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Automatic Control, IEEE Transactions on

Issue 5 • Date May 1997

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Displaying Results 1 - 21 of 21
  • Comments on "A note on two methods related to stability robustness of polynomials in a sector (Relative stability)"

    Publication Year: 1997 , Page(s): 712 - 714
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (139 KB)  

    In this paper, it is shown that the results of the above-mentioned paper (Katbab and Jury, 1993) are incorrect for the case of complex coefficients. A counterexample is provided. An alternative approach is presented for the calculation of sector-stability hypersolids in the coefficient space. View full abstract»

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  • Comments on "An asymptotic modal observer for linear autonomous time lag systems" [with reply]

    Publication Year: 1997 , Page(s): 742 - 745
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (23 KB)  

    It is show that the proof of theorem 1 in the original paper of J. Leyva-Ramos and A.E. Pearson (ibid., vol. 40, p. 1291-4, 1995) is incomplete and that the state observer scheme results in steady-state error. Alternatively, a memoryless state observer for linear time-delay systems is provided. The original authors acknowledge that the criticism is correct, and suggest an alternative way of overcoming the problem. View full abstract»

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  • Comments on "An Asymptotic Modal Observer For Linear Autonomous Time Lag Systems

    Publication Year: 1997 , Page(s): 742 - 745
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (127 KB)  

    First Page of the Article
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  • Author's reply

    Publication Year: 1997 , Page(s): 745
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (30 KB)  

    First Page of the Article
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  • Least squares parameter estimation of continuous-time ARX models from discrete-time data

    Publication Year: 1997 , Page(s): 659 - 673
    Cited by:  Papers (46)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (556 KB)  

    When modeling a system from discrete-time data, a continuous-time parameterization is desirable in some situations, In a direct estimation approach, the derivatives are approximated by appropriate differences. For an ARX model this lead to a linear regression. The well-known least squares method would then be very desirable since it can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. It is examined under what conditions a least squares fit for this linear regression will give adequate results for an ARX model. The choice of derivative approximation is crucial for this approach to be useful. Standard approximations like Euler backward or Euler forward cannot be used directly. The precise conditions on the derivative approximation are derived and analyzed. It is shown that if the highest order derivative is selected with care, a least squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation View full abstract»

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  • On the numerical solutions of stochastic optimization problem

    Publication Year: 1997 , Page(s): 727 - 729
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (88 KB)  

    In this paper we discuss the role of soft computing (SC) in optimization problems. We point out that SC is closely related to computational intelligence. Each aims at complementing the limitations of many conventional techniques View full abstract»

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  • Model quality evaluation in H2 identification

    Publication Year: 1997 , Page(s): 691 - 698
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (356 KB)  

    Model quality evaluation in set-membership identification is investigated, In the recent literature, two main approaches have been used to investigate this problem, based on the concepts of n-width and of radius of information. In this paper it is shown that the n-width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements. Upper and lower bounds of the conditional radius of information are derived for the H2 identification of exponentially stable systems using approximating n-dimensional models linear in the parameters in the presence of power bounded measurement errors. The derived bounds are shown to be convergent to the radius for a large number of data and model dimensions. Moreover, a formula for computing the worst case identification error for any linear algorithm is given. In particular, it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension (“peaking effect”), An almost-optimal linear algorithm is presented, that is not affected by this peaking effect, and indeed is asymptotically optimal View full abstract»

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  • Quadratic stabilizability of multi-input linear systems with structural independent time-varying uncertainties

    Publication Year: 1997 , Page(s): 699 - 703
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB)  

    This paper investigates the problem of designing a linear-state feedback control to stabilize a class of multi-input linear dynamical systems. We first show that to ensure a stabilizable system, some entries of the system matrices must be sign-invariant. We then derive a sufficient condition under which a system can he quadratically stabilized by a linear control View full abstract»

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  • Passivity-based control of a class of Blondel-Park transformable electric machines

    Publication Year: 1997 , Page(s): 629 - 647
    Cited by:  Papers (74)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (668 KB)  

    Concerns the extension to the general rotating electric machine model of the passivity-based controller method for induction motors. The motor's passivity properties are used at 2 levels. First, we prove that the motor model can be decomposed as the feedback interconnection of two passive subsystems (essentially, the electrical and mechanical dynamics). Then, we design a torque-tracking controller that preserves passivity for the electrical subsystem and leaves the mechanical part as a passive disturbance. This leads to the cascaded controller structure which is typically analyzed involving time-scale separation. Our aim is to characterize a class of machines for which such a passivity-based controller solves the output feedback torque-tracking problem. The class consists of machines whose nonactuated dynamics are damped and whose dynamics can be decoupled. This requires that the air-gap magnetomotive force must be suitably approximated by the first harmonic in its Fourier expansion. These conditions have a clear physical interpretation in terms of the couplings between its dynamics and are satisfied by many machines. The passivity-based controller presented reduces to the well-known indirect vector controller for current-fed induction machines. Our developments constitute an extension to voltage-fed machines of this de facto standard in industrial applications View full abstract»

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  • Decentralized adaptive output feedback design for large-scale nonlinear systems

    Publication Year: 1997 , Page(s): 729 - 735
    Cited by:  Papers (75)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (312 KB)  

    In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved View full abstract»

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  • Approximate set-valued observers for nonlinear systems

    Publication Year: 1997 , Page(s): 648 - 658
    Cited by:  Papers (30)  |  Patents (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (552 KB)  

    A set-valued observer (SVO) produces a set of possible states based on output measurements and a priori models of exogenous disturbances and noises. Previous work considered linear time-varying systems and unknown-but-bounded exogenous signals. In this case, the sets of possible state vectors take the form of polytopes whose centers are optimal state estimates. These polytopic sets can be computed by solving several small linear programs. An SVO can be constructed conceptually for nonlinear systems; however, the set of possible state vectors no longer takes the form of polytopes, which in turn inhibits their explicit computation. This paper considers an “extended SVO”. As in the extended Kalman filter, the state equations are linearized about the state estimate, and a linear SVO is designed along the linearization trajectory. Under appropriate observability assumptions, it is shown that the extended SVO provides an exponentially convergent state estimate in the case of sufficiently small initial condition uncertainty and provides a nondivergent state estimate in the case of sufficiently small exogenous signals View full abstract»

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  • Efficient zero location tests for delta-operator-based polynomials

    Publication Year: 1997 , Page(s): 722 - 727
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (244 KB)  

    Two different kinds of stability tests, or more generally zero location tests, are proposed when a real polynomial formulated in the delta-operator is given. The method used is a simple linear transformation based on some known discrete-time tests, including the Schur-Cohn test (SCT), and the proposed algorithms are computationally efficient. Furthermore, it is shown that as the sampling interval vanishes, all new algorithms converge to their continuous-time limits, therefore providing smooth transitions from the shift-operator-based discrete-time tests to the continuous-time ones. One of these limits is the classic Routh test (RT), and the other is a new test, closely related to the RT. Examples are given to demonstrate the tests which show clear numerical advantages over the traditional shift-operator-based ones such as the SCT in case of fast sampling. The significance of these new tests lies beyond the fact that they have provided efficient and reliable zero location tests directly in the delta-domain. These tests provide the missing links between the discrete-time shift-operator-based tests and the continuous-time ones. As a consequence, two separate and yet related families of zero location tests are established, which include the well-known RT and the SCT View full abstract»

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  • Two conditions concerning common quadratic Lyapunov functions for linear systems

    Publication Year: 1997 , Page(s): 719 - 722
    Cited by:  Papers (27)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (120 KB)  

    Concerning a pair of linear systems, some triangle conditions for the existence of a common quadratic Lyapunov function are presented in this paper. These conditions are derived from a criterion for judging the semipositiveness of a linear map defined on symmetric matrices View full abstract»

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  • Output feedback controllers for systems with structured uncertainty

    Publication Year: 1997 , Page(s): 715 - 719
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB)  

    This paper deals with the design of compensators that provide a guaranteed level of performance, in the sense of L2 gain, for systems with time-varying structured uncertainty. For stability, the notion of quadratic stability, using a single Lyapunov function, is used. The uncertainty is assumed to be polytopic (e.g., the uncertainty vector enters the state-space representation of the systems affinely). Earlier results in the characterization of H controllers are used to show that quadratic stability with performance is equivalent to a bi-affine problem. A set of conditions, under which the problem becomes convex, is discussed View full abstract»

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  • Decoupling of square linear systems with delays

    Publication Year: 1997 , Page(s): 736 - 742
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (276 KB)  

    The aim of this paper is to exhibit matricial necessary and sufficient conditions for the decoupling problem of linear systems with commensurate delays, under static nonpredictive and stable state feedbacks. A “matrix” approach is used which is similar to the Falb-Wolovich one for systems without delay. The conditions obtained here are quite simple, easily computable, and less restrictive than the previous ones. Moreover, we give the only possible design of the physically realizable control law that satisfies the problem View full abstract»

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  • An analysis of temporal-difference learning with function approximation

    Publication Year: 1997 , Page(s): 674 - 690
    Cited by:  Papers (180)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (732 KB)  

    We discuss the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of an infinite-horizon discounted Markov chain. The algorithm we analyze updates parameters of a linear function approximator online during a single endless trajectory of an irreducible aperiodic Markov chain with a finite or infinite state space. We present a proof of convergence (with probability one), a characterization of the limit of convergence, and a bound on the resulting approximation error. Furthermore, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. In addition to proving new and stronger positive results than those previously available, we identify the significance of online updating and potential hazards associated with the use of nonlinear function approximators. First, we prove that divergence may occur when updates are not based on trajectories of the Markov chain. This fact reconciles positive and negative results that have been discussed in the literature, regarding the soundness of temporal-difference learning. Second, we present an example illustrating the possibility of divergence when temporal difference learning is used in the presence of a nonlinear function approximator View full abstract»

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  • H control of a class of nonlinear systems using describing functions and simplicial algorithms

    Publication Year: 1997 , Page(s): 707 - 712
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (260 KB)  

    This paper describes a new method for generating an H controller for a nonlinear system whose nonlinearities are modeled as describing functions. It is a three-step approach: modeling (using the describing function approach), synthesis (using the H loop shifting technique), and robustness analysis (using the labeling technique of simplicial algorithms). The method is first demonstrated by designing an optimal H controller for a first-order linear unstable system driven by a bang-bang actuator. A more complex example is used next to demonstrate loop shifting and simplicial algorithms as applied to a suboptimal problem. This system was implemented on a digital computer and in analog circuit form to demonstrate the practicality of the method View full abstract»

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  • A simple alternative to the Barbalat lemma

    Publication Year: 1997
    Cited by:  Papers (29)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (36 KB)  

    This paper gives a simple proof of the property that if a signal is square integrable and has a bounded derivative, then the signal converges to zero asymptotically View full abstract»

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  • Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

    Publication Year: 1997 , Page(s): 614 - 628
    Cited by:  Papers (154)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (588 KB)  

    This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers View full abstract»

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  • Fault isolation filter design for linear time-invariant systems

    Publication Year: 1997 , Page(s): 704 - 707
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB)  

    This paper is concerned with the problem of detecting and isolating multiple faults by a full-order observer of the plant state. We first obtain the fault isolability condition from the dual concept, namely static-state feedback decoupling. A new full-state observer design method is then developed to isolate simultaneous multiple faults. The method can isolate m simultaneous faults with m output measurements (such that the isolability condition is satisfied) under zero initial error of state estimation. Asymptotic fault isolation results can also be obtained using the same observer design if the number of invariant eigenvalues is (n-m), and if they are stable, where n represents the system order, m is the number of faults in the system. In both cases m can be up to the system order n View full abstract»

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  • Controller design with multiple objectives

    Publication Year: 1997 , Page(s): 596 - 613
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (772 KB)  

    In this paper we study multi-objective control problems that give rise to equivalent convex optimization problems. We develop a uniform treatment of such problems by showing their equivalence to linear programming problems with equality constraints and an appropriate positive cone. We present some specialized results on duality theory, and we apply them to the study of three multi-objective control problems: the optimal l1 control with time-domain constraints on the response to some fixed input, the mixed H2/l1 -control problem, and the l1 control with magnitude constraint on the frequency response. What makes these problems complicated is that they are often equivalent to infinite-dimensional optimization problems. The characterization of the duality relationship between the primal and dual problem allows us to derive several results. These results establish connections with special convex problems (linear programming or linear matrix inequality problems), uncover finite-dimensional structures in the optimal solution, when possible, and provide finite-dimensional approximations to any degree of accuracy when the problem does not appear to have a finite-dimensional structure. To illustrate the theory and highlight its potential, several numerical examples are presented 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