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Automatic Control, IEEE Transactions on

Issue 10 • Date Oct. 2013

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Displaying Results 1 - 25 of 37
  • Table of Contents

    Publication Year: 2013 , Page(s): C1 - C4
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  • IEEE Transactions on Automatic Control publication information

    Publication Year: 2013 , Page(s): C2
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  • Scanning the issue

    Publication Year: 2013 , Page(s): 2433 - 2434
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  • Distributed Tracking of Correlated Equilibria in Regime Switching Noncooperative Games

    Publication Year: 2013 , Page(s): 2435 - 2450
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5969 KB) |  | HTML iconHTML  

    We consider a class of regime-switching noncooperative repeated games where agents exchange information over a graph. The parameters of the game (number of agents, payoffs, information exchange graph) evolve randomly over time according to a Markov chain. We present a regret-based stochastic approximation algorithm with constant step-size that prescribes how individual agents update their randomized strategies over time. We show that, if the Markov chain jump changes on the same timescale as the adaptation rate of the stochastic approximation algorithm and agents independently follow this algorithm, their collective behavior is agile in tracking the time-varying convex polytope of correlated equilibria. The analysis is carried out using weak convergence methods and Lyapunov stability of switched Markovian differential inclusions. View full abstract»

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  • Controlled Sensing for Multihypothesis Testing

    Publication Year: 2013 , Page(s): 2451 - 2464
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3839 KB) |  | HTML iconHTML  

    The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error probability corresponds to the maximum Chernoff information over the choice of controls, and a pure stationary open-loop control policy is asymptotically optimal within the larger class of all causal control policies. For multihypothesis testing in the fixed sample size setting, lower and upper bounds on the optimal error exponent are derived. It is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open-loop control policy. In the sequential setting, a test based on earlier work by Chernoff for binary hypothesis testing, is shown to be first-order asymptotically optimal for multihypothesis testing in a strong sense, using the notion of decision making risk in place of the overall probability of error. Another test is also designed to meet hard risk constrains while retaining asymptotic optimality. The role of past information and randomization in designing optimal control policies is discussed. View full abstract»

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  • Feedback Particle Filter

    Publication Year: 2013 , Page(s): 2465 - 2480
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4117 KB) |  | HTML iconHTML  

    The feedback particle filter introduced in this paper is a new approach to approximate nonlinear filtering, motivated by techniques from mean-field game theory. The filter is defined by an ensemble of controlled stochastic systems (the particles). Each particle evolves under feedback control based on its own state, and features of the empirical distribution of the ensemble. The feedback control law is obtained as the solution to an optimal control problem, in which the optimization criterion is the Kullback-Leibler divergence between the actual posterior, and the common posterior of any particle. The following conclusions are obtained for diffusions with continuous observations: 1) The optimal control solution is exact: The two posteriors match exactly, provided they are initialized with identical priors. 2) The optimal filter admits an innovation error-based gain feedback structure. 3) The optimal feedback gain is obtained via a solution of an Euler-Lagrange boundary value problem; the feedback gain equals the Kalman gain in the linear Gaussian case. Numerical algorithms are introduced and implemented in two general examples, and a neuroscience application involving coupled oscillators. In some cases it is found that the filter exhibits significantly lower variance when compared to the bootstrap particle filter. View full abstract»

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  • The Separation Principle in Stochastic Control, Redux

    Publication Year: 2013 , Page(s): 2481 - 2494
    Cited by:  Papers (1)
    Save to Project icon | Click to expandQuick Abstract | PDF file iconPDF (3184 KB) |  | HTML iconHTML  

    Over the last 50 years, a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with “real-life” engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded. View full abstract»

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  • Hermite Spectral Method to 1-D Forward Kolmogorov Equation and Its Application to Nonlinear Filtering Problems

    Publication Year: 2013 , Page(s): 2495 - 2507
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3623 KB) |  | HTML iconHTML  

    In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the nonlinear filtering (NLF) problems with a real-time algorithm developed by S.-T. Yau and the second author in 2008. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filters as a real-time solver to NLF. View full abstract»

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  • Polynomial Level-Set Method for Polynomial System Reachable Set Estimation

    Publication Year: 2013 , Page(s): 2508 - 2521
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3695 KB) |  | HTML iconHTML  

    In this paper, we present a polynomial level-set method for advecting a semi-algebraic set for polynomial systems. This method uses the sub-level representation of sets. The problem of flowing these sets under the advection map of a dynamical system is converted to a semi-definite program, which is then used to compute the coefficients of the polynomials. The method presented in this paper does not require either the sets being positively invariant or star-shaped. Hence, the proposed algorithm can describe the behavior of system states both inside and outside the domain of attraction and can also be used to describe more complex shapes of sets. We further address the related problems of constraining the degree of the polynomials. Various numerical examples are presented to show the effectiveness of advection approach. View full abstract»

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  • H-Optimal Actuator Location

    Publication Year: 2013 , Page(s): 2522 - 2535
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3338 KB) |  | HTML iconHTML  

    In many control applications, there is freedom to place the actuators. The actuator location should be chosen to optimize certain performance objectives. In this paper, H-performance with state-feedback is considered. That is, both the controller and the actuator locations are chosen to minimize the effect of disturbances on the output. A framework for calculating H-optimal actuator locations is developed. Conditions for well-posedness of the H-optimal actuator location problem are presented. Many optimal actuator problems involve systems modelled by partial differential equations and conditions under which approximations yield reliable results are given. A derivative-free optimization algorithm to calculate H-optimal actuator locations is described. The results are illustrated using several examples. View full abstract»

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  • Distributed Control of Uncertain Networked Systems: A Decoupled Design

    Publication Year: 2013 , Page(s): 2536 - 2549
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3694 KB) |  | HTML iconHTML  

    This paper studies interconnected networked control systems in the presence of communication constraints and plant uncertainties. We propose a novel control architecture, where a reference model is introduced in each subsystem with the objective of generating the data for network broadcast as well as local feedback control. With this structure, the co-design of an output-feedback control strategy and the required communication protocol can be decoupled: the local controller only needs to address the uncertainty in the system dynamics, while the communication protocol purely focuses on the limitations due to communication channels. As a result, one can integrate the existing communication protocols and robust control techniques into this architecture without worrying about the coupling between the control and the communication. We provide stability conditions for the overall closed-loop system and derive uniform bounds on the error signals between the real system, the reference model, and an ideal model, which has perfect communication and no uncertainties. It is shown that these bounds can be arbitrarily improved, subject only to the hardware limitations. View full abstract»

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  • Global Stabilization of Nonlinear Systems Based on Vector Control Lyapunov Functions

    Publication Year: 2013 , Page(s): 2550 - 2562
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (6935 KB) |  | HTML iconHTML  

    This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: practically checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor. View full abstract»

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  • Complete Real Time Solution of the General Nonlinear Filtering Problem Without Memory

    Publication Year: 2013 , Page(s): 2563 - 2578
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5406 KB) |  | HTML iconHTML  

    It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a memoryless manner. In this paper, we shall extend the algorithm developed previously by S.-T. Yau and the second author to the most general setting of nonlinear filterings, where the explicit time-dependence is in the drift term, observation term, and the variance of the noises could be a matrix of functions of both time and the states. To preserve the off-line virtue of the algorithm, necessary modifications are illustrated clearly. Moreover, it is shown rigorously that the approximated solution obtained by the algorithm converges to the real solution in the L1 sense. And the precise error has been estimated. Finally, the numerical simulation support the feasibility and efficiency of our algorithm. View full abstract»

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  • Stability of Two-Dimensional Linear Systems With Singularities on the Stability Boundary Using LMIs

    Publication Year: 2013 , Page(s): 2579 - 2590
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4406 KB) |  | HTML iconHTML  

    This paper gives results on stability and asymptotic stability of two-dimensional systems using linear matrix inequalities (LMIs). Despite a long history of research in this area, systems with singularities on the stability boundary (SSB) have received limited attention because they cannot produce a sign definite solution to the required LMI. However, 2D systems describing some classes of models of vehicle platoons generically involve an SSB. Therefore, commonly used definitions for (asymptotic) stability and strict LMI conditions are not suitable to discuss the stability of these systems. It is shown that the existence of a negative semidefinite solution together with simple additional conditions is sufficient to guarantee asymptotic stability. Thus, the stability conditions discussed here can be used to study a wider range of dynamical systems, including systems with singularities on the stability boundary (SSB), which cannot be exponentially stable. A unified framework is used to analyse continuous-continuous, continuous-discrete and discrete-discrete systems simultaneously. View full abstract»

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  • On Synchronous Steady States and Internal Models of Diffusively Coupled Systems

    Publication Year: 2013 , Page(s): 2591 - 2602
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3297 KB) |  | HTML iconHTML  

    We investigate the problem of synchronizing nonidentical nonlinear dynamical systems by means of generalized diffusive couplings. The focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing nonidentical models. We show that for the problem to be solvable a synchronous steady state needs to exist. This condition leads to the requirement that all individual system models need to embed an internal model of some common endosystem. The latter condition is expressed in terms of nonlinear partial differential equations. The conditions derived in this paper are related to those known from the theory of output regulation. View full abstract»

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  • Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

    Publication Year: 2013 , Page(s): 2603 - 2608
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1137 KB) |  | HTML iconHTML  

    We consider a classical control problem: the infinite horizon singular LQ problem, i.e., some inputs are unpenalized in the quadratic performance index. In this case, it is known that the slow dynamics is constrained to be in a proper subspace of the state-space, with the optimal input for the slow dynamics implementable by feedback. In this technical note we show that both the fast dynamics and the slow dynamics can be implemented by a feedback controller. Moreover, we show that the feedback controller cannot be a static feedback controller but can be PD, i.e., proportional+differentiate exactly once, in the state. We show that the closed loop system is a singular descriptor state space system and we also characterize the conditions on the system/performance index for existence of inadmissible initial conditions, i.e., initial conditions that cause impulsive solutions. There are no inadmissible initial conditions in the controlled system if and only if in the strictly proper transfer matrix from the unpenalized inputs to the penalized states, there exists at least one maximal minor of relative degree equal to the number of unpenalized inputs. In addition to the above, we prove solvability of the infinite horizon singular LQ problem under milder assumptions than in the literature. View full abstract»

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  • Plug-and-Play Decentralized Model Predictive Control for Linear Systems

    Publication Year: 2013 , Page(s): 2608 - 2614
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1628 KB) |  | HTML iconHTML  

    In this technical note, we consider a linear system structured into physically coupled subsystems and propose a decentralized control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. The design procedure is totally decentralized, since the synthesis of a local controller uses only information on a subsystem and its neighbors, i.e. subsystems coupled to it. We show how to automatize the design of local controllers so that it can be carried out in parallel by smart actuators equipped with computational resources and capable to exchange information with neighboring subsystems. In particular, local controllers exploit tube-based Model Predictive Control (MPC) in order to guarantee robustness with respect to physical coupling among subsystems. Finally, an application of the proposed control design procedure to frequency control in power networks is presented. View full abstract»

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  • Accuracy of Some Popular Non-Homogeneous 2-Sliding Modes

    Publication Year: 2013 , Page(s): 2615 - 2619
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    Asymptotic accuracy of nonsingular terminal sliding modes and 2-sliding modes with prescribed convergence law is calculated in the presence of small sampling periods and measurement errors. The controllers are shown to have practically equivalent performance. View full abstract»

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  • A Novel Event-Triggered Transmission Scheme and {cal L}_{2} Control Co-Design for Sampled-Data Control Systems

    Publication Year: 2013 , Page(s): 2620 - 2626
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1446 KB) |  | HTML iconHTML  

    This note is concerned with the event-triggered L2 control for a sampled-data control system. A novel event-triggered transmission scheme is first proposed to determine whether or not the sampled-data should be transmitted. Under this scheme, the sampled-data transmission should be executed only when a threshold is violated, which means that less sampled-data is transmitted. This scheme does not require any special hardware for continuous measurement. Then, the sampled-data control system is modeled as a sampled-data error dependent system. A stability criterion is derived by constructing a novel Lyapunov-Krasovskii functional which fully utilizes the sawtooth structure characteristic of an artificial delay. Based on this stability criterion, a sufficient condition on the existence of a state feedback controller is given. A co-design algorithm is provided to obtain the parameters of the event-triggered transmission scheme and the controller gain simultaneously. Finally, an inverted pendulum example is given to show the effectiveness of the event-triggered transmission scheme and the co-design algorithm. View full abstract»

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  • Degree Fluctuations and the Convergence Time of Consensus Algorithms

    Publication Year: 2013 , Page(s): 2626 - 2631
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1150 KB) |  | HTML iconHTML  

    We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node has no connections to other nodes), we show that consensus is achieved within a given accuracy ε on n nodes in time B+4n3 Bln(2n/ε). Because there is a direct relation between consensus algorithms in time-varying environments and in homogeneous random walks, our result also translates into a general statement on such random walks. Moreover, we give a simple proof of a result of Cao, Spielman, and Morse that the worst case convergence time becomes exponentially large in the number of nodes n under slight relaxation of the degree constancy assumption. View full abstract»

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  • Realization of Lossless Systems Via Constant Matrix Factorizations

    Publication Year: 2013 , Page(s): 2632 - 2636
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1068 KB) |  | HTML iconHTML  

    We study the realization problem for linear time-invariant systems described by higher-order differential equations, which are J-lossless with constant J. Our approach is based on the factorization of a constant matrix obtained in a straightforward way from the storage function of the system. State equations are obtained directly from this factorization and from the original system representation. View full abstract»

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  • Necessary and Sufficient Razumikhin-Type Conditions for Stability of Delay Difference Equations

    Publication Year: 2013 , Page(s): 2637 - 2642
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1242 KB) |  | HTML iconHTML  

    This technical note considers stability analysis of time-delay systems described by delay difference equations (DDEs). All existing analysis methods for DDEs that rely on the Razumikhin approach provide sufficient, but not necessary conditions for asymptotic stability. Nevertheless, Lyapunov-Razumikhin functions are of interest because they induce invariant sets in the underlying state space of the dynamics. Therefore, we propose a relaxation of the Razumikhin conditions and prove that the relaxed conditions are necessary and sufficient for asymptotic stability of DDEs. For linear DDEs, it is shown that the developed conditions can be verified by solving a linear matrix inequality. Moreover, it is indicated that the proposed relaxation of Lyapunov-Razumikhin functions has an important implication for the construction of invariant sets for linear DDEs. View full abstract»

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  • The Generalized Moment-Based Filter

    Publication Year: 2013 , Page(s): 2642 - 2647
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1122 KB) |  | HTML iconHTML  

    Can we solve the filtering problem from the only knowledge of few moments of the noise terms? In this technical note, by exploiting set of distributions based filtering, we solve this problem without introducing additional assumptions on the distributions of the noises (e.g., Gaussianity) or on the final form of the estimator (e.g., linear estimator). Given the moments (e.g., mean and variance) of random variable X, it is possible to define the set of all distributions that are compatible with the moments information. This set can be equivalently characterized by its extreme distributions: a family of mixtures of Dirac's deltas. The lower and upper expectation of any function g of X are obtained in correspondence of these extremes and can be computed by solving a linear programming problem. The filtering problem can then be solved by running iteratively this linear programming problem. In this technical note, we discuss theoretical properties of this filter, we show the connection with set-membership estimation and its practical applications. View full abstract»

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  • Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems

    Publication Year: 2013 , Page(s): 2648 - 2653
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (897 KB) |  | HTML iconHTML  

    This technical note deals with consensus output regulation of network connected multi-agent systems. Every agent or subsystem is a nonlinear system in the output feedback form with relative degree one, but subsystems may have different dynamics in terms of different nonlinear functions and even different system orders. The subsystem dynamics are influenced by state variables generated from an exosystem. The outputs of the subsystems are required to follow a desired trajectory which is a function of the exosystem state. Only some subsystems have access to the desired trajectory, and the other subsystems will have to rely on the exchange of information through the network. In this technical note, a consensus control design is proposed to ensure that the outputs of all the subsystems converge to the same desired output trajectory by exploiting the internal model design strategy. The proposed control design only uses the relative outputs of the subsystems, and does not require the estimation of subsystem state variables. View full abstract»

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  • Sampled-Data Design for Robust Control of a Single Qubit

    Publication Year: 2013 , Page(s): 2654 - 2659
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1126 KB) |  | HTML iconHTML  

    This technical note presents a sampled-data approach to the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for the design of a unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates. 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