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Automatic Control, IEEE Transactions on

Issue 4 • Date April 2003

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Displaying Results 1 - 25 of 29
  • On necessary conditions for almost global stability

    Publication Year: 2003 , Page(s): 631 - 634
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    In the year 2000, the sufficiency of the existence of density functions for the almost global stability of a system was proved. In this note, we prove the necessity of the existence of density functions for the particular case of global asymptotical stability. View full abstract»

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  • Stability analysis for nonlinear feedback control systems with linear actuators

    Publication Year: 2003 , Page(s): 649 - 654
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (353 KB) |  | HTML iconHTML  

    Often, nonlinear feedback controllers are implemented with linear actuators, which have faster dynamics when compared with non-linear dynamics of the plant and controller models. However, how faster should the dynamics of the linear actuator be to ensure stability of the given nonlinear feedback control system? This note gives an analysis for the underlying stability issues and provides quantitative measures for the linear actuators employed in nonlinear feedback control systems. View full abstract»

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  • Adaptive suboptimal tracking for the first-order plant with Lipschitz uncertainty

    Publication Year: 2003 , Page(s): 607 - 612
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (332 KB) |  | HTML iconHTML  

    A tracking problem for the first-order discrete-time plant with time-invariant uncertainty of the Lipschitz type and bounded exogenous disturbance is considered in the adaptive setting and two different adaptive laws are proposed. The first law is based on a natural estimation of the unknown linear part of the plant and introduces some conservatism in stability margin and tracking performance. The second adaptive law is suboptimal and includes additionally the estimation of the unknown Lipshitz constant and the unknown norm of exogenous disturbance. The suboptimality is achieved by exploiting a cone estimation algorithm and the linearity of the control criterion with respect to unknown parameters. Both adaptive laws utilize the nonlinear feedback by Xie and Guo based on nonparametric estimation of the uncertainty. View full abstract»

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  • Frequency domain identification of Hammerstein models

    Publication Year: 2003 , Page(s): 530 - 542
    Cited by:  Papers (38)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (961 KB) |  | HTML iconHTML  

    Discusses Hammerstein model identification in the frequency domain using sampled input-output data. By exploring the fundamental frequency and harmonics generated by the unknown nonlinearity, we propose a frequency domain approach and show its convergence for both the linear and nonlinear subsystems in the presence of noise. No a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric. View full abstract»

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  • On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form

    Publication Year: 2003 , Page(s): 618 - 621
    Cited by:  Papers (51)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A1 and A2 are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A1A2 does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result. View full abstract»

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  • Nonlinear discrete-time observer design with linearizable error dynamics

    Publication Year: 2003 , Page(s): 622 - 626
    Cited by:  Papers (27)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB) |  | HTML iconHTML  

    A necessary and sufficient condition for the existence of a discrete-time nonlinear observer with linearizable error dynamics is provided. The result can be applied to any real analytic nonlinear system whose linear part is observable. The necessary and sufficient condition is the solvability of a nonlinear functional equation. Furthermore, the well-known Siegel's theorem on the linearizability of a mapping is naturally reproduced in a corollary. The proposed observer design method is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics. View full abstract»

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  • Intersample and finite wordlength effects in sampled-data problems

    Publication Year: 2003 , Page(s): 639 - 643
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (266 KB) |  | HTML iconHTML  

    We consider the behavior of digital control systems while modeling intersample behavior and the effects of quantizations and finite wordlength computations. Our purpose in this note is to investigate the dependence of these two effects on the sampling rate. We indicate that there appears to be a tradeoff between guarding against these two effects, in that fast sampling will generally improve intersample behavior while it makes the system more sensitive to finite arithmetic effects. We develop quantitative measures for performance under these two combined effects using input-output norms. We address the problem of intersample behavior using the by now well known lifting technique, while we investigate roundoff error effects by modeling them as feedback with quantization nonlinearities. We present examples that exhibit these tradeoffs. View full abstract»

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  • A new approach to digital PID controller design

    Publication Year: 2003 , Page(s): 687 - 692
    Cited by:  Papers (22)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (577 KB) |  | HTML iconHTML  

    In this note, we present a new approach to the problem of designing a digital proportional-integral-derivative (PID) controller for a given but arbitrary linear time invariant plant. By using the Tchebyshev representation of a discrete-time transfer function and some new results on root counting with respect to the unit circle, we show how the digital PID stabilizing gains can be determined by solving sets of linear inequalities in two unknowns for a fixed value of the third parameter. By sweeping or gridding over this parameter, the entire set of stabilizing gains can be recovered. The precise admissible range of this parameter can be predetermined. This solution is attractive because it answers the question of whether there exists a stabilizing solution or not and in case stabilization is possible the entire set of gains is determined constructively. Using this characterization of the stabilizing set we present solutions to two design problems: 1) maximally deadbeat design, where we determine for the given plant, the smallest circle within the unit circle wherein the closed loop system characteristic roots may be placed by PID control and 2) maximal delay tolerance, where we determine, for the given plant the maximal-loop delay that can be tolerated under PID control. In each case, the set of controllers attaining the specifications is calculated. Illustrative examples are included. View full abstract»

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  • Input linearization of nonlinear systems via pulse-width control

    Publication Year: 2003 , Page(s): 635 - 638
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (265 KB) |  | HTML iconHTML  

    In this note, it is shown that a general nonlinear system can be transformed to an affine nonlinear system by virtue of the use of pulsewidth control. Therefore, the combined system from the pulse width control input to the nonlinear system output behaves as an affine (linear-in-control) system. By this way, a cumbersome nonlinear system model can be transformed to a simpler linear-in-control form without increasing the system dimension; this in turn enables simpler control design. Furthermore, using this methodology, some control design methods developed only for affine systems can be adapted to general nonlinear systems. View full abstract»

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  • Adaptive control with nonconvex parameterization

    Publication Year: 2003 , Page(s): 554 - 567
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1183 KB) |  | HTML iconHTML  

    Deals with the problem of nonconvex parameterization in adaptive control for a class of nonlinear dynamic systems. New algorithms for stable adaptive control are introduced. Sufficient conditions for achieving control objectives of adaptive control with new algorithms are investigated. Simulation examples are presented for illustration. View full abstract»

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  • Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems

    Publication Year: 2003 , Page(s): 590 - 606
    Cited by:  Papers (138)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (879 KB) |  | HTML iconHTML  

    A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application. View full abstract»

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  • Stability analysis of swarms

    Publication Year: 2003 , Page(s): 692 - 697
    Cited by:  Papers (343)  |  Patents (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (359 KB) |  | HTML iconHTML  

    In this note, we specify an "individual-based" continuous-time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model. View full abstract»

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  • Stability of linear discrete dynamics employing state saturation arithmetic

    Publication Year: 2003 , Page(s): 626 - 630
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (356 KB) |  | HTML iconHTML  

    This note is concerned with the stability of discrete-time dynamical systems employing saturation arithmetic in the state-space. A matrix measure is introduced so that it can administer the proximity evaluation of a matrix to the set of diagonal matrices, and the measure is utilized for making an additional condition to the Lyapunov-Stein matrix inequality. The solvability of the modified matrix inequality ensures not only the stability but also the absence of overflow oscillation under the state saturation arithmetic, and this approach has the advantage of being free from auxiliary parameters. As an application, the obtained result is applied to the stability analysis of two-dimensional dynamics. Numerical examples are given to illustrate the results. View full abstract»

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  • Rotational motion control of a spacecraft

    Publication Year: 2003 , Page(s): 643 - 646
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (262 KB) |  | HTML iconHTML  

    This note describes a systematic procedure for the control synthesis of a rigid spacecraft using the energy shaping method. The geometric concept of a mechanical system in a coordinate-independent form is used to derive a control algorithm for the Euler-Poincare equations. The main result of this note is a specialization of the method on the unit quaternion group. This note is concluded with the examples of the potential functions and implementation for the three-axis attitude control problem. View full abstract»

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  • On the extraction of dead-time controllers and estimators from delay-free parametrizations

    Publication Year: 2003 , Page(s): 543 - 553
    Cited by:  Papers (43)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (733 KB) |  | HTML iconHTML  

    An approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In the paper, the extraction procedures are developed in both H2 and H settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators. View full abstract»

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  • Markov decision processes with delays and asynchronous cost collection

    Publication Year: 2003 , Page(s): 568 - 574
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (497 KB) |  | HTML iconHTML  

    Markov decision processes (MDPs) may involve three types of delays. First, state information, rather than being available instantaneously, may arrive with a delay (observation delay). Second, an action may take effect at a later decision stage rather than immediately (action delay). Third, the cost induced by an action may be collected after a number of stages (cost delay). We de rive two results, one for constant and one for random delays, for reducing an MDP with delays to an MDP without delays, which differs only in the size of the state space. The results are based on the intuition that costs may be collected asynchronously, i.e., at a stage other than the one in which they are induced, as long as they are discounted properly. View full abstract»

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  • Constructive controllability algorithms for motion planning and optimization

    Publication Year: 2003 , Page(s): 575 - 589
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (963 KB) |  | HTML iconHTML  

    Presents algorithms for planning feasible and minimum energy paths. The algorithms rely on series expansions to characterize planning problems for polynomial control systems. The resulting inversion problem is solved through an iterative contraction or a power series inversion. While the design methodology is general, our focus is on a class of polynomial control systems for which we provide explicit convergence guarantees. We demonstrate performance and numerical characteristics using one dimensional and six dimensional systems. View full abstract»

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  • Static sliding-motion phenomena in dynamical systems

    Publication Year: 2003 , Page(s): 680 - 686
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (377 KB) |  | HTML iconHTML  

    We present a new type of sliding motion which results from a novel choice of the sliding surfaces. We define these sliding surfaces such that they become explicitly dependent on the outputs of the discontinuous block. We prove under this design, a special sliding mode characterises the system dynamics, which we name static sliding mode, because it occurs along a static contour of the closed-loop system. We give constructive conditions when this dynamical behavior begins and continues its motion in a static sliding mode. We show and simulate a control application in robust stabilization of nonlinear systems. View full abstract»

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  • Robust d-stability for linear uncertain discrete time-delay systems

    Publication Year: 2003 , Page(s): 709
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (164 KB) |  | HTML iconHTML  

    First Page of the Article
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  • Exact computation of traces and H2 norms for a class of infinite-dimensional problems

    Publication Year: 2003 , Page(s): 646 - 649
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (266 KB) |  | HTML iconHTML  

    We derive a formula for the trace of a class of differential operators defined by forced two point boundary value problems. The formula involves finite-dimensional computations with matrices whose dimension is no larger than the order of the differential operator. Thus, we achieve an exact reduction of an infinite-dimensional problem to a finite-dimensional one. We relate this trace calculation to computation of the H2 norm for certain infinite-dimensional systems. An example from fluid dynamics is included to illustrate the method. View full abstract»

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  • Delay-dependent/delay-independent stability of linear systems with multiple time-varying delays

    Publication Year: 2003 , Page(s): 697 - 701
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (368 KB) |  | HTML iconHTML  

    Delay-dependent/delay-independent uniform asymptotic stability and uniform stability criteria for linear systems with multiple time-varying delays are established respectively in this note. The results are derived based on a new-type stability theorem for retarded dynamical systems and a new analysis technique for estimating the derivative of a Lyapunov function along the solution of a system at certain specific instants. Four remarks together with an illustrative example are given to compare the obtained results with and to show their superiority to those in the literature. View full abstract»

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  • Set-valued state estimation via a limited capacity communication channel

    Publication Year: 2003 , Page(s): 676 - 680
    Cited by:  Papers (37)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (319 KB) |  | HTML iconHTML  

    This paper considers a state estimation problem for a linear continuous-time system via a limited capacity communication channel. The observation must be coded and transmitted via a limited capacity digital communication channel. A recursive order-decoder state estimation scheme is proposed and investigated. View full abstract»

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  • Quadratic characterization and use of output stabilizable subspaces

    Publication Year: 2003 , Page(s): 654 - 660
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (377 KB) |  | HTML iconHTML  

    This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C, A, B)-invariant subspaces. The work provides a new characterization of output stabilizable (C, A, B)-invariant subspaces through two coupled quadratic stabilization conditions. An equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback. An algorithm is provided and numerical examples are reported to illustrate the approach. View full abstract»

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  • Orthogonal rational functions for system identification: numerical aspects

    Publication Year: 2003 , Page(s): 705 - 709
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (328 KB) |  | HTML iconHTML  

    Recently, there has been a growing interest in the use of orthogonal rational functions (ORFs) in system identification. There are many advantages over more classical techniques. Probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 (the so called Malmquist basis), the attention has been on the development of methods using this basis. However, for some discrete identification problems, this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved. In this note, we give an algorithm based on a more general system of ORF to overcome the numerical problem and which allows for a fast-order update of the estimate. View full abstract»

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  • The problem of state estimation via asynchronous communication channels with irregular transmission times

    Publication Year: 2003 , Page(s): 670 - 676
    Cited by:  Papers (65)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (462 KB) |  | HTML iconHTML  

    We study a linear discrete-time partially observed system perturbed by white noises. The observations are transmitted to the estimator via communication channels with irregular transmission times. Various measurement signals and even parts of a given sensor output may incur independent delays; messages transferred via the channels may be lost or corrupted. The minimum variance state estimation problem is solved. It is shown that the proposed state estimator is exponentially stable under natural assumptions. 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