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  • 1.
    Abd-Elrady, Emad
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Söderström, Torsten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Periodic signal modeling based on Liénard's equation2004In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 49, no 10, p. 1773-1778Article in journal (Refereed)
  • 2. Carlemalm, Catharina
    et al.
    Halvarsson, Susanne
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Wahlberg, Bo
    Algorithms for time delay estimation using a low complexity exhaustive search1999In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 44, no 5, p. 1031-1037Article in journal (Refereed)
  • 3. Churilov, Alexander
    et al.
    Medvedev, Alexander
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Mattsson, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Periodical solutions in a pulse-modulated model of endocrine regulation with time-delay2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 3, p. 728-733Article in journal (Refereed)
  • 4.
    Dai, Liang
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    A new structure exploiting derivation of recursive direct weight optimization2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 6, p. 1683-1685Article in journal (Refereed)
    Abstract [en]

    The recursive direct weight optimization method is used to solve challenging nonlinear system identification problems. This note provides a new derivation and a new interpretation of the method. The key underlying the note is to acknowledge and exploit a certain structure inherent in the problem.

  • 5.
    Dey, Subhrakanti
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Chiuso, Alessandro
    Univ Padua, Dept Informat Engn, I-35131 Padua, Italy..
    Schenato, Luca
    Univ Padua, Dept Informat Engn, I-35131 Padua, Italy..
    Feedback Control Over Lossy SNR-Limited Channels: Linear Encoder-Decoder-Controller Design2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 6, p. 3054-3061Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the problem of encoding and decoding codesign for linear feedback control of a scalar, possibly unstable, stochastic linear system when the sensed signal is to be transmitted over a finite capacity communication channel. In particular, we consider a limited capacity channel which transmits quantized data and is subject to packet losses. We first characterize the optimal strategy when perfect channel feedback is available, i.e., the transmitter has perfect knowledge of the packet loss history. This optimal scheme, innovation forwarding hereafter, is reminiscent of differential pulse-code modulation schemes adapted to deal with state space models, and is strictly better than a scheme which simply transmits the measured data, called measurement forwarding (MF) hereafter. Comparison in terms of control cost as well as of critical regimes, i.e., regimes where the cost is not finite, are provided. We also consider and compare two popular suboptimal schemes from the existing literature, based on 1) state estimate forwarding and 2) measurement forwarding, which ignore quantization effects in the associated estimator and controller design. In particular, it is shown that surprisingly the suboptimal MF strategy is always better then the suboptimal state forwarding strategy for small signal-to-quantization-noise-ratios.

  • 6. Farokhi, Farhad
    et al.
    Teixeira, Andre M. H.
    Langbort, Cedric
    Estimation With Strategic Sensors2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 2, p. 724-739Article in journal (Refereed)
    Abstract [en]

    © 1963-2012 IEEE. We introduce a model of estimation in the presence of strategic, self-interested sensors. We employ a game-Theoretic setup to model the interaction between the sensors and the receiver. The cost function of the receiver is equal to the estimation error variance while the cost function of the sensor contains an extra term which is determined by its private information. We start by the single sensor case in which the receiver has access to a noisy but honest side information in addition to the message transmitted by a strategic sensor. We study both static and dynamic estimation problems. For both these problems, we characterize a family of equilibria in which the sensor and the receiver employ simple strategies. Interestingly, for the dynamic estimation problem, we find an equilibrium for which the strategic sensor uses a memory-less policy. We generalize the static estimation setup to multiple sensors with synchronous communication structure (i.e., all the sensors transmit their messages simultaneously). We prove the maybe surprising fact that, for the constructed equilibrium in affine strategies, the estimation quality degrades as the number of sensors increases. However, if the sensors are herding (i.e., copying each other policies), the quality of the receiver’s estimation improves as the number of sensors increases. Finally, we consider the asynchronous communication structure (i.e., the sensors transmit their messages sequentially).

  • 7. Ghadimi, Euhanna
    et al.
    Teixeira, André
    Shames, Iman
    Johansson, Mikael
    Optimal parameter selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic problems2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 3, p. 644-658Article in journal (Refereed)
    Abstract [en]

    The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of l2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.

  • 8.
    Hong, Mei
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Söderström, Torsten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Zheng, Wei Xing
    A simplified form of the bias-eliminating least squares method for errors-in-variables identification2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 9, p. 1754-1756Article in journal (Refereed)
  • 9.
    Knorn, Steffi
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Middleton, R H
    Stability of two-dimensional linear systems with singularities on the stability booundary using LMIs2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 10, p. 2579-2590Article in journal (Refereed)
  • 10. Kung, Enoch
    et al.
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Shi, L
    The performance and limitations of e-stealthy attacks on higher order systems2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 2, p. 941-947Article in journal (Refereed)
  • 11.
    Kung, Enoch
    et al.
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Hong Kong, Peoples R China.
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Shi, Ling
    Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Kowloon, Hong Kong, Peoples R China.
    The performance and limitations of ε-stealthy attacks on higher order systems2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 2, p. 941-947Article in journal (Refereed)
    Abstract [en]

    In a cyber-physical system, security problems are of vital importance as the failure of such system can have catastrophic effects. Detection methods can be employed to sense the existence of an attack. In a previous study of an attack on the controller while avoiding detection in scalar systems under a certain control assumption, the notion of epsilon-stealthiness was introduced and the strength of epsilon-stealthy attacks was fully characterized. We generalize to the vector system and prove the cases in which we show that the limitations of epsilon-stealthy attack do not extend, in the sense that epsilon-stealthy can inflict damage of arbitrary magnitude to a vector system.

  • 12.
    Larsson, Erik K.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Mossberg, Magnus
    Söderström, Torsten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Identification of Continuous-Time ARX Models From Irregularly Sampled Data2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 3, p. 417-427Article in journal (Refereed)
  • 13.
    Leong, Alex S
    et al.
    Paderborn Univ, Dept Elect Engn EIM E, D-33098 Paderborn, Germany.
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Quevedo, Daniel E
    Paderborn Univ, Dept Elect Engn EIM E, D-33098 Paderborn, Germany.
    Sensor scheduling in variance based event triggered estimation with packet drops2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 4, p. 1880-1895Article in journal (Refereed)
    Abstract [en]

    This paper considers a remote state estimation problem with multiple sensors observing a dynamical process, where sensors transmit local state estimates over an independent and identically distributed (i.i.d.) packet dropping channel to a remote estimator. At every discrete time instant, the remote estimator decides whether each sensor should transmit or not, with each sensor transmission incurring a fixed energy cost. The channel is shared such that collisions will occur if more than one sensor transmits at a time. Performance is quantified via an optimization problem that minimizes a convex combination of the expected estimation error covariance at the remote estimator and expected energy usage across the sensors. For transmission schedules dependent only on the estimation error covariance at the remote estimator, this work establishes structural results on the optimal scheduling which show that: 1) for unstable systems, if the error covariance is large then a sensor will always be scheduled to transmit and 2) there is a threshold-type behavior in switching from one sensor transmitting to another. Specializing to the single sensor case, these structural results demonstrate that a threshold policy (i.e., transmit if the error covariance exceeds a certain threshold and don't transmit otherwise) is optimal. We also consider the situation where sensors transmit measurements instead of state estimates, and establish structural results including the optimality of threshold policies for the single sensor, scalar case. These results provide a theoretical justification for the use of such threshold policies in variance based event triggered estimation. Numerical studies confirm the qualitative behavior predicted by our structural results.

  • 14.
    Leong, Alex S
    et al.
    Department of Electical Engineering, Paderborn University, Tyskland.
    Quevedo, Daniel
    Department of Electrical Engineering, Paderborn University, Tyskland.
    Dolz, D
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Remote state estimation over packet dropping links in the presence of an eavesdropper2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Refereed)
  • 15.
    Leong, Alex S
    et al.
    Univ Paderborn, Dept Elect Engn EIM E, D-33098 Paderborn, Germany.
    Quevedo, Daniel E
    Univ Paderborn, Dept Elect Engn EIM E, D-33098 Paderborn, Germany.
    Ahlén, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Johansson, K H
    Royal Inst Technol, ACCESS Linnaeus Ctr, Sch Elect Engn, S-10044 Stockholm, Sweden.
    On network topology reconfiguration for remote state estimation2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 12, p. 3842-3856Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate network topology reconfiguration in wireless sensor networks for remote state estimation, where sensor observations are transmitted, possibly via intermediate sensors, to a central gateway/estimator. The time-varying wireless network environment is modelled by the notion of a network state process, which is a randomly time-varying semi-Markov chain and determines the packet reception probabilities of links at different times. For each network state, different network configurations can be used, which govern the network topology and routing of packets. The problem addressed is to determine the optimal network configuration to use in each network state, in order to minimize an expected error covariance measure. Computation of the expected error covariance cost function has a complexity of O(2(M Delta max)), where M is the number of sensors and Delta max is the maximum time between transitions of the semi-Markov chain. A sub-optimal method which minimizes the upper bound of the expected error covariance, that can be computed with a reduced complexity of O(2(M)), is proposed, which in many cases gives identical results to the optimal method. Conditions for estimator stability under both the optimal and suboptimal reconfiguration methods are derived using stochastic Lyapunov functions. Numerical results and comparisons with other low complexity approaches demonstrate the performance benefits of our approach.

  • 16. Li, Y
    et al.
    Zhang, F
    Quevedo, Daniel E
    Department of Electrical Engineering, Paderborn University, Tyskland.
    Lau, V K
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Shi, L
    Power control of an energy harvesting sensor for remote state estimation2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 1, p. 277-290Article in journal (Refereed)
  • 17. Ling, Y
    et al.
    Zhang, F
    Quevedo, Daniel E
    Lau, VK
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Shi, L
    Power control of an energy harvesting sensor for remote state estimation2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Refereed)
  • 18. Mossberg, Magnus
    et al.
    Söderström, Torsten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Covariance matching for continuous-time errors-in-variables problems2011In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 56, no 6, p. 1478-1483Article in journal (Refereed)
  • 19. Nourian, M
    et al.
    Leong, Alex S
    Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC 3052, Australien.
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Optimal energy allocation for Kalman filtering over packet dropping links with imperfect acknowledgements and energy harvesting constraints2014In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 8, p. 2128-2143Article in journal (Refereed)
    Abstract [en]

    This paper presents a design methodology for optimal transmission energy allocation at a sensor equipped with energy harvesting technology for remote state estimation of linear stochastic dynamical systems. In this framework, the sensor measurements as noisy versions of the system states are sent to the receiver over a packet dropping communication channel. The packet dropout probabilities of the channel depend on both the sensor's transmission energies and time varying wireless fading channel gains. The sensor has access to an energy harvesting source which is an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The receiver performs optimal state estimation with random packet dropouts to minimize the estimation error covariances based on received measurements. The receiver also sends packet receipt acknowledgments to the sensor via an erroneous feedback communication channel which is itself packet dropping. The objective is to design optimal transmission energy allocation at the energy harvesting sensor to minimize either a finite-time horizon sum or a long term average (infinite-time horizon) of the trace of the expected estimation error covariance of the receiver's Kalman filter. These problems are formulated as Markov decision processes with imperfect state information. The optimal transmission energy allocation policies are obtained by the use of dynamic programming techniques. Using the concept of submodularity, the structure of the optimal transmission energy policies are studied. Suboptimal solutions are also discussed which are far less computationally intensive than optimal solutions. Numerical simulation results are presented illustrating the performance of the energy allocation algorithms.

  • 20.
    Nygren, Johannes
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Pelckmans, Kristiaan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    A direct proof of the discrete-time multivariate circle and Tsypkin criteria2016In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 61, no 2, p. 544-549Article in journal (Refereed)
    Abstract [en]

    This technical note presents a new proof of the circle criterion for multivariate, discrete-time systems with time-varying feedback nonlinearities. A new proof for the multivariate Tsypkin criterion for time-invariant monotonic feedback nonlinearities is derived as well. Both integrator- and non-integrator systems are considered. The proofs are direct in the sense that they do not resort to any existing result in systems theory, such as Lyapunov theory, passivity theory or the small-gain theorem. Instead, the proofs refer to the asymptotic properties of block-Toeplitz matrices. One major advantage of the new proof is that it elegantly handles integrator systems without resorting to loop transformation/pole shifting techniques. Additionally, less conservative stability bounds are derived by making stronger assumptions on the sector bound conditions on the feedback nonlinearities. In particular, it is exemplified how this technique relaxes stability conditions of (i) a model predictive control (MPC) rule and (ii) an integrator system.

  • 21.
    Nygren, Johannes
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Pelckmans, Kristiaan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On the stability and optimality of an output feedback control law2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Other academic)
  • 22.
    Quevedo, Daniel E
    et al.
    School of Electrical Engineering & Computer Science, The University of Newcastle, Newcastle, Australien.
    Ahlén, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Johansson, Karl H.
    KTH, Stockholm.
    State Estimation Over Sensor Networks With Correlated Wireless Channels2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 3, p. 581-593Article in journal (Refereed)
    Abstract [en]

    Stochastic stability for centralized time-varying Kalman filtering over a wireless sensor network with correlated fading channels is studied. On their route to the gateway, sensor packets, possibly aggregated with measurements from several nodes, may be dropped because of fading links. To study this situation, we introduce a network state process, which describes a finite set of configurations of the radio environment. The network state characterizes the channel gain distributions of the links, which are allowed to be correlated between each other. Temporal correlations of channel gains are modeled by allowing the network state process to form a (semi-)Markov chain. We establish sufficient conditions that ensure the Kalman filter to be exponentially bounded. In the one-sensor case, this new stability condition is shown to include previous results obtained in the literature as special cases. The results also hold when using power and bit-rate control policies, where the transmission power and bit-rate of each node are nonlinear mapping of the network state and channel gains.

  • 23. Simandl, M
    et al.
    Kravolec, J
    Söderström, T
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Anticipative grid design in point-mass approach to nonlinear state estimation2002In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 47, no 4, p. 699-702Article in journal (Refereed)
  • 24. Sviestins, Egils
    et al.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Optimal recursive state estimation with quantized measurements2000In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 45, no 4, p. 762-767Article in journal (Refereed)
  • 25.
    Söderström, Torsten
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Accuracy Analysis of the Frisch Scheme for Identifying Errors-in-Variables Systems2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 6, p. 985-997Article in journal (Refereed)
    Abstract [en]

    Several estimation methods have been proposedfor identifying errors-in-variables systems, where both input andoutput measurements are corrupted by noise. One of the promisingapproaches is the so-called Frisch scheme. This paper providesan accuracy analysis of the Frisch scheme applied to system iden-tification. The estimates of the system parameters and the noisevariances are shown to be asymptotically Gaussian distributed.An explicit expression for the covariance matrix of the asymptoticdistribution is given as well. Numerical simulations support thetheoretical results. A comparison with the Cramér–Rao lowerbound is also given in the examples, and it is shown that the Frischscheme gives a performance close to the Cramér–Rao bound forlarge signal-to-noise ratios (SNRs).

  • 26. Wahlberg, Bo
    et al.
    Hjalmarsson, Hakan
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On the Performance of Optimal Input Signals for Frequency Response Estimation2012In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 57, no 3, p. 766-771Article in journal (Refereed)
    Abstract [en]

    We consider the problem of minimum-variance excitation design for frequency response estimation based on finite impulse response (FIR) and output error (OE) models. The objective is to minimize the power of the input signal to be used in the system identification experiment subject to a model accuracy constraint. For FIR and OE models this leads to a finite dimensional semi-definite programming optimization problem. We study, in detail, how to apply this approach to the estimation of the frequency response at a given frequency,. The first case concerns minimizing the asymptotic variance of the estimated frequency response based on an FIR model estimate. We compare the optimal input signal with a sinusoidal signal with frequency that gives the same model accuracy, and show that the input power can, at best, be reduced by a factor of two when using the optimal input signal. Conditions are given under which the sinusoidal signal is optimal, and it is shown that this is a common case for higher order FIR models. Next, we study FIR model based estimation of the absolute value and phase of the frequency response at a given frequency,. We derive the corresponding optimal input signals and compare their performances with that of a sinusoidal input signal with frequency. The relative reduction of input power when using the optimal solution is at best a factor of two. Finally, we discuss how to extend the FIR results to OE system identification by using an input parametrization proposed by Stoica and Soderstrom (1982).

  • 27.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Circle criteria in recursive identification1997In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 42, no 7, p. 975-979Article in journal (Refereed)
  • 28.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model1994In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 39, no 11, p. 2191-2206Article in journal (Refereed)
  • 29.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    ODE analysis and redesign in blind adaptation1997In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 42, no 12, p. 1742-1747Article in journal (Refereed)
  • 30.
    Wigren, Torbjörn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Output error convergence of adaptive filters with compensation for output nonlinearities1998In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 43, no 7, p. 975-978Article in journal (Refereed)
  • 31.
    Wigren, Torbjörn
    et al.
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