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Automatic Control, IEEE Transactions on

Issue 8 • Date Aug. 2011

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Displaying Results 1 - 25 of 34
  • Table of contents

    Publication Year: 2011 , Page(s): C1 - C4
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  • IEEE Control Systems Society

    Publication Year: 2011 , Page(s): C2
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  • Scanning the issue

    Publication Year: 2011 , Page(s): 1749 - 1750
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  • Minimum Variance Control Over a Gaussian Communication Channel

    Publication Year: 2011 , Page(s): 1751 - 1765
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (615 KB) |  | HTML iconHTML  

    We consider the problem of minimizing the response of a plant output to a stochastic disturbance using a control law that relies on the output of a noisy communication channel. We discuss a lower bound on the performance achievable at a specified terminal time using nonlinear time-varying communication and control strategies and show that this bound may be achieved using strategies that are linear. We also consider strategies that are defined over an infinite horizon that may achieve better transient response that those that are optimal for the terminal time problem. View full abstract»

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  • Optimal Control of Logical Control Networks

    Publication Year: 2011 , Page(s): 1766 - 1776
    Cited by:  Papers (29)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (487 KB) |  | HTML iconHTML  

    This paper considers the infinite horizon optimal control of logical control networks, including Boolean control networks as a special case. Using the framework of game theory, the optimal control problem is formulated. In the sight of the algebraic form of a logical control network, its cycles can be calculated algebraically. Then the optimal control is revealed over a certain cycle. When the games, using memory μ >; 1 (which means the players only consider previous μ steps' action at each step), are considered, the higher order logical control network is introduced and its algebraic form is also presented, which corresponds to a conventional logical control network (i.e., μ = 1 ). Then it is proved that the optimization technique developed for conventional logical control networks is also applicable to this μ-memory case. View full abstract»

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  • Adaptive Gaussian Sum Filters for Space Surveillance

    Publication Year: 2011 , Page(s): 1777 - 1790
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (672 KB) |  | HTML iconHTML  

    The representation of the uncertainty of a stochastic state by a Gaussian mixture is well-suited for nonlinear tracking problems in high dimensional data-starved environments such as space surveillance. In this paper, the framework for a Gaussian sum filter is developed emphasizing how the uncertainty can be propagated accurately over extended time periods in the absence of measurement updates. To achieve this objective, a series of metrics constructed from tensors of higher-order cumulants are proposed which assess the consistency of the uncertainty and provide a tool for implementing an adaptive Gaussian sum filter. Emphasis is also placed on the algorithm's potential for parallelization which is complemented by the use of higher-order unscented filters based on efficient multidimensional Gauss-Hermite quadrature schemes. The effectiveness of the proposed Gaussian sum filter is illustrated in a case study in space surveillance involving the tracking of an object in a six-dimensional state space. View full abstract»

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  • Leader-Enabled Deployment Onto Planar Curves: A PDE-Based Approach

    Publication Year: 2011 , Page(s): 1791 - 1806
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (951 KB) |  | HTML iconHTML  

    We introduce an approach for stable deployment of agents onto families of planar curves, namely, 1-D formations in 2-D space. The agents' collective dynamics are modeled by the reaction-advection-diffusion class of partial differential equations (PDEs), which is a broader class than the standard heat equation and generates a rich geometric family of deployment curves. The PDE models, whose state is the position of the agents, incorporate the agents' feedback laws, which are designed based on a spatial internal model principle. Namely, the agents' feedback laws allow the agents to deploy to a family of geometric curves that correspond to the model's equilibrium curves, parameterized by the continuous agent identity α ∈ [0,1] . However, many of these curves are open-loop unstable. Stable deployment is ensured by leader feedback, designed in a manner similar to the boundary control of PDEs. By discretizing the PDE model with respect to α , we impose a fixed communication topology, specifically a chain graph, on the agents and obtain control laws that require communication with only an agent's nearest neighbors on the graph. A PDE-based approach is also used to design observers to estimate the positions of all the agents, which are needed in the leader's feedback, by measuring only the position of the leader's nearest neighbor. Hence, the leader uses only local information when employing output feedback. View full abstract»

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  • Controllability and Observability of Linear Time-Invariant Uncertain Systems Irrespective of Bounds of Uncertain Parameters

    Publication Year: 2011 , Page(s): 1807 - 1817
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (349 KB) |  | HTML iconHTML  

    In this paper, the controllability and observability of linear time-invariant uncertain systems are investigated. The systems under consideration contain time-invariant uncertain parameters that may take arbitrarily large values. In such a situation, the locations of uncertain parameters in system matrices play an important role. We examine the permissible locations of uncertain parameters in system matrices for a linear uncertain system to be controllable and observable independently of the bounds of the uncertain parameters. The objective of this paper is to show that a linear uncertain system is controllable and observable, irrespective of the bounds of uncertain parameters, if and only if the system has a particular configuration called a complete generalized antisymmetric stepwise configuration (CGASC). Furthermore, the dual configuration of a CGASC is introduced and studied here. View full abstract»

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  • Designing Compact and Maximally Permissive Deadlock Avoidance Policies for Complex Resource Allocation Systems Through Classification Theory: The Linear Case

    Publication Year: 2011 , Page(s): 1818 - 1833
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (802 KB) |  | HTML iconHTML  

    Most of the past research on the problem of deadlock avoidance for complex resource allocation systems (RAS) has acknowledged the fact that the computation of the maximally permissive deadlock avoidance policy (DAP) possesses super-polynomial complexity for most RAS classes, and therefore, it has resorted to solutions that trade off maximal permissiveness for computational tractability. In this paper, we distinguish between the off-line and the on-line computation that is required for the effective implementation of the maximally permissive DAP, and we seek to develop representations of this policy that will require minimal on-line computation. The particular representation that we adopt is that of a compact classifier that will effect the underlying dichotomy of the reachable state space into safe and unsafe subspaces. Furthermore, in this first study of the aforementioned problem, we restrict our attention to a particular RAS class that is motivated by an ongoing project of ours called Gadara, and accepts separation of the safe and unsafe subspaces of its instantiations through a set of linear inequalities. Through a series of reductions of the derived classification problem, we are also able to attain extensive reductions in the computational complexity of the off-line task of the construction of the sought classifier. We formally establish completeness and optimality properties for the proposed design procedures. We also offer heuristics that, if necessary, can alleviate the computational effort that is necessary for the construction of the sought classifier. Finally, we demonstrate the efficacy of the developed approaches through a series of computational experiments. To the best of our knowledge, these experiments also establish the ability of the proposed methodology to effectively compute tractable implementations of the maximally permissive DAP for problem instances significantly beyond the capacity of any other approach currently available in the literatur- - e. View full abstract»

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  • Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks

    Publication Year: 2011 , Page(s): 1834 - 1848
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (851 KB) |  | HTML iconHTML  

    A widely applied strategy for workload sharing is to equalize the workload assigned to each resource. In mobile multiagent systems, this principle directly leads to equitable partitioning policies whereby: 1) the environment is equitably divided into subregions of equal measure; 2) one agent is assigned to each subregion; and 3) each agent is responsible for service requests originating within its own subregion. The current lack of distributed algorithms for the computation of equitable partitions limits the applicability of equitable partitioning policies to limited-size multiagent systems operating in known, static environments. In this paper, first we design provably correct and spatially distributed algorithms that allow a team of agents to compute a convex and equitable partition of a convex environment. Second, we discuss how these algorithms can be extended so that a team of agents can compute, in a spatially distributed fashion, convex and equitable partitions with additional features, e.g., equitable and median Voronoi diagrams. Finally, we discuss two application domains for our algorithms, namely dynamic vehicle routing for mobile robotic networks and wireless ad hoc networks. Through these examples, we show how one can couple the algorithms presented in this paper with equitable partitioning policies to make these amenable to distributed implementation. More in general, we illustrate a systematic approach to devise spatially distributed control policies for a large variety of multiagent coordination problems. Our approach is related to the classic Lloyd algorithm and exploits the unique features of power diagrams. View full abstract»

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  • Hamilton–Jacobi Formulation for Reach–Avoid Differential Games

    Publication Year: 2011 , Page(s): 1849 - 1861
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (680 KB) |  | HTML iconHTML  

    A new framework for formulating reachability problems with competing inputs, nonlinear dynamics, and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems in hybrid systems. Earlier approaches to reach-avoid computations are either restricted to linear systems, or face numerical difficulties due to possible discontinuities in the Hamiltonian of the optimal control problem. The main advantage of the approach proposed in this paper is that it can be applied to a general class of target-hitting continuous dynamic games with nonlinear dynamics, and has very good properties in terms of its numerical solution, since the value function and the Hamiltonian of the system are both continuous. The performance of the proposed method is demonstrated by applying it to a case study, which involves the target-hitting problem of an underactuated underwater vehicle in the presence of obstacles. View full abstract»

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  • Opinion Dynamics With Decaying Confidence: Application to Community Detection in Graphs

    Publication Year: 2011 , Page(s): 1862 - 1873
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (707 KB) |  | HTML iconHTML  

    We study a class of discrete-time multi-agent systems modeling opinion dynamics with decaying confidence. We consider a network of agents where each agent has an opinion. At each time step, the agents exchange their opinion with their neighbors and update it by taking into account only the opinions that differ from their own less than some confidence bound. This confidence bound is decaying: an agent gives repetitively confidence only to its neighbors that approach sufficiently fast its opinion. Essentially, the agents try to reach an agreement with the constraint that it has to be approached no slower than a prescribed convergence rate. Under that constraint, global consensus may not be achieved and only local agreements may be reached. The agents reaching a local agreement form communities inside the network. In this paper, we analyze this opinion dynamics model: we show that communities correspond to asymptotically connected components of the network and give an algebraic characterization of communities in terms of eigenvalues of the matrix defining the collective dynamics. Finally, we apply our opinion dynamics model to address the problem of community detection in graphs. We propose a new formulation of the community detection problem based on eigenvalues of normalized Laplacian matrix of graphs and show that this problem can be solved using our opinion dynamics model. We consider three examples of networks, and compare the communities we detect with those obtained by existing algorithms based on modularity optimization. We show that our opinion dynamics model not only provides an appealing approach to community detection but that it is also effective. View full abstract»

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  • Solutions to the Hamilton-Jacobi Equation With Algebraic Gradients

    Publication Year: 2011 , Page(s): 1874 - 1885
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (340 KB) |  | HTML iconHTML  

    In this paper, the Hamilton-Jacobi equation (HJE) with coefficients consisting of rational functions is considered, and its solutions with algebraic gradients are characterized in terms of commutative algebra. It is shown that there exists a solution with an algebraic gradient if and only if an involutive maximal ideal containing the Hamiltonian exists in a polynomial ring over the rational function field. If such an ideal is found, the gradient of the solution is defined implicitly by a set of algebraic equations. Then, the gradient is determined by solving the set of algebraic equations pointwise without storing the solution over a domain in the state space. Thus, the so-called curse of dimensionality can be removed when a solution to the HJE with an algebraic gradient exists. New classes of explicit solutions for a nonlinear optimal regulator problem are given as applications of the present approach. View full abstract»

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  • A Framework for Control System Design Subject to Average Data-Rate Constraints

    Publication Year: 2011 , Page(s): 1886 - 1899
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (564 KB) |  | HTML iconHTML  

    This paper studies discrete-time control systems subject to average data-rate limits. We focus on a situation where a noisy linear system has been designed assuming transparent feedback and, due to implementation constraints, a source-coding scheme (with unity signal transfer function) has to be deployed in the feedback path. For this situation, and by focusing on a class of source-coding schemes built around entropy coded dithered quantizers, we develop a framework to deal with average data-rate constraints in a tractable manner that combines ideas from both information and control theories. As an illustration of the uses of our framework, we apply it to study the interplay between stability and average data-rates in the considered architecture. It is shown that the proposed class of coding schemes can achieve mean square stability at average data-rates that are, at most, 1.254 bits per sample away from the absolute minimum rate for stability established by Nair and Evans. This rate penalty is compensated by the simplicity of our approach. View full abstract»

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  • Fast Sensor Scheduling for Spatially Distributed Sensors

    Publication Year: 2011 , Page(s): 1900 - 1905
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (273 KB) |  | HTML iconHTML  

    This technical note addresses a sensor scheduling problem for a class of networked sensor systems whose sensors are spatially distributed and measurements are influenced by state dependent noise. A concept of sensor types is introduced without loss of generality to reduce combinatorial complexity. The computation time of the proposed algorithm increases exponentially with the number of the sensor types, while that of standard algorithms is exponential in the number of the sensors. This confirms high speed performance of the proposed algorithm, since the number of sensor types is usually far less than the number of sensors. View full abstract»

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  • Fault Detection and Isolation of Linear Impulsive Systems

    Publication Year: 2011 , Page(s): 1905 - 1910
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (397 KB) |  | HTML iconHTML  

    This technical note investigates the development of fault detection and isolation (FDI) filters for linear impulsive systems. The concept of an unobservability subspace is introduced for linear impulsive systems and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation for linear impulsive systems are obtained by utilizing our introduced unobservability subspace. Simulation results demonstrate the effectiveness of our proposed FDI strategy. View full abstract»

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  • Canonical Forms of Generic Piecewise Linear Continuous Systems

    Publication Year: 2011 , Page(s): 1911 - 1915
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (198 KB) |  | HTML iconHTML  

    This technical note reports a simple, but effective strategy to derive a single coordinate transformation of a generic n-dimensional piecewise-linear continuous vector field that puts both of its subsystems into the same observer or control canonical form. The only hypothesis required is that both subsystems are either observable or controllable. To derive the result, the structure of the system is used in order to prove that it suffices to consider the same transformation for both subsystems. The theoretical results are illustrated by means of the Colpitts oscillator as a practical case of study. View full abstract»

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  • A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected Time-Varying Networks

    Publication Year: 2011 , Page(s): 1915 - 1920
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (244 KB) |  | HTML iconHTML  

    The average consensus problem of continuous-time agents in undirected time-varying networks is studied. The network is allowed to be disconnected. A notion called infinite integral connectivity is proposed. Based on the notion, a necessary and sufficient condition for achieving consensus is given. That is, when the network topology is described by an undirected time-varying graph G(t), the agents achieve consensus if and only if the infinite integral graph of G(t) over [0,∞) is connected. This criterion does not hold for directed networks. View full abstract»

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  • State-Feedback Control of High-Order Stochastic Nonlinear Systems with SiISS Inverse Dynamics

    Publication Year: 2011 , Page(s): 1921 - 1926
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (281 KB) |  | HTML iconHTML  

    This technical note considers a class of high-order stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics, and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states. A new design and analysis approach to the problem of state-feedback global regulation is developed to guarantee that all the signals of the closed-loop system are bounded almost surely and the states can be regulated to zero almost surely. View full abstract»

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  • A Hybrid Statistical Technique for Modeling Recurrent Tracks in a Compact Set

    Publication Year: 2011 , Page(s): 1926 - 1931
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (399 KB) |  | HTML iconHTML  

    In this technical note we present a hybrid statistical approach for modeling a vehicle's behavior as it traverses a compact set in Euclidean space. We use Symbolic Transfer Functions (STF), developed by the authors for modeling stochastic input/output systems whose inputs and outputs are both purely symbolic. We apply STF to our problem by assuming that the input symbols represent regions of space through which a track is passing while the output represents specific linear functions that more precisely model the behavior of the track. A target's behavior is modeled at two levels of precision: The symbolic model provides a probability distribution on the next region of space and behavior (linear function) that a vehicle will execute, while the continuous model predicts the position of the vehicle using classical statistical methods. The following results are presented: (i) An algorithm that parsimoniously partitions the space of the vehicle and models the behavior in the partitions with linear functions. (ii) A demonstration of our approach using real-world ship track data. View full abstract»

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  • Continuous Piecewise Affine Dynamical Systems do not Exhibit Zeno Behavior

    Publication Year: 2011 , Page(s): 1932 - 1936
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (198 KB) |  | HTML iconHTML  

    In the context of continuous piecewise affine dynamical systems, we study the Zeno behavior, i.e., infinite number of mode transitions in finite time interval, in this note. The main result reveals that piecewise affine dynamical systems do not exhibit Zeno behavior. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of piecewise affine systems. View full abstract»

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  • Cardinality Constrained Linear-Quadratic Optimal Control

    Publication Year: 2011 , Page(s): 1936 - 1941
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (533 KB) |  | HTML iconHTML  

    As control implementation often incurs not only a variable cost associated with the magnitude or energy of the control, but also a setup cost, we consider a discrete-time linear-quadratic (LQ) optimal control problem with a limited number of control implementations, termed in this technical note the cardinality constrained linear-quadratic optimal control (CCLQ). We first derive a semi-analytical feedback policy for CCLQ problems using dynamic programming (DP). Due to the exponential growth of the complexity in calculating the action regions, however, DP procedure is only efficient for CCLQ problems with a scalar state space. Recognizing this fact, we develop then two lower-bounding schemes and integrate them into a branch-and-bound (BnB) solution framework to offer an efficient algorithm in solving general CCLQ problems. Adopting the devised solution algorithm for CCLQ problems, we can solve efficiently the linear-quadratic optimal control problem with setup costs. View full abstract»

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  • Robust Tubes in Nonlinear Model Predictive Control

    Publication Year: 2011 , Page(s): 1942 - 1947
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (375 KB) |  | HTML iconHTML  

    Nonlinear model predictive control (NMPC) strategies based on linearization about predicted system trajectories enable the online NMPC optimization to be performed by a sequence of convex optimization problems. The approach relies on bounds on linearization errors in order to ensure constraint satisfaction and convergence of the performance index, both during the optimization at each sampling instant and along closed loop system trajectories. This technical note proposes bounds based on robust tubes constructed around predicted trajectories. To ensure local optimality, the bounds are non-conservative for the case of zero linearization error, which requires the tube cross sections to vary along predicted trajectories. The feasibility, stability and convergence properties of the algorithm are established without the need for predictions to satisfy local optimality criteria. The strategy is illustrated by numerical examples. View full abstract»

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  • Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback

    Publication Year: 2011 , Page(s): 1948 - 1952
    Cited by:  Papers (59)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    This technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree. A leader node or command generator is considered, which generates the desired tracking trajectory. A framework for cooperative tracking control is proposed, including full state feedback control, observer design and dynamic output feedback control. The classical system theory notion of duality is extended to networked systems. It is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node. View full abstract»

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  • Second-Order Switching Time Optimization for Nonlinear Time-Varying Dynamic Systems

    Publication Year: 2011 , Page(s): 1953 - 1957
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (258 KB) |  | HTML iconHTML  

    This technical note gives a method for calculating the first and second derivatives of a cost function with respect to switching times for systems with piecewise second-differentiable dynamics. Differential equations governing the linear and bilinear operators required for calculating the derivatives are presented. Example optimizations of linear and nonlinear systems are presented as evidence for the value of second-order optimization methods. One example converges in 33 iterations using second-order methods whereas the first-order algorithm requires over 30 000 iterations. 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