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Automatic Control, IEEE Transactions on

Issue 9 • Date Sept. 2006

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Displaying Results 1 - 25 of 34
  • Table of contents

    Publication Year: 2006 , Page(s): c1 - c4
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  • IEEE Transactions on Automatic Control publication information

    Publication Year: 2006 , Page(s): c2
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  • Generalized Sliding Mode Control for Multi-Input Nonlinear Systems

    Publication Year: 2006 , Page(s): 1409
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  • Generalized Sliding-Mode Control for Multi-Input Nonlinear Systems

    Publication Year: 2006 , Page(s): 1410 - 1422
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (487 KB) |  | HTML iconHTML  

    The purpose of this paper is to present a framework for the design of sliding-mode based controllers for multi-input affine nonlinear systems. In this framework the control effort goes to zero as the state approaches the sliding surface, a key feature for practical implementation. The sliding surface is a submanifold with codimension equal to the dimension of the involutive distribution G generated by the controlled vector fields rather than the dimension of their linear span. We also allow nonzero vectors in G to be tangent to the sliding surface, the singular case in sliding-mode control View full abstract»

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  • Near Optimal LQR Performance for a Compact Set of Plants

    Publication Year: 2006 , Page(s): 1423 - 1439
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (506 KB) |  | HTML iconHTML  

    Here we consider the problem of providing near optimal performance (in this context, "near optimal performance" means performance as close to optimality as desired) for a large set of possible models. We adopt the linear quadratic regulator (LQR) framework in the single-input-single-output (SISO) setting, and prove that given a compact set of controllable and observable plant models of a fixed order, we can construct a single linear periodic controller (LPC) which provides near optimal LQR performance. Since the controller is linear, it automatically has the nice feature that there is some degree of tolerance to unmodeled dynamics. The approach is also shown to work if the goal is the more modest one of pole placement, and it can be simplified if there is additional structure to the plant model View full abstract»

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  • Global-Stabilizing Near-Optimal Control Design for Nonholonomic Chained Systems

    Publication Year: 2006 , Page(s): 1440 - 1456
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (694 KB)  

    It is well known that a nonlinear optimal control requires the solution to a two-point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration. In this paper, a new and near-optimal control design framework is proposed for controlling any nonholonomic system in the chained form. The proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system. It is shown that, no matter whether the first component u1d(t) of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero, uniform complete controllability of the (nominal) system can be recovered by employing the proposed time-folding/unfolding technique. Upon establishing the common property of uniform complete controllability, the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner. Using duality, uniform complete observability can also be established, a closed-form and exponentially convergent observer can be synthesized, and the controls designed using the proposed framework can be either state-feedback or output-feedback. The tracking controls are designed using the same three-step process. That is, design of the proposed controls starts with optimal control solutions to two linear nominal subsystems, one time-invariant and the other time varying. The two solutions combined together render a globally stabilizing suboptimal control for the overall system. Then, the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one. Consequently, an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form. An example is used to show that regulation con- - trol can be designed similarly. All the controls designed are in simple closed forms and hence real-time implementable, they are time varying and smooth, globally and exponentially/asymptotically stabilizing, and they are near optimal since their closeness to the optimal control (attainable only offline) can be measured, monitored on line, and has been minimized View full abstract»

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  • Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems

    Publication Year: 2006 , Page(s): 1457 - 1471
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (575 KB) |  | HTML iconHTML  

    We present a nonsmooth output feedback framework for local and/or global stabilization of a class of nonlinear systems that are not smoothly stabilizable nor uniformly observable. A systematic design method is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Houmllder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design algorithm, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented manner. Such a nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems in the Hessenberg form studied in a previous paper, where global stabilizability by nonsmooth state feedback was already proved to be possible View full abstract»

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  • Deadlock-Freeness Analysis of Continuous Mono-T-Semiflow Petri Nets

    Publication Year: 2006 , Page(s): 1472 - 1481
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (605 KB) |  | HTML iconHTML  

    Most verification techniques for highly populated discrete systems suffer from the state explosion problem. The "fluidification" of discrete systems is a classical relaxation technique that aims to avoid the state explosion problem. Continuous Petri nets are the result of fluidifying traditional discrete Petri nets. In continuous Petri nets the firing of a transition is not constrained to the naturals but to the non-negative reals. Unfortunately, some important properties, as liveness, may not be preserved when the discrete net model is fluidified. Therefore, a thorough study of the properties of continuous Petri nets is required. This paper focuses on the study of deadlock-freeness in the framework of mono-T-semiflow continuous Petri nets, i.e., conservative nets with a single repetitive sequence (T-semiflow). The study is developed both on untimed and timed systems. Topological necessary conditions are extracted for this property. Moreover, a bridge relating deadlock-freeness conditions for untimed and timed systems is established View full abstract»

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  • Delay-Independent Stability Conditions for Time-Varying Nonlinear Uncertain Systems

    Publication Year: 2006 , Page(s): 1482 - 1486
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB) |  | HTML iconHTML  

    A new stability criterion for time-varying systems consisting of linear and norm bounded nonlinear terms with uncertain time-varying delays is formulated. An explicit delay-independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms. The obtained condition turns out to be also necessary if the matrix of the linear part is time-invariant and symmetric; it is shown that these systems satisfy the well-known Aizerman's conjecture. The obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems; in all cases the proposed criterion provides less conservative stability bounds View full abstract»

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  • Accessibility of Switched Linear Systems

    Publication Year: 2006 , Page(s): 1486 - 1491
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (299 KB) |  | HTML iconHTML  

    This note considers the controllability of switched linear systems. The structure of accessibility Lie algebra is revealed. Some accessibility properties are proved. Certain necessary and sufficient conditions for (local or global, weak or normal) controllability of a large class of switched linear systems are obtained View full abstract»

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  • Robust Stabilization for Single-Input Polytopic Nonlinear Systems

    Publication Year: 2006 , Page(s): 1492 - 1496
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (203 KB) |  | HTML iconHTML  

    This note deals with the stabilization problem of single-input polytopic nonlinear systems. The robust control Lyapunov function approach is used to derive a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controllers. The obtained sufficient condition is proven also necessary for the existence of stabilizing state feedback controllers such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. In addition, a universal formula for constructing stabilizing controllers when the presented sufficient condition is met is provided. The results are illustrated by a numerical example View full abstract»

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  • Affine Controller Parameterization for Decentralized Control Over Banach Spaces

    Publication Year: 2006 , Page(s): 1497 - 1500
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (170 KB) |  | HTML iconHTML  

    We cast the problem of optimal decentralized control as one of minimizing a closed-loop norm subject to a subspace constraint on the controller. In this note, we consider continuous linear operators on Banach spaces, and show that a simple property called quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback, and thus allows optimal synthesis to be recast as a convex optimization problem. These results hold for any norm and any Banach space View full abstract»

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  • New Exponential Estimates for Time-Delay Systems

    Publication Year: 2006 , Page(s): 1501 - 1505
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (215 KB) |  | HTML iconHTML  

    This note considers the problem of exponential stability for time-delay systems. In terms of linear matrix inequalities, a new sufficient condition for exponential stability is obtained. Based on this, an improved upper bound of the decay rate can be easily calculated. When time-varying norm-bounded parameter uncertainties appear, a new sufficient condition for robust exponential stability of uncertain time-delay systems is also provided. The reduced conservatism of the proposed conditions is illustrated via two numerical examples View full abstract»

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  • Eigenvalue Inequalities for Matrix Product

    Publication Year: 2006 , Page(s): 1506 - 1509
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (179 KB) |  | HTML iconHTML  

    We present a family of eigenvalue inequalities for the product of a Hermitian matrix and a positive-semidefinite matrix. Our theorem contains or extends some existing results on trace and eigenvalues View full abstract»

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  • Exact Stability Analysis of 2-D Systems Using LMIs

    Publication Year: 2006 , Page(s): 1509 - 1513
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (251 KB) |  | HTML iconHTML  

    In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (2-D) systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced View full abstract»

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  • Boundedness and Global Stability of a Nonlinear Congestion Control With Delays

    Publication Year: 2006 , Page(s): 1514 - 1519
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (268 KB) |  | HTML iconHTML  

    This note concerns the global dynamics of a "dual" nonlinear congestion control with time-delays. It has been shown that such control laws are able to maintain local dynamic stability around their unique equilibrium point for networks of arbitrary delay, capacity and topology. We focus here on the case of a single bottleneck network, shared by traffic sources with heterogeneous delays. We first prove that, for any parameter values, an a priori bound can be given on the system state after a certain amount of time. Next, we prove global exponential stability of the delay-differential equations under constraints on its gain parameter and the delays; these are more restrictive than conditions for linear stability, but only mildly so in the homogeneous delay case. The proof is based on a detailed investigation and bounding of the system trajectories View full abstract»

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  • Robustness With Respect to Sampling for Stabilization of Riesz Spectral Systems

    Publication Year: 2006 , Page(s): 1519 - 1522
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (193 KB) |  | HTML iconHTML  

    We suppose that a continuous-time feedback is input-output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying idealized sample-and-hold to this continuous-time feedback is also input-output stabilizing if the sampling time is small enough. This question has been previously addressed for fairly general systems under various conditions. In this note, we restrict our attention to Riesz spectral systems, for which we generalize the existing results. Specifically, we give two relatively simple conditions which, combined, are sufficient for the sampled-data controller to be stabilizing. The first condition is a spectrum decomposition for the open-loop system generator, which by itself is necessary, but not sufficient, for the system to be stabilizable by sampled-data control. The second is a summability condition relating the real part of the spectrum of the generator and the expansion coefficients for the input and feedback operators View full abstract»

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  • A Policy Improvement Method in Constrained Stochastic Dynamic Programming

    Publication Year: 2006 , Page(s): 1523 - 1526
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (203 KB) |  | HTML iconHTML  

    This note presents a formal method of improving a given base-policy such that the performance of the resulting policy is no worse than that of the base-policy at all states in constrained stochastic dynamic programming. We consider finite horizon and discounted infinite horizon cases. The improvement method induces a policy iteration-type algorithm that converges to a local optimal policy View full abstract»

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  • Sliding-Mode Control of Retarded Nonlinear Systems Via Finite Spectrum Assignment Approach

    Publication Year: 2006 , Page(s): 1527 - 1531
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB) |  | HTML iconHTML  

    In the present study, a sliding-mode control design method based on the finite spectrum assignment procedure is proposed. The finite spectrum assignment for retarded nonlinear systems can transform retarded nonlinear systems into delay-free linear systems via a variable transformation and a feedback, which contain the past values of the state. This method can be considered to be an extension of both the finite spectrum assignment for retarded linear systems with controllability over polynomial rings of the delay operator and the exact linearization for finite dimensional nonlinear systems. The proposed method is to design a sliding surface via the variable transformation used in the finite spectrum assignment and to derive a switching feedback law. The obtained surface contains not only the current values of the state variables but also the past values of the state variables in the original coordinates. The effectiveness of the proposed method is tested by an illustrative example View full abstract»

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  • On Discretization of Continuous-Time Terminal Sliding Mode

    Publication Year: 2006 , Page(s): 1532 - 1536
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (212 KB) |  | HTML iconHTML  

    In terminal sliding-mode control, the system states are brought to the origin in finite time using the concept of sliding-mode control. Though the theory of terminal sliding mode is well studied for continuous time systems, a discrete-time terminal sliding mode concept has not been investigated. This note analyses the applicability of terminal sliding-mode control in the discrete-time framework and discusses the problems involved in the discretization of continuous-time terminal sliding mode. The note also suggests a method to approach the discrete-time terminal sliding-mode control problem View full abstract»

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  • Compositional Contraction Analysis of Resetting Hybrid Systems

    Publication Year: 2006 , Page(s): 1536 - 1541
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (252 KB) |  | HTML iconHTML  

    This note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems. Using nonlinear contraction theory, the analysis first develops a unified formulation of continuous-time and discrete-time nonlinear dynamics based on a differential transition matrix. This yields enhanced dwell-time based conditions for stability of such systems analogous to those existing for switched systems. It turns out that such dwell-time based conditions, unlike their counterparts for switched systems, include arbitrary stability conditions as a special case, and are less conservative and much simpler to verify View full abstract»

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  • Robust Detectability From the Measurements Plus State Feedback Stabilization Imply Semiglobal Stabilization From the Measurements

    Publication Year: 2006 , Page(s): 1542 - 1547
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (336 KB) |  | HTML iconHTML  

    We study the problem of stabilizing with large regions of attraction a general class of nonlinear system consisting of a linear nominal system plus uncertainties. A similar result was given by the same author in previous works; in this note, we prove that what was referred in these works to as "nonlinear coupling condition" can be reformulated in the control design as a "nonlinear rescaling" of the Lyapunov functions of the closed-loop system plus the requirement for a suitably faster convergence of the state estimation error. We obtain a paradigm very similar to the linear case, for which if a couple of Riccati-like inequalities (state feedback and observer design) are satisfied then a measurement feedback stabilizing controller can be readily found. Examples are given for showing improvements over the existing literature View full abstract»

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  • Regional Input-to-State Stability for Nonlinear Model Predictive Control

    Publication Year: 2006 , Page(s): 1548 - 1553
    Cited by:  Papers (41)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    In this note, regional input-to-state stability (ISS) is introduced and studied in order to analyze the domain of attraction of nonlinear constrained systems with disturbances. ISS is derived by means of a non smooth ISS-Lyapunov function with an upper bound guaranteed only in a sub-region of the domain of attraction. These results are used to study the ISS properties of nonlinear model predictive control (MPC) algorithms View full abstract»

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  • On Pole Placement via Eigenstructure Assignment Approach

    Publication Year: 2006 , Page(s): 1554 - 1558
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (230 KB) |  | HTML iconHTML  

    This note comes back to the hard problem of pole placement by static output feedback: let a triplet of matrices {A;B;C} be given with n state variables, m inputs and p ouputs, find a matrix K such that the spectrum of A+BKC equals a specified set. When mp>m+p, a simple noniterative technique based upon the notion of eigenstructure that, in most cases, assigns m+p roots is proposed. It, therefore, enables the designer to assign the whole of the desired spectrum when m+p=n<mp View full abstract»

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  • Uniform Sample Generations from Contractive Block Toeplitz Matrices

    Publication Year: 2006 , Page(s): 1559 - 1565
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (358 KB) |  | HTML iconHTML  

    This note deals with generating a series of random matrices uniformly and independently from contractive lower triangular block Toeplitz (LTBT) matrices. All the contractive LTBT matrices are parameterized nonlinearly but recursively in a closed-form by a sequence of contractive unstructured matrices. Moreover, the conditional probability density function (PDF) is obtained in a closed-form for all the matrix parameters, as well as the squares of their singular values. It has been made clear that the conditional PDFs of the matrix parameters are unitarily invariant. A procedure is developed to accurately produce the required random matrix samples 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