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Automatic Control, IEEE Transactions on

Issue 2 • Date Feb 1990

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Displaying Results 1 - 25 of 29
  • Generalization of the Hermite-Biehler theorem and applications

    Page(s): 222 - 225
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    A generalization of the Hermite-Biehler theorem for the open left half plane is derived. Using this generalization, a graphical method for checking the stability of linear uncertain continuous-time systems is presented. The stability regions belong to a class of simply connected regions that includes most of the regions of interest in control View full abstract»

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  • A dual result to Kharitonov's theorem

    Page(s): 195 - 198
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    A dual problem to Kharitonov's problem, involving a diamond instead of a rectangle, is considered. The results show that a family of polynomials with coefficients varying in the diamond is strictly Hurwitz if and only if eight one-dimensional exposed edges of the diamond are strictly Hurwitz View full abstract»

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  • Extended table for eliminating the singularities in Routh's array

    Page(s): 218 - 222
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB)  

    A simple procedure for eliminating the classical ε-method introduced by the Routh-Hurwitz test is given. The procedure extends the construction of the Routh table in the special case of vanishing leading array elements without introducing complementary multiplications. It is shown that it is always possible to associate with any polynomial g an extended Routh table. The number of sign changes in the first column of the table equals the number of zeros of g with positive real part View full abstract»

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  • State-space design of low-order stabilizers

    Page(s): 182 - 186
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB)  

    An algorithm is presented for stabilizing a linear multivariable system with a controller of fixed dynamic order. This is an output feedback stabilization problem. The algorithm attempts to solve this by a sequence of approximate pole assignment problems. The approximation is driven by the optimization of an objective function consisting of a weighted sum of the condition number of the closed-loop eigenvectors and the norm of the difference between the computed and actual equivalent state-feedback controls View full abstract»

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  • A parametrization of stabilizing controllers for multirate sampled-data systems

    Page(s): 233 - 236
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB)  

    All linear multirate controllers for a given multirate sampled-data system plant are parameterized in terms of a single parameter Q(z) that is allowed to be any stable transfer matrix provided that certain causality conditions are met. The result parallels a well-known parameterization result for single-rate sampled-data plants. The parameterization suggests architectures for multirate controllers View full abstract»

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  • Robust stability of state-space models with structured uncertainties

    Page(s): 191 - 195
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    A method for robust eigenvalue location analysis of linear state-space models affected by structured real parametric perturbations is proposed. The approach, based on algebraic matrix properties, deals with state-space models in which system matrix entries are perturbed by polynomial functions of a set of uncertain physical parameters. A method converting the robust stability problem into nonsingularity analysis of a suitable matrix is proposed. The method requires a check of the positivity of a multinomial form over a hyperrectangular domain in parameter space. This problem, which can be reduced to finding the real solutions of a system of polynomial equations, simplifies considerably when cases with one or two uncertain parameters are considered. For these cases, necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems View full abstract»

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  • Robustness analysis for linear dynamical systems with linearly correlated parametric uncertainties

    Page(s): 186 - 191
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    The authors propose an approach for robust pole location analysis of linear dynamical systems with parametric uncertainties. Linear control systems with characteristic polynomials whose coefficients are affine in a vector of uncertain physical parameters are considered. A design region in complex plane for system pole placement and a nominal parameter vector generating a characteristic polynomial with roots in that region are given. The proposed method allows the computation of maximal domains bounded by linear inequalities and centered at the nominal point in system parameter space, preserving system poles in the given region. The solution of this problem is shown to also solve the problem of testing robot location of a given polytope of polynomials in parameter space. It is proved that for stability problems for continuous-time systems with independent perturbations on polynomial coefficients, this method generates the four extreme Kharitonov polynomials View full abstract»

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  • Design of a self-tuning rule based controller for a gasoline refinery catalytic reformer

    Page(s): 156 - 164
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (700 KB)  

    Design concepts for self-tuning knowledge-based controllers are studied. To accomplish this, two interacting rule-based controllers are constructed for supervisory control and system optimization of a gasoline catalytic reformer. The knowledge bases incorporate human operator experience and basic engineering knowledge about the process dynamics. Inference is provided by a fuzzy logic engine. After manual tuning of the controller scaling coefficient is accomplished, a crisp heuristic is developed for self-tuning. The performance of the self-tuning controller is tested against perturbations of a simulation model of the catalytic reformer View full abstract»

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  • Contribution to the solution of the linear-quadratic problem for large systems

    Page(s): 239 - 243
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (408 KB)  

    The feasibility of using a previously published algorithm as a tool for the computation of the Kalman gain for large systems is demonstrated. Some aspects of its implementation and its numerical properties are explored. Numerical examples demonstrate the suitability of the algorithm for the computation of the optimal gain for very-high-order systems. The optimal gain is computed for a sparse system with 401 states View full abstract»

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  • Persistency of excitation and overparametrization in model reference adaptive control

    Page(s): 254 - 256
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    The problem of overparameterization of the plant in model reference adaptive control (MRAC) is analyzed. Overparametrization may arise when an upper bound for the order of the plant is used in the design of the MRAC or when the transfer function of the modeled part of the plant has common zeros and poles. It is shown that under parametrization the parameters for model-plant transfer function matching lie in a linear variety. If the reference input signal has enough frequencies, the estimated parameters will converge to this variety. In the presence of modeling errors such as bounded disturbances, the parameters may drift to infinity along the linear variety independently of the number of frequencies in the reference input signal. In the case of exact parameterization but close zero-pole cancellation, the signal vector is shown to be persistently exciting with a low level of excitation. Such a low level of excitation may lead to poor rate of convergence and to loss of robustness with respect to modeling errors View full abstract»

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  • Robust parameter adjustment with nonparametric weighted-ball-in-H uncertainty

    Page(s): 225 - 229
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB)  

    Using a parameter adjustment law, robust monotonic parameter error reduction is proved for a linear parameter estimation problem in which the signal is corrupted by the presence of nonparametric dynamical uncertainty. The nonparameterized dynamics are characterized by a known frequency-domain magnitude bound. A nonconservative bound on the finite-time energy of the nonparametric-dynamics output is constructed in real time. When the error single energy is small enough to be due to nonparametric dynamics alone, the parameter adjustment is shut off to avoid misadjustment. The approach is an extension of existing adaptive control error-dead-zone ideas to the case of frequency-domain bounded uncertainty View full abstract»

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  • On the norms used in computing the structured singular value

    Page(s): 201 - 203
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB)  

    Different norms are considered to replace the Euclidean norm in an algorithm given by M.H.K. Fan and A.L. Tits (ibid., vol.33, p.284-9, 1988), which is used for the computation of the structured singular value of any matrix. The algorithm is explained, and it is shown that the l1 norm is the best possible norm in a certain sense View full abstract»

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  • Construction of linear predictors for stationary vector sequences

    Page(s): 236 - 239
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB)  

    The class of all linear predictors of minimal order for a stationary vector-valued process is specified in terms of linear transformations on the associated Hankel covariance matrix. Two particular transformations, yielding computationally efficient construction schemes, are proposed View full abstract»

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  • A criterion for estimating robust time delays for closed-loop stability

    Page(s): 209 - 210
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB)  

    A formula for estimating robust time delays for closed-loop stability is presented. Continuous, single-input-single-output, linear, time-invariant systems represented by their rational transfer functions, which are not necessarily stable, are considered. The proposed formula is derived using the symmetric Rouche form. An illustrative example is included, and some closing remarks concerning the merits of the formula are made View full abstract»

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  • A Schur vector method to solve higher order Lyapunov equations

    Page(s): 215 - 218
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    A general Schur vector method for solving a partial differential equation which appears in designing nonlinear optimal control laws for linear or nonlinear dynamical systems is proposed. The method reduces the dimensionality problem of the direct method. Numerical experiments show that it also reduces the numerical instability of the eigenvector method View full abstract»

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  • The largest singular value of eXA0e -X is convex on convex sets of commuting matrices

    Page(s): 229 - 230
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    A short and direct proof of the convexity property is given. It is shown that the theorem applies to any convex, commuting set of matrices in RnXn, where A0RnXn is fixed. It is also shown that the result does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices View full abstract»

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  • Quadratic stability with real and complex perturbations

    Page(s): 198 - 201
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    It is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear, fractional, unstructured perturbations does not hold when the perturbations are block structured. For a limited class of problems, quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms, and hence appropriate synthesis techniques, coupled with diagonal constant scalings, can be used to design quadratically stable systems View full abstract»

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  • Richness and excitation on an interval-with application to continuous-time adaptive control

    Page(s): 165 - 171
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    Richness and excitation on an interval is presented as a useful tool, which offers flexibility and mathematical simplification of the excitation issue. Feedback laws are considered which, when they are applied to any controllable time-invariant linear system, result in a closed-loop system such that the feedback signal, the measure of excitation which it produces, and the state vector of the system are all of the same order of magnitude on an interval. Such feedback laws generate excitation of time-varying linear systems, provided these systems are almost time-invariant and controllable in the interval of interest. Using these results, a smooth adaptive controller which controls and adapts simultaneously all the time and stabilizes and asymptotically regulates an arbitrary time-invariant controllable linear system of known order is obtained View full abstract»

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  • From receiver operating characteristic to system operating characteristic: evaluation of a track formation system

    Page(s): 172 - 179
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    The authors discuss the application of multitarget tracking techniques in combination with a Markov chain model to the evaluation of a track formation system based on a composite logic. Target track detection probability is computed in the presence of false alarms. The target track detection probability versus the false track probability is plotted; the values of target detection probability and the false alarm probability are varied to conform to the system's operating signal-to-noise ratio. This allows choice of the detector's operating point so to satisfy the overall system requirements. A procedure for inferring the overall system capacity in terms of the minimum spacing of targets that ensures tracking with a certain reliability is presented. The entire methodology is illustrated by a case study of an actual system View full abstract»

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  • All stabilizing controllers as frequency-shaped state estimate feedback

    Page(s): 203 - 208
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB)  

    It is shown that the class of all strictly proper stabilizing controllers for proper linear plants can be structured as state estimate feedback with frequency shaping in the state estimates and/or in the state estimate feedback law. The selection of where the frequency shaping takes place is at the designer's discretion. The parameterization of the controller class can be in terms of an arbitrary proper stable transfer function, with the closed-loop system transfer functions affine in the transfer function. With constant output feedback permitted in addition to the state estimate feedback, the class of all proper stabilizing controllers can be generated in a like manner View full abstract»

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  • Tracking analysis of an ARMA parameter estimation algorithm

    Page(s): 247 - 250
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (324 KB)  

    The problem of adaptively estimating parameters of a time-varying autoregressive moving-average (ARMA) process using a constant-step-size Gauss-Newton algorithm is studied. Using weak convergence theory and the concept of prescaling, it is shown that an ordinary differential equation can be used to describe the mean behavior of the adaptive filter coefficients. Computer simulations are provided to substantiate the analysis View full abstract»

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  • Lyapunov redesign for structural convergence improvement in adaptive control

    Page(s): 250 - 253
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    The relative improvement of the convergence rate in adaptive error models is discussed. It is shown how to improve convergence, positive realness, and robustness by modifying the structure of the error model. The proposed approaches to designing adaptive control algorithms using the Lyapunov method not only improve the rate of convergence but also provide flexibility in choosing nonlinear control inputs. Boundedness of the nonlinear functions of the modified schemes is shown View full abstract»

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  • Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence

    Page(s): 141 - 147
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (448 KB)  

    Convergence and stability properties of the Kalman filter-based parameter estimator are established for linear stochastic time-varying regression models. The main features are: both the variances and sample path averages of the parameter tracking error are shown to be bounded; the regression vector includes both stochastic and deterministic signals, and no assumptions of stationarity or independence are requires; and the unknown parameters are only assumed to have bounded variations in an average sense View full abstract»

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  • Knowledge based fuzzy control of systems

    Page(s): 148 - 155
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB)  

    A method of fuzzy control of systems based on a concept of human thinking is investigated. The fuzzy controller consists of a knowledge base containing a number of time responses of a process. The elements of this base are cells in which an input and a corresponding output of a system are stored. The cells are organized according to different types of relations. The result is a knowledge structure which contains a model of the process to be controlled. The following phases are distinguished: the learning phase, during which the relation between the imput and the output of a system is learned and the knowledge structure is constructed; and a phase in which the knowledge structure is applied to control the process. The method also provides an indication of the reliability of the control action View full abstract»

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  • On finding the minimum possible peak value of multi-input infinite-horizon steering controls

    Page(s): 243 - 246
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB)  

    A computational method for the infinite-dimensional optimization problem of finding the minimum possible peak value of a multi-input infinite-horizon steering control is presented. It is shown that the problem is equivalent to a convex program in a finite-dimensional Euclidean space. The convex program is approximated by a sequence of linear programs, the objective values of which converge to the objective of the convex program. A bound above and below are given for the error between the objective value of the convex program and the objective of any linear program in the approximating sequence. The bounds show convergence and are geometric with ratio given by the minimum modulus over all unstable plant poles View full abstract»

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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