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Automatic Control, IEEE Transactions on

Issue 9 • Date Sept. 2012

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Displaying Results 1 - 25 of 36
  • 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): 2161 - 2162
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  • Dead-Beat Control in the Behavioral Approach

    Page(s): 2163 - 2175
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (429 KB) |  | HTML iconHTML  

    In this paper, the concepts of controllability and zero-controllability of a variable w , appearing either in a standard or in a latent variable description (as manifest variable), are introduced and characterized. By assuming this perspective, the dead-beat control (DBC) problem is posed as the problem of designing a controller, involving both w and the latent variable c, such that, for the resulting controlled behavior, the variable w goes to zero in a finite number of steps in every trajectory. Zero-controllability of w turns out to be a necessary and sufficient condition for the existence of “admissible” DBCs as well as for the existence of regular DBCs. The class of minimal DBCs, namely DBCs with the least possible number of rows, is singled-out and a parametrization of such controllers is provided. Finally, a necessary and sufficient condition for the existence of DBCs that can be implemented via a feedback law, for which w is the input and the latent variable c the corresponding output, is provided. View full abstract»

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  • Feedback Stabilization of Discrete-Time Networked Systems Over Fading Channels

    Page(s): 2176 - 2189
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3749 KB) |  | HTML iconHTML  

    This paper addresses the mean square stabilization problem for discrete-time networked control systems over fading channels. We show that there exists a requirement on the network over which an unstable plant can be stabilized. In the case of state feedback, necessary and sufficient conditions on the network for mean square stabilizability are derived. Under a parallel transmission strategy and the assumption that the overall mean square capacity of the network is fixed and can be assigned among parallel input channels, a tight lower bound on the overall mean square capacity for mean square stabilizability is presented in terms of the Mahler measure of the plant. The minimal overall capacity for stabilizability is also provided under a serial transmission strategy. For the case of dynamic output feedback, a tight lower bound on the capacity requirement for stabilization of SISO plants is given in terms of the anti-stable poles, nonminimum phase zeros and relative degree of the plant. Sufficient and necessary conditions are further derived for triangularly decoupled MIMO plants. The effect of pre- and post-channel processing and channel feedback is also discussed, where the channel feedback is identified as a key component in eliminating the limitation on stabilization induced by the nonminimum phase zeros and high relative degree of the plant. Finally, the extension to the case with output fading channels and the application of the results to vehicle platooning are presented. View full abstract»

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  • Modelling and Estimation for Finite State Reciprocal Processes

    Page(s): 2190 - 2202
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3063 KB) |  | HTML iconHTML  

    A reciprocal equation is a kind of descriptor linear discrete-index stochastic system which is well known be satisfied (pathwise) by all Gaussian reciprocal processes. From a system-theoretic point of view, it is a kind of `noncausal' linear system, in the sense that the solution of it cannot be determined by only an `initial' condition, indeed requiring the `terminal' state as well, besides all the `input' function between initial and terminal states. Also, nice properties are known of a reciprocal equation, such as the equivalence of it with a couple of ordinary (causal) dynamic systems running in opposite directions. For these reasons, here we assume a reciprocal equation as the target of stochastic realization for the class of finite state reciprocal processes, also named reciprocal chains. The central result of the present paper is showing that any canonical reciprocal chain, i.e. valued in the canonical base of REALRN , N being the cardinality of the set of chain's states, satisfies (pathwise) a reciprocal equation in a N2 dimensional canonical variable, or in other word a quadratic reciprocal equation, named `Augmented state reciprocal model' (ASRM). Also, for a partially observed reciprocal chain, a linear-optimal smoother is derived. All the results here presented are based upon the idea that a reciprocal chain is a `combination' of Markov bridges, to this purpose other forms, besides the ASRM, are presented in order to make clear the meaning of this `combination', as well as to prove that the linear smoother can be actually implemented as N smoothers all operating independently on each Markov bridge component. View full abstract»

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  • Optimal Control of Vehicular Formations With Nearest Neighbor Interactions

    Page(s): 2203 - 2218
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1129 KB) |  | HTML iconHTML  

    We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single- and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedback gain. This solution is used to initialize a homotopy-based Newton's method to find the optimal localized gain. To investigate the performance of localized controllers, we examine how the coherence of large-scale stochastically forced formations scales with the number of vehicles. We establish several explicit scaling relationships and show that the best performance is achieved by a localized controller that is both non-symmetric and spatially-varying. View full abstract»

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  • Gain-Scheduled Control Synthesis Using Dynamic D -Scales

    Page(s): 2219 - 2234
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5635 KB) |  | HTML iconHTML  

    For systems that are affected by a priori unknown but on-line measurable dynamic components (such as parameters, nonlinearities or delays), we propose a novel design algorithm for controllers that are on-line scheduled by these so-called structured uncertainties in order to achieve closed-loop stability and a certain desired level of performance. Both the plant and the controller are assumed to admit a description in terms of a linear time-invariant system in feedback with the uncertainties as is standard in robust control. In contrast to the existing results in the literature, dynamic (i.e., frequency-dependent) D -scales are used to guarantee robust stability (and performance) of the closed-loop system in the form of frequency-dependent inequalities. Based on these well-known analysis results, it is shown in this paper how to completely reduce the synthesis of gain-scheduled controllers with dynamic D-scalings to a system of linear matrix inequalities. We sketch various potential applications of our main result and illustrate the advantages of frequency dependence in the D-scales by a simple numerical example. View full abstract»

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  • Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

    Page(s): 2235 - 2249
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (722 KB) |  | HTML iconHTML  

    We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2, and higher dimensions, with vehicular platoons corresponding to the 1-D case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent 1-D vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways. View full abstract»

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  • Moderate Deviations of a Random Riccati Equation

    Page(s): 2250 - 2265
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (625 KB) |  | HTML iconHTML  

    The paper characterizes the invariant filtering measures resulting from Kalman filtering with intermittent observations in which the observation arrival is modeled as a Bernoulli process with packet arrival probability γ̅. Our prior work showed that, for γ̅ >; 0 , the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution μγ̅. This paper shows that, as γ̅ approaches one, the family {μγ̅}γ̅ >; 0 satisfies a moderate deviations principle with good rate function I (·): (1) as γ̅ ↑ 1 , the family {μγ̅} converges weakly to the Dirac measure δP* concentrated on the fixed point of the associated discrete time Riccati operator; (2) the probability of a rare event (an event bounded away from P*) under μγ̅ decays to zero as a power law of (1-γ̅) as γ̅↑ 1; and, (3) the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function I (·). For specific scenarios, the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under μγ̅. View full abstract»

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  • Mean Field for Markov Decision Processes: From Discrete to Continuous Optimization

    Page(s): 2266 - 2280
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (846 KB) |  | HTML iconHTML  

    We study the convergence of Markov decision processes, composed of a large number of objects, to optimization problems on ordinary differential equations. We show that the optimal reward of such a Markov decision process, which satisfies a Bellman equation, converges to the solution of a continuous Hamilton-Jacobi-Bellman (HJB) equation based on the mean field approximation of the Markov decision process. We give bounds on the difference of the rewards and an algorithm for deriving an approximating solution to the Markov decision process from a solution of the HJB equations. We illustrate the method on three examples pertaining, respectively, to investment strategies, population dynamics control and scheduling in queues. They are used to illustrate and justify the construction of the controlled ODE and to show the advantage of solving a continuous HJB equation rather than a large discrete Bellman equation. View full abstract»

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  • A Converse Sum of Squares Lyapunov Result With a Degree Bound

    Page(s): 2281 - 2293
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (623 KB) |  | HTML iconHTML  

    Although sum of squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems, several fundamental questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector field on a bounded set implies the existence of a Lyapunov function which is a sum of squares of polynomials. In particular, the main result states that if a system is exponentially stable on a bounded nonempty set, then there exists a sum of squares Lyapunov function which is exponentially decreasing on that bounded set. Furthermore, we derive a bound on the degree of this converse Lyapunov function as a function of the continuity and stability properties of the vector field. The proof is constructive and uses the Picard iteration. Our result implies that semidefinite programming can be used to answer the question of stability of a polynomial vector field with a bound on complexity. View full abstract»

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  • Signal Transformation Approach to Tracking Control With Arbitrary References

    Page(s): 2294 - 2307
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1455 KB) |  | HTML iconHTML  

    In this paper, we introduce a signal transformation (ST) methodology for tracking control of a large class of arbitrary references. The method can improve tracking performance of ordinary one-degree-of-freedom (1-DoF) feedback control structure, while keeping robustness against unmodeled dynamics and limiting the projected measurement noise by ensuring a low closed-loop bandwidth. Using singular perturbation theory, sufficient conditions for stability and convergence of the tracking error are derived. Effectiveness of the proposed method is demonstrated by simulations. It is shown how ST method can provide a better control performance compared to ordinary 2-DoF feedback control systems having similar projected noise power, and maintain robustness against uncertainties, disturbances, and unmodeled dynamics. View full abstract»

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  • Stochastic Source Seeking by Mobile Robots

    Page(s): 2308 - 2321
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4186 KB) |  | HTML iconHTML  

    We consider the problem of designing controllers to steer mobile robots to the source (the minimizer) of a signal field. In addition to the mobility constraints, e.g., posed by the nonholonomic dynamics, we assume that the field is completely unknown to the robot and the robot has no knowledge of its own position. Furthermore, the unknown field is randomly switching. In the case where the information of the field (e.g., the gradient) is completely known, standard motion planning techniques for mobile robots would converge to the known source. In the absence of mobility constraints, convergence to the minimum of unknown fields can be pursued using the framework of numerical optimization. By considering these facts, this paper exploits an idea of the stochastic approximation for solving the problem mentioned in the beginning and proposes a source seeking controller which sequentially generates the next waypoints such that the resulting discrete trajectory converges to the unknown source and which steers the robot along the waypoints, under the assumption that the robot can move to any point in the body fixed coordinate frame. To this end, we develop a rotation-invariant and forward-sided version of the simultaneous-perturbation stochastic approximation algorithm as a method to generate the next waypoints. Based on this algorithm, we design source seeking controllers. Furthermore, it is proven that the robot converges to a small set including the source in a probabilistic sense if the signal field switches periodically and sufficiently fast. The proposed controllers are demonstrated by numerical simulations. View full abstract»

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  • Explicit MPC for LPV Systems: Stability and Optimality

    Page(s): 2322 - 2332
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2502 KB) |  | HTML iconHTML  

    This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution. View full abstract»

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  • Deadbeat Observer: Construction via Sets

    Page(s): 2333 - 2337
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (217 KB) |  | HTML iconHTML  

    A geometric generalization of discrete-time linear deadbeat observer is presented. The proposed method to generate a deadbeat observer for a given nonlinear system is constructive and makes use of sets that can be computed iteratively. For demonstration, derivations of observer dynamics are provided for two example systems. Based on the method, a simple algorithm that computes the deadbeat gain for a linear system with scalar output is given. View full abstract»

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  • Power Allocation and Spectrum Sharing in Multi-User, Multi-Channel Systems With Strategic Users

    Page(s): 2338 - 2342
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (200 KB) |  | HTML iconHTML  

    We consider the decentralized power allocation and spectrum sharing problem in multi-user, multi-channel systems with strategic users. We present a mechanism/game form that has the following desirable features: 1) it is individually rational; 2) it is budget balanced at every Nash equilibrium of the game induced by the game form as well as off equilibrium; and 3) the allocation corresponding to every Nash equilibrium (NE) of the game induced by the mechanism is a Lindahl allocation, that is, a weakly Pareto optimal allocation; conversely, every Lindahl equilibrium results in a NE of the game induced by the game form. Our proposed game form/mechanism achieves all the above desirable properties without any assumption about, concavity, monotonicity, or quasi-linearity of the users' utility functions. View full abstract»

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  • Robust Stability of a Multi-Agent System Under Arbitrary and Time-Varying Communication Topologies and Communication Delays

    Page(s): 2343 - 2347
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (298 KB) |  | HTML iconHTML  

    This technical note considers formation control of a group of identical agents that can communicate with each other. A necessary and sufficient condition for robust stability in the case of arbitrary time-invariant communication topologies and sufficient conditions in the case of arbitrary time-varying topology and communication delays are derived, that reduce the stability analysis and controller design problems to analysis or synthesis, respectively, for a single agent. View full abstract»

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  • Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case

    Page(s): 2348 - 2354
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (289 KB) |  | HTML iconHTML  

    This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization. View full abstract»

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  • Receding Horizon Control Strategies for Constrained LPV Systems Based on a Class of Nonlinearly Parameterized Lyapunov Functions

    Page(s): 2354 - 2360
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (511 KB) |  | HTML iconHTML  

    In this technical note, we present a Receding Horizon Control (RHC) design method for linear parameter varying (LPV) systems subject to input and/or state constraints based on a class of nonlinearly parameterized Lyapunov functions recently introduced by Guerra and Vermeiren. As it will be made clear, their use gives rise to less conservative stabilizability conditions w.r.t. those arising from quadratic Lyapunov functions. A workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state-feedback control laws complying with the prescribed constraints. This control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed. Numerical comparisons with existing RHC methods for LPV systems are reported in the final example. View full abstract»

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  • Moving Horizon State Estimation for Networked Control Systems With Multiple Packet Dropouts

    Page(s): 2360 - 2366
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (718 KB) |  | HTML iconHTML  

    This technical note studies some of the challenging issues on moving horizon state estimation for networked control systems in the presence of multiple packet dropouts in both sensor-to-controller and controller-to-actuator channels, which both situations are modeled by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. Compared with standard Kalman filter, this study proposes a novel moving horizon estimator to deal with the uncertainties induced from the multiple packet dropouts, which has a larger degree of freedom to obtain better behavior by tuning the weight parameters. A sufficient condition for the convergence of the norm of the average estimation error is also presented to guarantee the performance of the estimator. Finally, a real-time simulation experiment is presented to demonstrate the feasibility and efficiency of the proposed method. View full abstract»

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  • Strong Stability of an Unstable Wave Equation by Boundary Feedback With Only Displacement Observation

    Page(s): 2367 - 2372
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (246 KB) |  | HTML iconHTML  

    The stabilization of a 1-D wave equation that contains instability at its free end and control at the other end is considered. The controller is designed through the estimated state that is designed in the case that only displacement is available. The method of “backstepping” is adopted in investigation. The C0 -semigroup theory and Lyapunov method are used to show that the closed-loop system is asymptotically stable. View full abstract»

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  • The Explicit Constrained Min-Max Model Predictive Control of a Discrete-Time Linear System With Uncertain Disturbances

    Page(s): 2373 - 2378
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (261 KB) |  | HTML iconHTML  

    In this technical brief, we develop an algorithm to determine the explicit solution of the constrained min-max model predictive control problem. For a discrete-time linear system with bounded additive uncertain disturbance, the control law is determined to be piecewise affine from a quadratic cost function and the state space is partitioned into corresponding polyhedral cones. By moving the on-line implementation to an off-line explicit evaluation, the computational burden is decreased and the applicability of min-max optimization is broadened. The results of this approach are shown via computer simulations. View full abstract»

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  • An Improved Stabilization Method for Sampled-Data Control Systems With Control Packet Loss

    Page(s): 2378 - 2384
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (315 KB) |  | HTML iconHTML  

    This technical note presents a new method for stability analysis and stabilization of sampled-data systems with control packet loss. It is assumed that if the control packet from the controller to the actuator is lost, then the actuator input to the plant is set to zero. The new method is based on a novel construction of piecewise differentiable Lyapunov functionals by using an impulsive system representation of sampled-data systems. A significant feature of the new Lyapunov functionals is that they are continuous at impulse times but not necessarily positive definite inside the impulse intervals. Applying the new Lyapunov functionals to sampled-data systems with control packet loss, improved criteria for stability and stabilization are derived. The new criteria are proved theoretically to be less conservative than the existing results. Illustrative examples are given which substantiate the usefulness of the proposed method. View full abstract»

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  • Lack of Separation Principle for Quantized Linear Quadratic Gaussian Control

    Page(s): 2385 - 2390
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (210 KB) |  | HTML iconHTML  

    This technical note studies the quantized linear quadratic Gaussian (LQG) control problem which is generalized from the classical LQG control but with the constraint that the feedback signal is quantized with a fixed bit rate. We show that state feedback control, state estimation and quantization can not be fully separated in general. Only a weak separation principle holds which converts the quantized LQG control problem into a quantized state estimation problem. Further separation of estimation and quantization is not possible in general. A concrete example is provided to demonstrate this fact. It is also shown that the so-called “whitening” approach to quantized state estimation is not optimal. 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