
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (250 KB) |  | HTML iconHTML  

    We consider comparator-based nonlinear feedback systems, and use Tsypkin's method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function technique predicts spurious limit cycles, and also provide a more practical example in which limit cycles are erroneously predicted. View full abstract»

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  • Should model-based inverse inputs be used as feedforward under plant uncertainty?

    Publication Year: 2002 , Page(s): 1865 - 1871
    Cited by:  Papers (88)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (364 KB) |  | HTML iconHTML  

    Bounds on the size of the plant uncertainties are found such that the use of the inversion-based feedforward input improves the output-tracking performance when compared to the use of feedback alone. The output-tracking error is normalized by the size of the desired output and used as a measure of the output tracking performance. The worst-case performance is compared for two cases: (1) with the use of feedback alone and (2) with the addition of the feedforward input. It is shown that inversion-based feedforward controllers can lead to performance improvements at frequencies w where the uncertainty Δ (jw) in the nominal plant is smaller than the size of the nominal plant G0(jw) divided by its condition number KG0 (jw), i.e., ||Δ(jw)||2 < ||G0(jw) ||2/kG0 (jw). A modified feedforward input is proposed that only uses the model information in frequency regions where plant uncertainty is sufficiently small. The use of this modified inverse with (any) feedback results in improvement of the output tracking performance, when compared to the use of the feedback alone. View full abstract»

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  • Estimation under unknown correlation: covariance intersection revisited

    Publication Year: 2002 , Page(s): 1879 - 1882
    Cited by:  Papers (37)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    Addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the note. The member in this family having minimal trace is said to be "family-optimal." When the gains are to be optimized in order to achieve minimal trace of the family-optimal estimate of the covariance matrix, it is proved that the global optimal solution is actually given by the covariance intersection algorithm, which conducts the search only along a one-dimensional curve in the n-squared-dimensional space of combination gains. View full abstract»

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  • Global configuration stabilization for the VTOL aircraft with strong input coupling

    Publication Year: 2002 , Page(s): 1949 - 1952
    Cited by:  Papers (47)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (262 KB) |  | HTML iconHTML  

    Trajectory tracking and configuration stabilization for the vertical takeoff and landing (VTOL) aircraft has been so far considered in the literature only in the presence of a slight (or zero) input coupling (i.e., for a small ε). In this paper, our main contribution is to address global configuration stabilization for the VTOL aircraft with a strong input coupling using a smooth static state feedback. In addition, the differentially flat outputs for the VTOL aircraft are automatically obtained as a by-product of applying a decoupling change of coordinates. View full abstract»

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  • Existence and uniqueness of risk-sensitive estimates

    Publication Year: 2002 , Page(s): 1945 - 1948
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (291 KB) |  | HTML iconHTML  

    Risk-sensitive criteria have been used to derive robust filters, identifiers, and controllers. The fundamental issues of existence and uniqueness of an estimate of a random variable given a random vector with respect to an order-(λ, p) risk-sensitive criterion are studied in this note. More precisely, we prove the existence of a unique risk-sensitive estimate provided λ>0 and p>1. For the remaining cases, a general existence result is not available at this time. We do, however, prove the existence in certain special cases. Moreover, we present examples with uncountably many optimal risk-sensitive estimates, i.e., exhibiting an extremely high level of nonuniqueness. 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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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame