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Automatic Control, IEEE Transactions on

Issue 1 • Date Jan. 1995

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Displaying Results 1 - 25 of 35
  • Comments on "Explicit asymmetric bounds for robust stability of continuous and discrete-time systems"

    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (58 KB)  

    Referring to the original paper by Gao and Antsaklis (ibid., vol. 38, p. 332-5, 1993), the authors state that Theorem 2 is incorrectly stated. A correct version of the theorem is provided.<> View full abstract»

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  • Comments on "On the robust Popov criterion for interval Lur"e systems

    Page(s): 136 - 137
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (198 KB)  

    This paper supplements the remarks made in a paper by Dahleh et al. (IEEE Trans. Automat. Contr. vol.38, p.1400-5 (1993)) regarding the Popov sector of Lur'e systems with interval plants. A numerical example is provided to show that strict inequalities hold among three sectors: those obtained by the theorem of the paper, by applying Popov theorem to each member system, and by applying that to each of the systems with Kharitonov plants. This counterexample negates a tempting conjecture on "strong" robust Popov criterion.<> View full abstract»

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  • Design of a class of Luenberger observers for descriptor systems

    Page(s): 133 - 136
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    A new approach to the design of a class of Luenberger observers for descriptor systems is presented. The design is performed in a straightforward manner. The conditions required in the design are given in terms of the original system matrices. The relationship among these and other well-known conditions is highlighted View full abstract»

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  • A linear algebraic framework for dynamic feedback linearization

    Page(s): 127 - 132
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (608 KB)  

    To any accessible nonlinear system we associate a so-called infinitesimal Brunovsky form. This gives an algebraic criterion for strong accessibility as well as a generalization of Kronecker controllability indices. An output function which defines a right-invertible system without zero dynamics is shown to exist if and only if the basis of the Brunovsky form can be transformed into a system of exact differential forms. This is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability View full abstract»

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  • Methods and theory for off-line machine learning

    Page(s): 161 - 165
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (448 KB)  

    Many problems in machine learning can be abstracted to the sequential design task of finding the minimum of an unknown erratic and possibly discontinuous function on the basis of noisy measurements. In the present work, it is presumed that there is no penalty for bad choices during the experimental stage, and at some time, not known to the decision maker, or under his control, the experimentation will be terminated, and the decision maker will need to specify the point considered best, on the basis of the experimentation. In this paper, we seek the best trade-off between: i) acquiring new test points, and ii) retesting at points previously selected so as to improve the estimates of relative performance. The algorithm is shown to achieve a performance standard described herein. This decision setting would seem natural for function minimization in a simulation contest or for tuning up a production process prior to putting it into service View full abstract»

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  • Note on decentralized adaptive controller design

    Page(s): 89 - 91
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    This note extends the decentralized adaptive controller design of Gavel and Siljak (1989) to the case when the relative order of each isolated subsystem does not exceed two View full abstract»

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  • On solving Diophantine equations by real matrix manipulation

    Page(s): 118 - 122
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    This note presents simple algorithms for obtaining the solutions of the Diophantine equation. Our methods can produce classes of all solutions with lower degree than a specified number. The previous algorithms involve some troublesome computations, e.g., the calculation of both the controllability indexes and the observability indexes or the solution of a pole assignment problem, etc. Our contribution is that our algorithm requires only basic matrix operations such as addition, subtraction, multiplication, and inversion of given real matrices. In addition, by solving simple linear equations, the class of all minimum degree solutions can be given. Therefore the computational efforts are reduced compared with previous algorithms View full abstract»

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  • Pole assignment for uncertain systems in a specified disk by state feedback

    Page(s): 184 - 190
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    This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the “quadratic d stabilizability” concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation View full abstract»

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  • Preservation of reachability and observability under sampling with a first-order hold

    Page(s): 104 - 107
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB)  

    This paper gives the necessary and sufficient condition for the reachability of the sampled-data system S1 obtained by the discretization of a linear time-invariant continuous-time system with a first-order hold. Equivalence of the reachability and controllability of S1 is also shown. Similar results are given also for observability and reconstructibility. It turns out that S1 is reachable only if S0 is reachable, while S1 is observable if and only if S4l0 is observable, where S0 is the sampled-data system obtained by the discretization with a zero-order hold of the same sampling period View full abstract»

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  • A version of Hautus' test for tandem connection of linear systems

    Page(s): 111 - 114
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    In this note, we consider systems which can be decomposed as a cascade connection of linear subsystems. The second subsystem is assumed to have the controller canonical form. The main result is a version of Hautus' test, which allows us to check controllability and stabilizability properties of these systems by means of reduced-order rank computations View full abstract»

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  • Routing and scheduling in heterogeneous systems: a sample path approach

    Page(s): 156 - 161
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    Consider the problem of routing customers to a set of K parallel servers that have different rates. Each server has a buffer with infinite capacity. The arrival process is general and the service times are assumed to be i.i.d. exponential random variables. Using sample path arguments, we show that, given any Bernoulli policy π, there exists another policy ρ which outperforms π by partially using a randomized version of a round-robin policy. Moreover, ρ is easily specified and implemented. We present extensions of our results to systems with finite capacities and service times that have an increasing hazard rate. Finally, a similar result is shown to hold in the context of scheduling customers from a set of K parallel queues View full abstract»

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  • Stochastic approximation with averaging and feedback: rapidly convergent “on-line” algorithms

    Page(s): 24 - 34
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (916 KB)  

    Consider the stochastic approximation Xn+1=Xn+ang(Xn, ξn ), where 0<an→0, Σn an =∞ and {ξn} is the “noise” sequence. Suppose that an→0 slowly enough such that a n/an+1=1+o(an). Then various authors have shown that the rate of convergence of the average X¯n =1/n Σi=1n Xi is optimal in the sense that √n(X¯n-θ) converged in distribution to a normal random variable with mean zero and covariance V, where V was the smallest possible in an appropriate sense. V did not depend on {an}. The analogs of the advantages of averaging extend to the constant parameter systems Xn+1=Xn+εg(Xn, ξn) for small ε>0. The averaging method is essentially “off line” in the sense that the actual SA iterate Xn is not influenced by the averaging. In many applications, Xn itself is of greatest interest, since that is the “operating parameter”. This paper deals with the problem of stochastic approximation with averaging and with appropriate feedback of the averages into the original algorithm. It is shown both mathematically and via simulation that it works very well and has numerous advantages. It is a clear improvement over the system Xn by itself. It is fairly robust, and quite often it is much preferable to the use of the above averages without feedback. The authors deal, in particular, with “linear” algorithms of the type appearing in parameter estimators, adaptive noise cancellers, channel equalizers, adaptive control, and similar applications. The main development is for the constant parameter case because of its importance in applications. But analogous results hold for the case where an→0 View full abstract»

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  • Global total least squares modeling of multivariable time series

    Page(s): 50 - 63
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1312 KB)  

    Presents a novel approach for the modeling of multivariable time series. The model class consists of linear systems, i.e., the solution sets of linear difference equations. Restricting the model order, the aim is to determine a model with minimal l2-distance from the observed time series. Necessary conditions for optimality are described in terms of state-space representations. These conditions motivate a relatively simple iterative algorithm for the nonlinear problem of identifying optimal models. Attractive aspects of the proposed method are that the model error is measured globally, it can be applied for multi-input, multi-output systems, and no prior distinction between inputs and outputs is required. The authors give an illustration by means of some numerical simulations View full abstract»

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  • Semi-global stabilizability of linear null controllable systems with input nonlinearities

    Page(s): 96 - 100
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    An H-based Lyapunov proof is provided for a result established by Lin and Saberi (1993): if a linear system is asymptotically null controllable with bounded controls then, when subject to input saturation, it is semi-globally stabilizable by linear state feedback. A new result is that if the system is also detectable then it is semi-global stabilizable by completely linear output feedback. Further, an extension which relaxes the requirements on the input characteristic is obtained View full abstract»

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  • Modified output error identification-elimination of the SPR condition

    Page(s): 190 - 193
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB)  

    In this note, we present a modified adaptive output error algorithm for identification. We refer to both the continuous time and the discrete time cases. In the standard algorithm, stability requires that a certain transfer function should be strictly positive real (SPR); however, in the present algorithm, the SPR condition, which is difficult to satisfy, is eliminated. This is achieved by adding a fixed feedback gain. When there exists an a priori partial knowledge about the parameters of the plant, we provide a simple procedure to design that gain. An illustrative example comparing the modified algorithm to the standard one is provided View full abstract»

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  • An output feedback globally stable controller for induction motors

    Page(s): 138 - 143
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    We present a globally stable nonlinear dynamic output feedback controller for torque tracking and flux regulation of induction motors. The control law is globally defined, requires only measurement of stator variables and rotor speed, and does not rely on cancellation of the systems nonlinearities. Our work extends the result of the paper by Ortega et al.(1993), where the torque tracking problem was solved for a model and the variables are expressed in a frame rotating at an arbitrary angular frequency (dq model). First, we obviate the need to transfer the dq control signals of the paper by Ortega et al., to the physical input variables in the stator frame, hence providing a directly implementable control law. Second, besides the torque tracking objective, we include the practically important rotor flux regulation task. Third, by choosing a more suitable representation of the motor model, we simplify the controller structure and provide a better understanding of its derivation and behavior View full abstract»

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  • Design and analysis of fuzzy identifiers of nonlinear dynamic systems

    Page(s): 11 - 23
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    Uses fuzzy systems as identifiers for nonlinear dynamic systems. The author provides a theoretical justification for the fuzzy identifiers by proving that they are capable of following the output of a general nonlinear dynamic system to arbitrary accuracy in any finite time interval. The fuzzy identifiers are constructed from a set of adaptable fuzzy IF-THEN rules and can combine both numerical information (in the form of input-output pairs obtained by exciting the system with an input signal and measuring the corresponding outputs) and linguistic information (in the form of IF-THEN rules about the behavior of the system in terms of vague and fuzzy words) into their designs in a uniform fashion. The author develops two fuzzy identifiers. The first one is designed through the following four steps: 1) define some fuzzy sets in the state space U⊂Rn of the system; these fuzzy sets do not change; 2) construct fuzzy rule bases of the fuzzy identifier which comprise rules whose IF parts constitute all the possible combinations of the fuzzy sets defined in 1); 3) design the fuzzy systems in the fuzzy identifier based on the fuzzy rule bases of 2); and 4) develop an adaptive law for the free parameters in the fuzzy identifier. The second fuzzy identifier is designed in a similar way as the first one except that: a) the parameters characterizing the fuzzy sets in the state space change during the adaptation procedure; and b) the fuzzy systems and the adaptive law are different. The author proves that: 1) both fuzzy identifiers are globally stable in the sense that all variables in the fuzzy identifiers are uniformly bounded, and 2) under some conditions the identification errors of both fuzzy identifiers converge to zero asymptotically. Finally, the author simulates the fuzzy identifiers for identifying the chaotic glycolytic oscillator, and the results show that: 1) the fuzzy identifiers can approximate the chaotic system at a reasonable speed and accuracy without using any linguistic information, and 2) by incorporating some fuzzy linguistic IF-THEN rules about the behavior of the system into the fuzzy identifiers, the speed and accuracy of the fuzzy identifiers are greatly improved View full abstract»

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  • A note on robust pole placement

    Page(s): 181 - 184
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    Pole placement algorithm in single input-single output (SISO) systems is discussed with respect to the corresponding, real stability radius of the resulting closed loop polynomial View full abstract»

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  • Nevanlinna-Pick interpolation problem for two frequency scale systems

    Page(s): 169 - 173
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (392 KB)  

    The Nevanlinna-Pick interpolation problem for a parametric set of data is considered. Sufficient conditions are obtained that guarantees a two frequency scale solution. Decomposition of the problem into two Nevanlinna-Pick interpolation problems with smaller data size is presented. An algorithm is developed which computes the solution as the result of combining the solutions for these two smaller problems View full abstract»

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  • On robust asymptotic tracking: perturbations on coprime factors and parameterization of all solutions

    Page(s): 107 - 111
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    The robust asymptotic tracking problem is analyzed in this paper relative to unstructured perturbations on each coprime factor of the transfer functions from the control input to the measured and controlled outputs. In each case, necessary and sufficient conditions for the existence of solutions are presented which are explicitly given in terms of problem data. Under such conditions, explicit parameterizations are given of all controllers which achieve robust asymptotic tracking, in terms of free, rational proper, and stable matrices View full abstract»

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  • Frequency-domain criteria of robust stability for slowly time-varying systems

    Page(s): 153 - 155
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    The problem of stability of feedback systems with structured slowly time-varying uncertain gains is considered. For the case when the pair “uncertain gain/derivative” belongs to a given convex set, a sufficient frequency-domain condition of stability is obtained. This condition is an MIMO generalization of the SISO results derived in the 60s in the context of the positivity theory View full abstract»

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  • Multiscale smoothing error models

    Page(s): 173 - 175
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    A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. These models are interesting because they can be used to represent a broad class of physical phenomena and because they lead to efficient algorithms for estimation and likelihood calculation. In this paper, we provide a complete statistical characterization of the error associated with smoothed estimates of the multiscale stochastic processes described by these models. In particular, we show that the smoothing error is itself a multiscale stochastic process with parameters that can be explicitly calculated View full abstract»

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  • Discrete-time observers with random noises in dynamic block

    Page(s): 165 - 169
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    The minimum variance state estimation of linear stochastic discrete-time systems by an observer of reduced-order is investigated. There is an additional random noise with known intensity in the dynamic block of the observer. The local optimal reduced-order state estimator is found which takes into account the presence of such noise. The equations of an optimal stationary observer are derived for linear stochastic time-invariant system View full abstract»

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  • The use of symbolic computation in nonlinear control: is it viable?

    Page(s): 84 - 89
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    To help along the analysis and design of nonlinear control systems the NONLINCON package, an acronym for nonlinear control, was developed. This note addresses the usefulness of symbolic computation, and of the NONLINCON package in particular, for the symbolic analysis and design of nonlinear control systems. The symbolic computation program MAPLE is used as computing substratum. Textbook problems show that the NONLINCON package can be used successfully. A larger scale problem is too complex, however, to be solved with the current versions of NONLINCON and MAPLE. The conclusion is that symbolic computation is a viable approach for textbook problems, but not yet for more complex ones View full abstract»

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  • Exponential stabilization of nonholonomic chained systems

    Page(s): 35 - 49
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    This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown 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