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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug. 2006

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Displaying Results 1 - 25 of 31
  • 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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  • Impulse Control: Boolean Programming and Numerical Algorithms

    Publication Year: 2006 , Page(s): 1229
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  • Impulse control: Boolean programming and numerical algorithms

    Publication Year: 2006 , Page(s): 1230 - 1248
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (649 KB) |  | HTML iconHTML  

    A numerical algorithmic approach to the impulse control problem is considered. Impulse controls are modelled by Boolean binary variables. The impulse Gateaux derivatives for impulse times, impulse volumes and Boolean variables are derived, and these are applied to the numerical algorithms. These algorithms require significantly less computation time and memory storage than the quasi-variational inequalities by Bensoussan-Lions. By using our algorithms, complicated models of hybrid or constrained systems can be more easily treated numerically than by using Pontryagin's Minimum Principle. Numerical experiments are performed for models on capacity expansion in a manufacturing plant, and on impulse control of Verhulst systems and Lotka-Volterra systems; the results confirm the effectiveness of the proposed method View full abstract»

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  • Relaxing dynamic programming

    Publication Year: 2006 , Page(s): 1249 - 1260
    Cited by:  Papers (47)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (674 KB) |  | HTML iconHTML  

    The idea of dynamic programming is general and very simple, but the "curse of dimensionality" is often prohibitive and restricts the fields of application. This paper introduces a method to reduce the complexity by relaxing the demand for optimality. The distance from optimality is kept within prespecified bounds and the size of the bounds determines the computational complexity. Several computational examples are considered. The first is optimal switching between linear systems, with application to design of a dc/dc voltage converter. The second is optimal control of a linear system with piecewise linear cost with application to stock order control. Finally, the method is applied to a partially observable Markov decision problem (POMDP) View full abstract»

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  • Towards a multiresolution approach to linear control

    Publication Year: 2006 , Page(s): 1261 - 1270
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (454 KB) |  | HTML iconHTML  

    We develop a multiresolution approximation framework for linear control. We construct a multiresolution analysis of the set of input functions of a linear system. The approximation of an input u at a scale j is defined as the input uj of minimal energy such that the trajectories of the system associated with u and uj coincide on a grid of step length 2-j. We propose a set of wavelet functions which generate this multiresolution analysis. These functions, called control theoretic wavelets, satisfy useful properties for the representation of control inputs of a linear system. As an example of application of our multiresolution approximation framework, we propose a method for efficient encoding of control inputs with regard to several criteria View full abstract»

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  • Stability of linear systems with interval time delays excluding zero

    Publication Year: 2006 , Page(s): 1271 - 1288
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (667 KB) |  | HTML iconHTML  

    The stability of linear systems with multiple, time-invariant, independent and uncertain delays is investigated. Each delay is assumed to reside within a known interval excluding zero. A delay-free sufficient comparison system is formed by replacing the delay elements with parameter-dependent filters, satisfying certain properties. It is shown that robust stability of this finite dimensional parameter-dependent comparison system, guarantees stability of the original time-delay system. This result is novel in the sense that it does not require any a priori knowledge regarding stability of the time-delay system for some fixed delay. When the parameter-dependent filters are formed in a particular manner using Pade approximations, an upper bound on the degree-of-conservatism of the comparison system may be obtained, which is independent of the time-delay system considered. With this, it is shown that the conservatism of this comparison system may be made arbitrarily small. A linear matrix ineqaulity (LMI) formulation is presented for analysis of the stability of the parameter-dependent comparison system. In the single-delay case, an eigenvalue criterion is also available for stability analysis which incurs no additional conservatism View full abstract»

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  • Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions

    Publication Year: 2006 , Page(s): 1289 - 1298
    Cited by:  Papers (200)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (698 KB) |  | HTML iconHTML  

    This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arbitrary dimensions under weak requirements on the switching and failing communication topology. The novel correctness proof relies on proximity graphs and their properties and on a general LaSalle invariance principle for nondeterministic discrete-time dynamical systems View full abstract»

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  • Asymptotic variance of closed-loop subspace identification methods

    Publication Year: 2006 , Page(s): 1299 - 1314
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (629 KB) |  | HTML iconHTML  

    In this paper, the asymptotic properties of a version of the "innovation estimation" algorithm by Qin and Ljung as well as of a version of the "whitening filter" based algorithm introduced by Jansson are studied. Expressions for the asymptotic error as the sum of a "bias" term plus a "variance" term are given. The analysis is performed under rather mild assumptions on the spectrum of the joint input-output process; however, in order to avoid unnecessary complications, the asymptotic variance formulas are computed explicitly only for finite memory systems, i.e., of the ARX type. This assumption could be removed at the price of some technical complications; the simulation results confirm that when the past horizon is large enough (as compared to the predictor dynamics) the asymptotic expressions provide a good approximation of the asymptotic variance also for ARMAX systems View full abstract»

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  • Information flow and its relation to stability of the motion of vehicles in a rigid formation

    Publication Year: 2006 , Page(s): 1315 - 1319
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB) |  | HTML iconHTML  

    In this note, we consider the effect of information flow on the propagation of errors in spacing in a collection of vehicles trying to maintain a rigid formation during translational maneuvers. The motion of each vehicle is described using a linear time-invariant (LTI) system. We consider undirected and connected information flow graphs, and assume that each vehicle can communicate with a maximum of q vehicles, where q may vary with the size n of the collection. We consider translational maneuver of a reference vehicle, where its steady state velocity is different from its initial velocity. In the absence of any disturbing forces acting on the vehicles during the maneuver, it is desired that the collection be controlled in such a way that its motion asymptotically resembles that of a rigid body. In the presence of bounded disturbing forces acting on the vehicles, it is desired that the maximum deviation of the motion of the collection from that of a rigid body be bounded and be independent of the size of the collection. We consider a decentralized feedback control scheme, where the controller of each vehicle takes into account the aggregate errors in position and velocity from the vehicles with which it is in direct communication. We assume that all vehicles start at their respective desired positions and velocities. Since the displacement of every vehicle at the end of the maneuver of the reference vehicle must be the same, we show that the loop transfer function must have at least two poles at the origin. We then show that if the loop transfer function has three or more poles at the origin, then the motion of the collection is unstable, that is, its deviation from the rigid body motion is arbitrarily large, if the size of the formation is sufficiently large. If l is the number of poles of the transfer function relating the position of a vehicle with its control input, we show that if (q(n)/n)rarr0 as nrarrinfin, then there is a low frequency sinusoidal disturbance- - of at most unit amplitude acting on each vehicle such that the maximum errors in spacing response increase at least as Omega(((radicn/q(n))l+1)).A function p(n) is Omega(q(n)) if there exists a nonzero constant c>0 and a N* such that |p(n)|gesc|q(n)| for all n>N* . A consequence of the results presented in this note is that the maximum errors in spacing and velocity of any vehicle can be made insensitive to the size of the collection only if there is at least one vehicle in the collection that communicates with at least Omega(n) other vehicles in the collection View full abstract»

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  • On performance limitation in tracking a sinusoid

    Publication Year: 2006 , Page(s): 1320 - 1325
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (249 KB) |  | HTML iconHTML  

    This note studies the performance limitation of a feedback system with a given linear time-invariant (LTI) plant in tracking a sinusoidal signal. It continues and goes beyond some recent studies in the same topic in which it is assumed that the controller can access all the past and future values of the reference signal. In this note, we consider the more realistic (and more difficult) situation where the controller only accesses the current and past values of the reference. An explicit formula of the best attainable performance is obtained for a single-input-single-output (SISO) system which depends on the nonminimum phase zeros of the plant and the frequency of the reference sinusoid. Compared to the previously studied case when the future of the reference is available, this formula clearly shows the extra effort one has to pay due to the lack of the reference information. A partial result for a multiple-input-multiple-output (MIMO) system is also given View full abstract»

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  • Analysis of a second-order sliding-mode algorithm in presence of input delays

    Publication Year: 2006 , Page(s): 1325 - 1332
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (371 KB) |  | HTML iconHTML  

    In this note, a double integrator system under the action of a second-order sliding-mode control algorithm is considered, and the resulting closed-loop behavior in presence of an input delay is analysed. Due to the delay, in the limit the system trajectories are periodic. Whenever the control modulus is chosen to be constant, the amplitude and period of the resulting oscillations are fixed for any initial value. If the control behaves asymmetrically, it is shown that this is no more true, since the overall dynamical system can admit diverse limit cycles View full abstract»

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  • Optimality of first-order ILC among higher order ILC

    Publication Year: 2006 , Page(s): 1332 - 1336
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (231 KB) |  | HTML iconHTML  

    Higher order iterative learning control (HO-ILC) algorithms use past system control information from more than one past iterative cycle. This class of ILC algorithms have been proposed aiming at improving the learning efficiency and performance. This paper addresses the optimality of HO-ILC in the sense of minimizing the trace of the control error covariance matrix in the presence of a class of uncorrelated random disturbances. It is shown that the optimal weighting matrices corresponding to the control information associated with more than one cycle preceding the current cycle are zero. That is, an optimal HO-ILC does not add to the optimality of standard first-order ILC in the sense of minimizing the trace of the control error covariance matrix. The system under consideration is a linear discrete-time varying systems with different relative degree between the input and each output View full abstract»

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  • State estimation in stochastic hybrid Systems with sparse observations

    Publication Year: 2006 , Page(s): 1337 - 1342
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (377 KB) |  | HTML iconHTML  

    In this note we study the problem of state estimation for a class of sampled-measurement stochastic hybrid systems, where the continuous state x satisfies a linear stochastic differential equation, and noisy measurements y are taken at assigned discrete-time instants. The parameters of both the state and measurement equation depend on the discrete state q of a continuous-time finite Markov chain. Even in the fault detection setting we consider-at most one transition for q is admissible-the switch may occur between two observations, whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable, so that the known estimation techniques cannot be applied. We derive and implement an algorithm for the estimation of the states x, q and of the discrete-state switching time that is convenient for both recursive update and the eventual numerical quadrature. Numerical simulations are illustrated View full abstract»

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  • H/sub /spl infin// design with first-order controllers

    Publication Year: 2006 , Page(s): 1343 - 1347
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (453 KB) |  | HTML iconHTML  

    The problem of determining all first order controllers (C(s)=(x 1s+x2/s+x3)) which stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) plant of arbitrary order has been recently solved. In this note, these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific Hinfin norm constraints. The problem is solved by converting the Hinfin problem into the simultaneous stabilization of the closed-loop characteristic polynomial and a family of related complex polynomials. The stability boundary of each of these polynomials can be computed explicitly for fixed x3 by solving linear equations. The union of the resulting stability regions yields the set of all x1 and x2 which simultaneously satisfy the Hinfin condition and closed-loop stability for a fixed x3. The entire three-dimensional set meeting specifications is obtained by sweeping x3 over the stabilizing range View full abstract»

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  • On H/sub 2/ control of systems with multiple I/O delays

    Publication Year: 2006 , Page(s): 1347 - 1354
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (504 KB) |  | HTML iconHTML  

    The H2 optimal control problem of systems with multiple I/O delays is solved. The problem is tackled by first transforming it to what is called the two-sided regulator problem. The latter is solved using orthogonal projection arguments and spectral factorization. The resulting controller is an interconnection of rational blocks, nonrational blocks having finite impulse response, and delay operators, all of which are implementable View full abstract»

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  • Robust Kalman filter for descriptor systems

    Publication Year: 2006 , Page(s): 1354
    Cited by:  Papers (25)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (257 KB) |  | HTML iconHTML  

    This note is concerned with the problem of state estimation for descriptor systems subject to uncertainties. A Kalman type recursive algorithm is derived. Numerical examples are included to demonstrate the performance of the proposed robust filter View full abstract»

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  • Stabilization of a chain of integrators with an unknown delay in the input by adaptive output feedback

    Publication Year: 2006 , Page(s): 1359 - 1363
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (290 KB) |  | HTML iconHTML  

    In this note, we consider a stabilization problem of a chain of integrators with an unknown delay in the input. We propose an adaptive output feedback control scheme in which the delay-related low-gain parameter is tuned online by utilizing the integral value of the input norm-bound. Thus, a priori knowledge on the delay is not required for controller design View full abstract»

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  • Stability analysis and stabilization of systems presenting nested saturations

    Publication Year: 2006 , Page(s): 1364 - 1371
    Cited by:  Papers (27)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (374 KB)  

    This note addresses the problems of stability analysis and stabilization of systems presenting nested saturations. Depending on the open-loop stability assumption, the global stability analysis and stabilization problems are considered. In the (local) analysis problem, the objective is the determination of estimates of the basin of attraction of the system. Considering the stabilization problem, the goal is to design a set of gains in order to enlarge the basin of attraction of the closed-loop system. Based on the modelling of the system presenting nested saturations as a linear system with dead-zone nested nonlinearities and the use of a generalized sector condition, linear matrix inequality (LMI) stability conditions are formulated. From these conditions, convex optimization strategies are proposed to solve both problems View full abstract»

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  • A numerical analysis of the Nash strategy for weakly coupled large-scale systems

    Publication Year: 2006 , Page(s): 1371 - 1377
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (316 KB) |  | HTML iconHTML  

    This note discusses the feedback Nash equilibrium of linear quadratic N-player Nash games for infinite-horizon large-scale interconnected systems. The asymptotic structure along with the uniqueness and positive semidefiniteness of the solutions of the cross-coupled algebraic Riccati equations (CAREs) is newly established via the Newton-Kantorovich theorem. The main contribution of this study is the proposal of a new algorithm for solving the CAREs. In order to improve the convergence rate of the algorithm, Newton's method is combined with a new decoupling algorithm; it is shown that the proposed algorithm attains quadratic convergence. Moreover, it is shown for the first time that solutions to the CAREs can be obtained by solving the independent algebraic Lyapunov equation (ALE) by using the reduced-order calculation View full abstract»

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  • On overshoot and nonminimum phase zeros

    Publication Year: 2006 , Page(s): 1378 - 1382
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB) |  | HTML iconHTML  

    It is widely known that real nonminimum phase zeros lead to step response undershoot, and that the size of the undershoot necessarily tends to infinity as the settling time tends to zero. In this note, we show that the presence of two or more real nonminimum phase zeros can lead to step response overshoot in addition to undershoot. A lower bound on the overshoot is derived, and it is shown that the overshoot, like the undershoot, necessarily tends to infinity as the settling time tends to zero. The results are derived for single-input-single-output linear time-invariant continuous-time systems, and apply to both open-loop control and general two degree-of-freedom closed-loop control View full abstract»

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  • Stochastic stability of Ito differential equations with semi-Markovian jump parameters

    Publication Year: 2006 , Page(s): 1383 - 1387
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (225 KB) |  | HTML iconHTML  

    In this note, the problem of stochastic stability for linear systems with jump parameters being semi-Markovian rather than full Markovian is further investigated. In particular, the system under consideration is described by Ito type nonlinear stochastic differential equations with phase type semi-Markovian jump parameters. Stochastic stability conditions are presented View full abstract»

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  • On the observability of linear differential-algebraic systems with delays

    Publication Year: 2006 , Page(s): 1387 - 1392
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    The problem of Ropfn-observability is considered for the simplest linear time- delay differential-algebraic system consisting of differential and difference equations. A determining equation system is introduced and a number of algebraic properties of the determining equation solutions is established, in particular, the well-known Hamilton-Cayley matrix theorem is generalized to the solutions of determining equation. As a result, an effective parametric rank criterion for the Ropfn-observability is given. A dual controllability result is also formulated View full abstract»

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  • Stability of TCP/RED systems in AQM routers

    Publication Year: 2006 , Page(s): 1393 - 1398
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (681 KB) |  | HTML iconHTML  

    By applying the time-delay control theory to a TCP/RED dynamic model, this note establishes some explicit conditions under which the TCP/RED system is stable in terms of the average queue length. Then, the stability region is discussed. Finally, the results are illustrated by using ns2 simulations, which demonstrates that it is able to choose an appropriate control parameter maxp of RED based on the stability conditions derived in this note, to achieve satisfactory network performance. It is found, by comparison, that this improved performance is better than that of three other typical active queue management (AQM) schemes-the random exponential marking (REM), proportional-integral (PI) controller, and adaptive virtual queue (AVQ) schemes View full abstract»

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  • Robust explicit MPC based on approximate multiparametric convex programming

    Publication Year: 2006 , Page(s): 1399 - 1403
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (418 KB)  

    Many robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set 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