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Automatic Control, IEEE Transactions on

Issue 5 • Date May 2006

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Displaying Results 1 - 25 of 37
  • Table of contents

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

    Page(s): c2
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  • Scanning the issue

    Page(s): 725
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  • Optimal control of continuous-time switched affine systems

    Page(s): 726 - 741
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (856 KB) |  | HTML iconHTML  

    This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law. View full abstract»

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  • The scenario approach to robust control design

    Page(s): 742 - 753
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    This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense. View full abstract»

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  • Control of nondeterministic discrete-event systems for bisimulation equivalence

    Page(s): 754 - 765
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (656 KB) |  | HTML iconHTML  

    Most prior work on supervisory control of discrete event systems is for achieving deterministic specifications, expressed as formal languages. In this paper we study supervisory control for achieving nondeterministic specifications. Such specifications are useful when designing a system at a higher level of abstraction so that lower level details of system and its specification are omitted to obtain higher level models that may be nondeterministic. Nondeterministic specifications are also meaningful when the system to be controlled has a nondeterministic model due to the lack of information (caused for example by partial observation or unmodeled dynamics). Language equivalence is not an adequate notion of behavioral equivalence for nondeterministic systems, and instead we use the finest known notion of equivalence, namely the bisimulation equivalence. Choice of bisimulation equivalence is also supported by the fact that bisimulation equivalence specification is equivalent to a specification in the temporal logic of μ-calculus that subsumes the complete branching-time logic CTL*. Given nondeterministic models of system and its specification, we study the design of a supervisor (possibly nondeterministic) such that the controlled system is bisimilar to the specification. We obtain a small model theorem showing that a supervisor exists if and only if it exists over a certain finite state space, namely the power set of Cartesian product of system and specification state spaces. Also, the notion of state-controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor. In the special case of deterministic systems, we provide an existence condition that can be verified polynomially in both system and specification states, when the existence condition holds. View full abstract»

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  • Utility maximization for communication networks with multipath routing

    Page(s): 766 - 781
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (672 KB) |  | HTML iconHTML  

    In this paper, we study utility maximization problems for communication networks where each user (or class) can have multiple alternative paths through the network. This type of multi-path utility maximization problems appear naturally in several resource allocation problems in communication networks, such as the multi-path flow control problem, the optimal quality-of-service (QoS) routing problem, and the optimal network pricing problem. We develop a distributed solution to this problem that is amenable to online implementation. We analyze the convergence of our algorithm in both continuous-time and discrete-time, and with and without measurement noise. These analyses provide us with guidelines on how to choose the parameters of the algorithm to ensure efficient network control. View full abstract»

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  • Nonblocking supervisory control of state tree structures

    Page(s): 782 - 793
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (648 KB) |  | HTML iconHTML  

    It is well known that the nonblocking supervisory control problem is NP-hard, subject in particular to state space explosion that is exponential in the number of system components. In this paper we propose to manage complexity by organizing the system as a state tree structure (STS). STS are an adaptation of statecharts to supervisory control theory. Based on STS we present an efficient recursive symbolic algorithm that can perform nonblocking supervisory control design (in reasonable time and memory) for systems of state size 1024 and higher. The resulting controllers are tractable and readily comprehensible. View full abstract»

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  • On the supervisory control of multiagent product systems

    Page(s): 794 - 799
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB) |  | HTML iconHTML  

    In this note, we use the formal framework of multiagent (MA) product systems (introduced and developed in previous works) for the analysis of complex systems. The results of this note constitute a natural extension of the classical supervisory control results for scalar systems to the more general MA product system case. The notion of MA controllability is introduced and is shown to essentially constitute a necessary and sufficient condition for the synthesis of an MA supervisor. View full abstract»

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  • On minimal representations of Petri net languages

    Page(s): 799 - 804
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    Given a measure of size of a labeled Petri net, we consider the existence of a procedure that takes as input a description of an arbitrary, labeled Petri net, and returns a description of a (possibly different) labeled Petri net with the smallest size that generates the same language as the input. We refer to such procedures as minimization procedures. In this note, we investigate the existence of minimization procedures for a variety of measures. We show that these procedures cannot exist for Petri net languages for a large class of measures. However, for families of Petri net languages where controllability (cf. ), and consequently language-containment, is decidable , there can be minimization procedures for a restricted class of measures. After showing that minimization procedures for a family of measures are intractable for languages generated by bounded Petri nets, it is argued that a similar conclusion has to be reached for any family of Petri net languages that includes the family of regular languages for which there are minimization procedures. View full abstract»

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  • Solution to the second-order Sylvester matrix equation MVF2+DVF+KV=BW

    Page(s): 805 - 809
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB) |  | HTML iconHTML  

    This note provides a complete general parametric solution (V,W) to the generalized second-order Sylvester matrix equation MVF2+DVF+KV=BW, with F being an arbitrary square matrix. The primary feature of this solution is that the matrix F does not need to be in any canonical form, or may be even unknown a priori. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems involving second-order dynamical systems. View full abstract»

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  • A unified setting for decoupling with preview and fixed-lag smoothing in the geometric context

    Page(s): 809 - 813
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (240 KB) |  | HTML iconHTML  

    Exact decoupling with preview, perfect tracking of previewed references, unknown-input state observation with fixed lag, and left inversion with fixed lag are considered from a unifying perspective where exact decoupling with preview is the basic problem. Necessary and sufficient constructive conditions for decoupling with finite preview are proved in the geometric framework. Structural and stabilizability conditions are considered separately and the use of self-bounded controlled invariant subspaces allows the dynamic compensator with the minimal unassignable dynamics to be straightforwardly derived. A steering along zeros technique is devised to guarantee decoupling with stability also in the presence of unstable unassignable dynamics of the minimal self-bounded controlled invariant. View full abstract»

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  • Applying discrete-time proportional Integral observers for state and disturbance estimations

    Page(s): 814 - 818
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB) |  | HTML iconHTML  

    In this note, we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete-time nonminimum phase systems. Conditions for providing the existence of such observer are given. When the disturbances do not vary too much between two consecutive sampling instances, the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region. Simulation results support the theoretical developments. View full abstract»

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  • Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation

    Page(s): 818 - 823
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    This note considers the generalized quadratic stability problem for continuous-time singular system with nonlinear perturbation. The perturbation is a function of time and system state and satisfies a Lipschitz constraint. In this work, a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented. Then by using S-procedure and matrix inequality approach, a necessary and sufficient condition is presented in terms of linear matrix inequality, under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system. That is, the system remains exponential stable and the nominal system is regular and impulse free. Furthermore, robust stability for nonsingular systems with perturbation can be obtained as a special case. Finally, the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples. View full abstract»

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  • Optimal estimation for continuous-time systems with delayed measurements

    Page(s): 823 - 827
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (544 KB) |  | HTML iconHTML  

    This note focuses on the traditional problem of the Kalman filtering for linear continuous-time systems. Although the problem has been studied widely in the past decades, little work has been done for the time-delayed systems and some fundamental problems remain to be solved. This note proposes a new tool, namely, reorganization innovation analysis approach , to investigate the filtering problem for systems with delayed measurements. The Kalman filter is given in terms of the solution of standard Riccati equations. The performance is clearly demonstrated through analytical results and simulation. The solved problem in this note is related with some more complicated problems such as H fixed-lag smoothing, H control with preview and control with input delays. View full abstract»

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  • C*-algebra of strong limit power functions

    Page(s): 828 - 831
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB) |  | HTML iconHTML  

    Motivated by problems in robust control of power signal set H2 (e.g,, H2 is not a vector space, Fourier analysis cannot be carried out on H2 in general), we study those functions in H2 which we call strong limit power. We show that the set of all such functions is a sufficiently large C*-algebra. Fourier Analysis is carried out on the functions. In particular, the uniqueness of the Fourier expansion of a strong limit power function is established. Finally we point out how to analyze and reconstruct such functions. View full abstract»

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  • On the stability of constrained MPC without terminal constraint

    Page(s): 832 - 836
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB) |  | HTML iconHTML  

    The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented. View full abstract»

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  • Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems

    Page(s): 836 - 841
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (248 KB) |  | HTML iconHTML  

    This note deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the derived results. View full abstract»

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  • On some norms for descriptor systems

    Page(s): 842 - 847
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB) |  | HTML iconHTML  

    We present generalizations of the impulse and frequency responses as well as convolution and Hankel operators for continuous-time and discrete-time descriptor systems. Some norms for descriptor systems are introduced and their representations via the different linear system concepts are considered. View full abstract»

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  • A noncooperative game approach to OSNR optimization in optical networks

    Page(s): 848 - 852
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (208 KB) |  | HTML iconHTML  

    We consider a game theory framework for power control in optical networks. Channel optical signal-to-noise ratio (OSNR) optimization is formulated as an m-player noncooperative game, based on a general network OSNR model. Conditions for existence and uniqueness of the game equilibrium solution are given. An iterative algorithm for power control is proposed, that uses only channel specific feedback measurements and is shown to converge to the equilibrium solution. View full abstract»

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  • Analysis and design of integral sliding manifolds for systems with unmatched perturbations

    Page(s): 853 - 858
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (232 KB) |  | HTML iconHTML  

    The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination. View full abstract»

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  • Adaptive finite-time control of nonlinear systems with parametric uncertainty

    Page(s): 858 - 862
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (224 KB) |  | HTML iconHTML  

    In this note, global finite time stabilization is investigated for a class of nonlinear systems in p normal form with parametric uncertainties. To achieve finite-time stabilization, a constructive control design approach is proposed by following backstepping methodology, and an adaptive finite-time control law is obtained in the form of continuous time-invariant feedback. View full abstract»

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  • Circuit allocation in all optical networks with average packet delay cost criterion

    Page(s): 862 - 867
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    An optimal circuit allocation problem for all-optical circuit-switched backbone networks with average packet delay cost criterion is considered. Multiple classes of traffic flows arrive at the network edge routers, where they can be queued until an end-to-end optical circuit can be allocated. Assuming fluid traffic and circuit allocation of fixed periods, a lower bound on the optimal average packet delay is derived and the cost of two allocation policies are evaluated exactly. The cost of both policies are demonstrated for a variety of deterministic and random networks and are compared with the lower bound. View full abstract»

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  • Design of ℓ1-optimal controllers with flexible disturbance rejection level

    Page(s): 868 - 873
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (312 KB) |  | HTML iconHTML  

    This note presents a new design methodology that allows for flexible management of the tradeoff between the ability of a system to attenuate disturbance signals versus its expected worst peak-to-peak amplification. The proposed strategy applies to linear time-invariant systems which are subject to persistent disturbance signals and combines a recently developed quasi-robust linear programming concept with a well-known ℓ1-optimal controller synthesis approach. The benefit of the resulting technique is demonstrated using an example. View full abstract»

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  • Asymptotic tracking for constrained monotone systems

    Page(s): 873 - 879
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB)  

    This note addresses tracking control of nonlinear discrete-time monotone systems subject to input and state constraints. Forcing saturation on a previously designed controller may, in general, lead to destabilization or, at least, result in constraint violation and performance losses. Hereby, it is shown that for a certain class of nonlinear monotone systems it is possible to design a static nonlinear output feedback which, saturated among suitable state-dependent bounds, is able to guarantee constraint satisfaction and asymptotic tracking of piecewise constant references, with a moderate online computational burden. Simulation experiments concerning the synthesis of a protein demonstrate the effectiveness of the proposed control strategy. 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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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame