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Automatic Control, IEEE Transactions on

Issue 12 • Date Dec. 2007

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Displaying Results 1 - 25 of 29
  • Table of contents

    Publication Year: 2007 , Page(s): C1 - C4
    Save to Project icon | Request Permissions | PDF file iconPDF (38 KB)  
    Freely Available from IEEE
  • IEEE Transactions on Automatic Control publication information

    Publication Year: 2007 , Page(s): C2
    Save to Project icon | Request Permissions | PDF file iconPDF (36 KB)  
    Freely Available from IEEE
  • Scanning the issue

    Publication Year: 2007 , Page(s): 2197 - 2198
    Save to Project icon | Request Permissions | PDF file iconPDF (39 KB) |  | HTML iconHTML  
    Freely Available from IEEE
  • On Synchronous Robotic Networks—Part I: Models, Tasks, and Complexity

    Publication Year: 2007 , Page(s): 2199 - 2213
    Cited by:  Papers (24)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (720 KB) |  | HTML iconHTML  

    This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics, and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We illustrate our model and compute the proposed complexity measures in the example of a network of locally connected agents on a circle that agree upon a direction of motion and pursue their immediate neighbors. View full abstract»

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  • On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms

    Publication Year: 2007 , Page(s): 2214 - 2226
    Cited by:  Papers (22)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (703 KB) |  | HTML iconHTML  

    This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward-average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices. View full abstract»

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  • From Chronological Calculus to Exponential Representations of Continuous and Discrete-Time Dynamics: A Lie-Algebraic Approach

    Publication Year: 2007 , Page(s): 2227 - 2241
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (567 KB) |  | HTML iconHTML  

    In this paper, formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived. It is shown that the chronological exponential admits an ordinary exponential representation, the exponent being given by an explicitly computable Lie series expansion. The results are then used to describe controlled dynamics, dynamics under sampling and forced discrete-time dynamics. The study emphasizes the role of Lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations, dynamics under sampling and forced discrete-time dynamics up to hybrid ones. View full abstract»

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  • Hierarchical Supervisory Control Based on Discrete Event Systems With Flexible Marking

    Publication Year: 2007 , Page(s): 2242 - 2253
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (555 KB) |  | HTML iconHTML  

    This paper proposes a two-level hierarchical supervisory control scheme for a discrete event system (DES), where the low-level is represented in the standard Ramadge-Wonham framework and the high level is represented by a DES with flexible marking (DESFM). As shown, the flexibility in the definition of marking provided by a DESFM simplifies the modeling of the high-level marking behavior. This approach, when compared with other approaches, requires less events and states to model the high-level, while guaranteeing hierarchical consistency. View full abstract»

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  • Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications

    Publication Year: 2007 , Page(s): 2254 - 2269
    Cited by:  Papers (90)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1034 KB) |  | HTML iconHTML  

    Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition. In the existing literature, distributed implementations are typically achieved by means of the so-called dual decomposition technique. However, the span of decomposition possibilities includes many other elements that, thus far, have not been fully exploited, such as the use of the primal decomposition technique, the versatile introduction of auxiliary variables, and the potential of multilevel decompositions. This paper presents a systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture. Several specific applications are considered to illustrate the proposed framework, including resource-constrained and direct-control rate allocation, and rate allocation among QoS classes with multipath routing. For each of these applications, the associated generalized NUM formulation is first presented, followed by the development of novel alternative decompositions and numerical experiments on the resulting new distributed algorithms. A systematic enumeration and comparison of alternative vertical decompositions in the future will help complete a mathematical theory of network architectures. View full abstract»

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  • Constrained Optimal Hybrid Control of a Flow Shop System

    Publication Year: 2007 , Page(s): 2270 - 2281
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (417 KB) |  | HTML iconHTML  

    We consider an optimal control problem for the hybrid model of a deterministic flow shop system, in which the jobs are processed in the order they arrive at the system. The problem is decomposed into a higher-level discrete-event system control problem of determining the optimal service times, and a set of lower-level classical control problems of determining the optimal control inputs for given service times. We focus on the higher-level problem which is nonconvex and nondifferentiable. The arrival times are known and the decision variables are the service times that are controllable within constraints. We present an equivalent convex optimization problem with linear constraints. Under some cost assumptions, we show that no waiting is observed on the optimal sample path. This property allows us to simplify the convex optimization problem by eliminating variables and constraints. We also prove, under an additional strict convexity assumption, the uniqueness of the optimal solution and propose two algorithms to decompose the simplified convex optimization problem into a set of smaller convex optimization problems. The effects of the simplification and the decomposition on the solution times are shown on an example problem. View full abstract»

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  • Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability

    Publication Year: 2007 , Page(s): 2282 - 2297
    Cited by:  Papers (87)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (659 KB) |  | HTML iconHTML  

    This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given. View full abstract»

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  • A Closed-Form Feedback Controller for Stabilization of the Linearized 2-D Navier–Stokes Poiseuille System

    Publication Year: 2007 , Page(s): 2298 - 2312
    Cited by:  Papers (20)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (518 KB) |  | HTML iconHTML  

    We present a formula for a boundary control law which stabilizes the parabolic profile of an infinite channel flow, which is linearly unstable for high Reynolds numbers. Also known as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence, whose stabilization for arbitrary Reynolds numbers, without using discretization, has so far been an open problem. Our result achieves exponential stability in the L2, H1, and H2 norms, for the linearized Navier-Stokes equations. Explicit solutions are obtained for the closed loop system. This is the first time explicit formulae are produced for solutions of the linearized Navier-Stokes equations in a channel flow, with feedback in the boundary conditions used to make this possible. The result is presented for the 2D case for clarity of exposition. An extension to 3D is available and will be presented in a future publication. View full abstract»

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  • A Simple Robust Controller for the Approximate Regulation of Almost Periodic Signals for Linear Systems

    Publication Year: 2007 , Page(s): 2313 - 2324
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (414 KB) |  | HTML iconHTML  

    By using a delay line as a signal generator, we design a simple robust controller for the approximate regulation (i.e., approximate asymptotic tracking and rejection) of almost periodic signals for linear systems. As opposed to the related existing results, our controller design does not require online parameter tuning. Besides the usual assumptions about stabilizability, detectability, and nonexistence of transmission zeros for the plant, the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy . Based on this information alone, we can only design a robust controller achieving, in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller, . Here, is the output of the plant and is an arbitrary almost periodic reference signal taken from an infinite-dimensional generalized Sobolev space of almost periodic functions. In this paper, we also study robust output regulation in the limiting case where . It turns out that, due to the general loss of exponential closed loop stability, asymptotic tracking/rejection can also be lost as , unless the exogenous signals are smooth enough. This last result extends some recent theorems on (nonrobust) open loop output regulation for infinite-dimensional exosystems. The results of this paper are new and potentially useful for finite-dimensional plants, but the main results are also true for infinite-dimensional systems with bounded control and observation operators. View full abstract»

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  • Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

    Publication Year: 2007 , Page(s): 2325 - 2331
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (508 KB) |  | HTML iconHTML  

    This correspondence deals with a class of ergodic control problems for systems described by Markov chains with strong and weak interactions. These systems are composed of a set of subchains that are weakly coupled. Using results already available in the literature one formulates a limit control problem the solution of which can be obtained via an associated nondifferentiable convex programming (NDCP) problem. The technique used to solve the NDCP problem is the Analytic Center Cutting Plane Method (ACCPM) which implements a dialogue between, on one hand, a master program computing the analytical center of a localization set containing the solution and, on the other hand, an oracle proposing cutting planes that reduce the size of the localization set at each main iteration. The interesting aspect of this implementation comes from two characteristics: (i) the oracle proposes cutting planes by solving reduced sized Markov Decision Problems (MDP) via a linear program (LP) or a policy iteration method; (ii) several cutting planes can be proposed simultaneously through a parallel implementation on processors. The correspondence concentrates on these two aspects and shows, on a large scale MDP obtained from the numerical approximation ldquoa la Kushner-Dupuisrdquo of a singularly perturbed hybrid stochastic control problem, the important computational speed-up obtained. View full abstract»

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  • Adaptive Monitoring and Accommodation of Nonlinear Actuator Faults in Positive Real Infinite Dimensional Systems

    Publication Year: 2007 , Page(s): 2332 - 2338
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (573 KB) |  | HTML iconHTML  

    We consider a class of positive real infinite dimensional systems which are subjected to incipient actuator faults. The actuator fault is modeled as a time varying transition from an initial (linear or even nonlinear) map into another unknown nonlinear map at the onset of the fault occurrence. An infinite dimensional adaptive detection observer is utilized to generate a residual signal in order to detect the fault occurrence and to assist in the fault accommodation. This is done via an automated control reconfiguration which utilizes information on the new actuator map and adjusts the controller via a right inverse of the new actuator map. A robust modification is utilized in order to avoid false alarms caused by unmodeled dynamics. An example is included to illustrate the applicability of the proposed detection scheme. View full abstract»

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  • Approximation of Escape Time for Lagrangian Systems With Fast Noise

    Publication Year: 2007 , Page(s): 2338 - 2341
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (170 KB) |  | HTML iconHTML  

    This note is concerned with the large deviations asymptotics estimate of the mean escape time for Lagrangian systems subjected to fast Gaussian noise. The solution to the Hamilton-Jacobi equation of the associated variational problem is derived as a sum of two terms dependent on kinetic and potential energy of the system, respectively. A closed-form solution for classes of linear and nonlinear systems is obtained. An application to a controlled pointing problem is discussed as an example. View full abstract»

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  • Synthesis of Stabilizing Antiwindup Controllers Using Piecewise Quadratic Lyapunov Functions

    Publication Year: 2007 , Page(s): 2341 - 2345
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (376 KB) |  | HTML iconHTML  

    We consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in Kothare (Automatica, vol. 30, no. 12, pp. 1869-1883, 1994) applicable to linear time-invariant systems (LTI) subject to a saturating actuator. Our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory Johansson and Rantzer (IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998), Rantzer and Johansson (IEEE Trans. Autom. Control, vol. 45, no. 4, pp. 629-637, Apr. 2000), and Johansson (Proc. 14th World Congr., Beijing, China, 1999, pp. 521-5260) to determine a stabilizing antiwindup control law. The synthesis problem is expressed in terms of bilinear matrix inequalities (BMIs) and is solved using an iterative approach as well as using commercial software. The performance of the system is optimized by minimizing an upper bound on the induced gain of the system. The proposed approach is demonstrated using examples. View full abstract»

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  • Generalized Algebraic Deadlock Avoidance Policies for Sequential Resource Allocation Systems

    Publication Year: 2007 , Page(s): 2345 - 2350
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (327 KB) |  | HTML iconHTML  

    Currently, one of the most actively researched approaches regarding the design of deadlock avoidance policies for sequential resource allocation systems is based on concepts and techniques provided by the, so called, theory of regions, that addresses the broader problem of synthesizing PN models with prespecified behaviors. However, one limitation of the theory of regions and its aforementioned derivatives is that they cannot be applied when the target behavior has a nonconvex representation in the underlying state space. In this note, we show how this problem can be circumvented by appropriately generalizing the employed class of the candidate policies. View full abstract»

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  • Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation

    Publication Year: 2007 , Page(s): 2351 - 2355
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (290 KB) |  | HTML iconHTML  

    In this note, we establish a set of conditions under which an ellipsoid is contractively invariant with respect to a singular linear system under a saturated linear feedback. These conditions can be expressed in terms of linear matrix inequalities, and the largest contractively invariant ellipsoid can be determined by solving an optimization problem with LMI constraints. With the feedback gain viewed as an additional variable, this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid. Moreover, in the degenerate case where the singular linear system reduces to a regular system, our set invariance conditions reduce to the existing set invariance conditions for normal linear systems. View full abstract»

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  • Detectability of Discrete Event Systems

    Publication Year: 2007 , Page(s): 2356 - 2359
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (658 KB) |  | HTML iconHTML  

    In this note, we investigate the detectability problem in discrete event systems. We assume that we do not know initially which state the system is in. The problem is to determine the current and subsequent states of the system based on a sequence of observations. The observation includes partial event observation and/or partial state observation, which leads to four possible cases. We further define four types of detectabilities: strong detectability, (weak) detectability, strong periodic detectability, and (weak) periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observations. The theory developed in this note can be used in feedback control and diagnosis. If the system is detectable, then the observer can be used as a diagnoser to diagnose the failure states of the system. View full abstract»

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  • Adaptive Dynamic Surface Control for Stabilization of Parametric Strict-Feedback Nonlinear Systems With Unknown Time Delays

    Publication Year: 2007 , Page(s): 2360 - 2365
    Cited by:  Papers (50)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (252 KB) |  | HTML iconHTML  

    The robust stabilization method via the dynamic surface control (DSC) is proposed for uncertain nonlinear systems with unknown time delays in parametric strict-feedback form. That is, the DSC technique is extended to state time delay nonlinear systems with linear parametric uncertainties. The proposed control system can overcome not only the problem of ldquoexplosion of complexityrdquo inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate Lyapunov-Krasovskii functionals. In addition, we prove that all the signals in the closed-loop system are semiglobally uniformly bounded. Finally, an example is provided to illustrate the effectiveness of the proposed control system. View full abstract»

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  • Robust Nonlinear Observer for Lipschitz Nonlinear Systems Subject to Disturbances

    Publication Year: 2007 , Page(s): 2365 - 2369
    Cited by:  Papers (26)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (185 KB) |  | HTML iconHTML  

    This note proposes a robust nonlinear observer for systems with Lipschitz nonlinearity. The proposed nonlinear observer, whose linear part adopts the linear LTR observer design technique, has two important advantages over previous designs. First, the new observer does not impose the small-Lipschitz-constant condition on the system nonlinearity, nor other structural conditions on the system dynamics as in the existing observer designs. Second, it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances. View full abstract»

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  • Parameterization of Suboptimal Solutions of the Nehari Problem for Infinite-Dimensional Systems

    Publication Year: 2007 , Page(s): 2369 - 2374
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (467 KB) |  | HTML iconHTML  

    The Nehari problem plays an important role in Hinfin control theory. It is well known that Hinfin control problem can be reduced to solving this problem. This note gives a parameterization of all suboptimal solutions of the Nehari problem for a class of infinite-dimensional systems. Many earlier solutions of this problem are seen to be special cases of this new parameterization. It is also shown that for finite impulse response systems this parameterization takes a particularly simple form. View full abstract»

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  • Attitude Tracking With Adaptive Rejection of Rate Gyro Disturbances

    Publication Year: 2007 , Page(s): 2374 - 2379
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1156 KB) |  | HTML iconHTML  

    The classical attitude control problem for a rigid body is revisited under the assumption that measurements of the angular rates obtained by means of rate gyros are corrupted by harmonic disturbances, a setup of importance in several aerospace applications. This note extends previous methods developed to compensate bias in angular rate measurements by accounting for a more general class of disturbances, and by allowing uncertainty in the inertial parameters. By resorting to adaptive observers designed on the basis of the internal model principle, it is shown how converging estimates of the angular velocity can be used effectively in a passivity-based controller yielding global convergence within the chosen parametrization of the group of rotations. Since a persistence of excitation condition is not required for the convergence of the state estimates, only an upper bound on the number of distinct harmonic components of the disturbance is needed for the applicability of the method. View full abstract»

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  • Condition Numbers of the Generalized Sylvester Equation

    Publication Year: 2007 , Page(s): 2380 - 2385
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB) |  | HTML iconHTML  

    This note is devoted to the perturbation analysis for the generalized Sylvester equations (AX-YB, DX-YE)= (C, F), which have some important applications in control and system theory. Expressions and upper bounds for normwise, mixed, and componentwise condition numbers are presented. The results are illustrated by numerical examples. View full abstract»

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  • Optimal Fractional Controllers for Rational Order Systems: A Special Case of the Wiener-Hopf Spectral Factorization Method

    Publication Year: 2007 , Page(s): 2385 - 2389
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    In this note, the authors propose a generalization of the well known Wiener-Hopf design method of optimal controllers and filters, applicable to a certain class of systems described by fractional order differential equations, the so called rational order systems that, in the Laplace domain, are described by transfer functions which are quotients of polynomials in salpha, alpha = (1 /q), q being a positive integer. As can be verified in the literature, such transfer functions arise in the characterization of some industrial processes and physical systems which can be adequately modeled using fractional calculus, or when modeling some distributed parameter systems by finite dimensional models. A brief exposition of the standard Wiener-Hopf method, and some fundamental considerations about rational order systems are given before presenting the proposed procedure. Illustrative examples are discussed. 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

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame