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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug 1993

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Displaying Results 1 - 25 of 27
  • Adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds

    Page(s): 1246 - 1250
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB)  

    An adaptive regulation method is presented for a class of uncertain systems where the uncertainty bounds are partially known. Both the state and the parameter error of the closed-loop system are shown to be ultimately bounded. The proposed method improves on the adaptive control method of M.J. Corless and G. Leitmann (1981), so that performance degradation and the destabilization of the control system can be effectively presented in practical situations View full abstract»

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  • Two formulations of exponentially weighted enhanced LQ controllers

    Page(s): 1308 - 1312
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    Properties of a class of multiinput multioutput digital controllers are examined. The controllers incorporate three features: (1) optimal gains associated with known exogenous inputs; (2) penalties imposed both on squares of first backward differences in control actions and on control actions squared; and (3) exponential weighting to ensure bounds on closed-loop eigenvalues. Two versions of exponential weighting are treated. Results are given for both the finite-horizon and infinite-horizon versions of the problems. The results include expressions for optimal feedback gains and for optimal preview gains. For the infinite-horizon versions, relationships are derived between the optimal closed-loop eigenvalues and the eigenvalues associated with the preview gains. Two examples are given to illustrate properties of three controllers View full abstract»

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  • H control and filtering for sampled-data systems

    Page(s): 1162 - 1175
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    H control and filtering problems for sampled-data systems are studied. Necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified H performance bound. When these conditions hold, explicit formulas for a controller and a filter satisfying the H performance bound are also given View full abstract»

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  • Optimal asymptotic identification under bounded disturbances

    Page(s): 1176 - 1190
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1364 KB)  

    The intrinsic limitation of worst-case identification of linear time-invariant systems using data corrupted by bounded disturbances, when the unknown plant is known to belong to a given model set, is studied. This is done by analyzing the optimal worst-case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm. It is shown that under some topological conditions on the model set, there is an identification algorithm which is asymptotically optimal for any input, and the optimal asymptotic error is characterized as a function of the inputs. These results, which hold for any error metric and disturbance norm, are applied to three specific identification problems: identification of stable systems in the l1 norm, identification of stable rational systems in the H norm and identification of unstable rational systems in the gap metric. For each of these problems, the general characterization of optimal asymptotic error is used to find near-optimal inputs to minimize the error View full abstract»

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  • Control of vector discrete-event systems. I. The base model

    Page(s): 1214 - 1227
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    A vector discrete-event system (VDES) is a discrete-event system model in which the system state is represented by a vector with integer components, and state transitions by integer vector addition. The authors investigate such structures from the viewpoint of control theory. The objective is to specialize to VDES the general automation-based control theory of P.J. Ramadge and W.M. Wonham (1987) and W.M. Wonham and P.J. Ramadge (1988). It is shown that within the VDES framework a useful class of control systems can be compactly modeled, and some of the associated control problems of Ramadge and Wonham can be more efficiently solved View full abstract»

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  • Frequency response computation via rational interpolation

    Page(s): 1203 - 1213
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    A simple rational interpolation method is given for estimating a frequency response matrix. The method is based on a generalization of the resolvent identity that avoids the potential inaccuracies introduced by the subtraction of nearly equal values in the calculation of the difference terms. When coupled with a pole cancellation method, the resulting interpolation algorithm is accurate and efficient. The error in this procedure has the form of a modified response matrix, which means that the interpolation algorithm can be used to approximate both the response matrix and the error View full abstract»

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  • A modification and the Tustin approximation

    Page(s): 1313 - 1316
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    The Tustin approximation for determining a discrete-time representation of a continuous-time control system is sufficiently precise. If a sampling interval is chosen properly, it results in some errors in time responses of a plant model, though they are not critical and the static gain value is the same as in the original transfer function. However, this method generally increases the number of coefficients in the numerator of the approximate discrete-time transfer function by one in comparison with the exact transformation. A simple modification of the Tustin approximation that does not have this disadvantage and is far more precise than the original approximation is presented. The additional numerical effort is negligible. Examples of the transformation for three simple continuous systems are presented View full abstract»

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  • A modified model reference adaptive control scheme for improved transient performance

    Page(s): 1255 - 1259
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (480 KB)  

    The author proposes a modified model reference adaptive control (MRAC) scheme aimed at improving the transient performance of adaptive systems while maintaining the ideal asymptotic properties possessed by standard MRAC. In the modified scheme, the estimation error, which is generated by the identification scheme, is used directly as a control signal to counteract errors resulting from the certainty equivalence design. It is shown that the modified scheme provides essentially the same stability and robustness properties as the standard adaptive MRAC approach but with the transient performance substantially improved. Simulation results are presented to illustrate the effectiveness of the proposed scheme View full abstract»

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  • Optimal use of an extra server in a two station tandem queueing network

    Page(s): 1296 - 1299
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    A two station tandem queueing system with given numbers of customers initially at each station and no arrivals is considered. There is a fixed server at each station, but also an additional server that can be dynamically allocated to wherever its use will do most good. There are differing linear holding costs at each station, and the aim is to use the extra server to minimize the expected total holding cost incurred until the system empties. It is shown that if either the extra server can be switched between the two stations at any time, or if it is restricted in use to just one station, where it can be turned on or off, then the optimal use of the server is such that after a service completion at one station, the effort devoted there never increases, and the effort devoted to the other station never decreases View full abstract»

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  • Nonlinear oscillations in magnetic bearing systems

    Page(s): 1242 - 1245
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (376 KB)  

    Nonlinear oscillations in magnetic bearings caused by gyroscopic effects at high speeds are analyzed. First a nonlinear model for the magnetic bearing is set in state-variable form using airgap flux, gap displacement, and velocity as state variables. The system, which is unstable in nature, is stabilized locally around the equilibrium point of zero speed using an optimal robust servo controller. It is shown that as the speed changes the system undergoes Hopf bifurcation to periodic solutions around some critical speed. The periodic solutions are shown to be unstable, so the methods of nonlinear bifurcation control are used to stabilize them. An easily implemented nonlinear feedback control of quadratic order is derived to control the Hopf bifurcation occurring in the system. The transient response of the system with and without nonlinear feedback is obtained to show the effectiveness of nonlinear feedback View full abstract»

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  • Robust Hurwitz lp stability of polynomials with complex coefficients

    Page(s): 1304 - 1308
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (404 KB)  

    Necessary and sufficient conditions for robust stability of a family of polynomials with complex coefficients are provided. This work generalizes a frequency-domain criteria for robust stability of continuous linear systems reported on by Y.Z. Tsypkin and B.T. Polyak (1991) View full abstract»

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  • Some explicit formulas for the matrix exponential

    Page(s): 1228 - 1232
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB)  

    Formulas are derived for the exponential of an arbitrary 2×2 matrix in terms of either its eigenvalues or entries. These results are then applied to the second-order mechanical vibration equation with weak or strong damping. Some formulas for the exponential of n×n matrices are given for matrices that satisfy an arbitrary quadratic polynomial. Besides the above-mentioned 2×2 matrices, these results encompass involutory, rank 1, and idempotent matrices. Consideration is then given to n×n matrices that satisfy a special cubic polynomial. These results are applied to the case of a 3×3 skew symmetric matrix whose exponential represents the constant rotation of a rigid body about a fixed axis View full abstract»

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  • A linear interpolatory algorithm for robust system identification with corrupted measurement data

    Page(s): 1236 - 1241
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (564 KB)  

    A linear, robustly convergent interpolatory algorithm for system identification in the presence of bounded noise is presented. The algorithm converges in the actual, but unknown, system in the frequency domain in the noise-free case and maintains the robust convergence result in the face of bounded noise. This robustness property distinguishes the algorithm from existing linear schemes. A key idea of this robust linear algorithm is that the approximation is separated into real and imaginary parts and into Fejer (Hermite) interpolation. Because of the Fejer interpolation the data points are required at the Chebyshev points View full abstract»

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  • A sufficient condition for simultaneous stabilization

    Page(s): 1264 - 1266
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (328 KB)  

    The condition under which it is possible to find a single controller that stabilizes k single-input single-output linear time-invariant systems pi(s) (i=1,. . .,k) is investigated. The concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable. A method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example View full abstract»

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  • A direct computation of state deadbeat feedback gains

    Page(s): 1283 - 1284
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (160 KB)  

    A method for computing a feedback gain that achieves state deadbeat control is given. From systems given in the staircase form, this method derives the deadbeat gain in a numerically reliable way. It is shown that the gain turns out to be LQ optimal for some weightings View full abstract»

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  • On Morse's new adaptive controller: parameter convergence and transient performance

    Page(s): 1191 - 1202
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (924 KB)  

    Some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by A.S. Morse (Proc. US-Italy Joint Seminar Syst., Models Feedback 1992). It is proved that the L2 norm of the tracking error is uniformly bounded by the initial parameter estimation error. Further, if the initial conditions are sufficiently small, it is shown that the L norm of the tracking error is uniformly bounded by the Lm2 norm of the reference signal. These transient bounds are independent of the signals richness and the adaptation gain, making them arguably the strongest transient results available in the literature. Second, excitation conditions for exponential stability, a property which is well known to insure some local performance measures, are given. To this end, it is shown that, modulo a signal dependent time scale change, Morse's estimator is equivalent to a normalized gradient plus filtering identifier View full abstract»

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  • Discrete-time saturation constrained adaptive pole assignment control

    Page(s): 1250 - 1254
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (416 KB)  

    The performance of a discrete-time adaptive pole assignment controller subject to a saturation control constraint is analyzed. Closed-loop system stability is established for a class of type-I plants. In the presence of plant modeling uncertainties and disturbances, it is shown that the stability is maintained by implementing a simple fixed deadzone in the parameter estimator. If the plant is free from the modeling uncertainties and disturbances, the deadzone threshold can be set to zero. Then, the closed-loop system can be characterized by the desired poles when the control input is not saturated View full abstract»

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  • An optimal volume ellipsoid algorithm for parameter set estimation

    Page(s): 1292 - 1296
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (444 KB)  

    A recursive ellipsoid algorithm is derived for estimating the parameter set of a single-input single-output linear time-invariant system with bounded noise. The algorithm's objective is to seek the minimal volume ellipsoid bounding the feasible parameter set. Cast in a recursive framework, where a minimal volume ellipsoid results at each recursion, the algorithm extends a result due to Khachian (see Aspvall and Stone, 1980) in which a technique was developed to solve a class of linear programming problems. This extension and application to the parameter set estimation problem have intuitive geometric appeal and are easy to implement. Comparisons are made to the optimal bounding ellipsoid algorithm of Fogel and Huang (1982), and the results are demonstrated through computer simulations View full abstract»

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  • Structure and optimality of multivariable periodic controllers

    Page(s): 1300 - 1303
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (400 KB)  

    A linear periodic plant to be controlled by measurement feedback is considered. The general optimal synthesis problem in which the objective is to select a compensator to minimize the norm of the induced map between the controlled output and the exogeneous input is analyzed. It is shown that the performance of any linear compensator (possibly time varying, nonperiodic) can be matched by a compensator contained in the restricted class of periodic controllers. This result is established in the discrete-time case for bounded amplitude (l) signals. In the continuous-time case the result is shown for bounded energy signals (L2,l2) View full abstract»

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  • Inversion of nonlinear time-varying systems

    Page(s): 1259 - 1264
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (504 KB)  

    A procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or, more generally, to mechanical structures, is given. The procedure is presented in a general setting, for nonlinear time-varying systems. An iterative algorithm that computes a smooth controlled invariant time-varying manifold, the mathematical properties of which are illustrated and exploited, is also proposed. An application to a flexible two-link manipulator illustrates the algorithm and its computational advantages View full abstract»

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  • On the optimality of two-stage state estimation in the presence of random bias

    Page(s): 1279 - 1283
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (300 KB)  

    Sufficient conditions for the optimality of a two-stage state estimator in the presence of random bias are derived. Under an algebraic constraint on the correlation between the state and bias process noises, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). Because the algebraic constraint is restrictive in practice, the results indirectly indicate that for most practical systems the proposed solution to the two-stage estimation problem will be suboptimal View full abstract»

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  • Single-loop stability margins for multirate and periodic control systems

    Page(s): 1232 - 1236
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (440 KB)  

    It is shown how to compute the stability margin of periodic systems with respect to compatible periodic perturbations of such systems. It is suggested that the nonstandard time-invariant model for periodic systems introduced by the author (Syst. Contr. Lett., vol.17, pp.9-14, 1991) leads to a simpler computation, although the standard model gives the same result View full abstract»

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  • Extension of Friedland's separate-bias estimation to randomly time-varying bias of nonlinear systems

    Page(s): 1270 - 1273
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB)  

    By extending B. Friedland's (1969) separate-bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended Kalman filter proposed by D.H. Zhou (1990) and by D.H. Zhou et al., a pseudo-separate-bias estimation algorithm for randomly time-varying bias of a class of nonlinear time-varying stochastic systems is obtained. A simulation example is presented to illustrate the effectiveness of the algorithm View full abstract»

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  • The pole placement map, its properties, and relationships to system invariants

    Page(s): 1266 - 1270
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    A number of properties of the complex and real pole placement map (PPM) which relate to the dimensions of their images and relate them to known system invariants are derived. It is shown that the two dimensions are equal and that their computation is equivalent to determining the rank of the corresponding differential. A new expression for the differential of the PPM allows the derivation of relationships between the Markov parameters and the Plucker matrix invariant of the system. Conditions for pole assignability are derived, based on the relationships between the rank of the Plucker matrix and the rank of the differential of the PPM View full abstract»

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  • Two new estimation algorithms for linear models with unknown but bounded measurement noise

    Page(s): 1273 - 1279
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (700 KB)  

    Attention is given to linear systems described by y=A θ+e where the measurement error vector e is unknown but bounded. Two algorithms for sequential parameter identification are introduced. Their convergence properties are illustrated and compared with those of existing algorithms. A simulation study is carried out using simulated data to investigate the possible practical use of the algorithms. Their performances are compared with those of other offline algorithms as well as with those of the widely used least-squares estimates 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