Erik Johannesson

Lund University, Lund, Skane, Sweden

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Publications (9)2.92 Total impact

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    Erik Johannesson, Anders Rantzer, Bo Bernhardsson
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    ABSTRACT: We consider a networked control system where a linear time-invariant (LTI) plant, subject to a stochastic disturbance, is controlled over a communication channel with colored noise and a signal-to-noise ratio (SNR) constraint. The controller is based on output feedback and consists of an encoder that measures the plant output and transmits over the channel, and a decoder that receives the channel output and issues the control signal. The objective is to stabilize the plant and minimize a quadratic cost function, subject to the SNR constraint. It is shown that optimal LTI controllers can be obtained by solving a convex optimization problem in the Youla parameter and performing a spectral factorization. The functional to minimize is a sum of two terms: the first is the cost in the classical linear quadratic control problem and the second is a new term that is induced by the channel noise. %todo ta bort meningen? A necessary and sufficient condition on the SNR for stabilization by an LTI controller follows directly from a constraint of the optimization problem. It is shown how the minimization can be approximated by a semidefinite program. The solution is finally illustrated by a numerical example.
    03/2012;
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    ABSTRACT: The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is induced by the channel noise and whose coefficient is the inverse of the channel's signal-to-noise ratio. This result is shown to also hold in the case of vector-valued signals, assuming parallel additive white Gaussian noise channels. It is also shown that optimal LTI encoders and decoders generally require infinite memory, which implies that approximations are necessary. A numerical example is provided, which compares the performance to the lower bound provided by rate-distortion theory.
    03/2012;
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    Erik Johannesson, Anders Rantzer, Bo Bernhardsson
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    ABSTRACT: We consider the problem of stabilizing and minimizing the disturbance response of a SISO LTI plant, subject to a stochastic disturbance, over an analog communication channel with additive white noise and a signal-to-noise ratio (SNR) constraint. The controller is linear, based on output feedback and has a structure with two degrees of freedom: One part represents sensing and encoding operations and the other part represents decoding and issuing the control signal. It is shown that the problem of simultaneously designing the two optimal controller parts can be solved in two stages: First a functional depending both on the 1- and 2-norms of the Youla parameter is minimized. This minimization can be arbitrarily well approximated by a quasiconvex program. The second stage consists of a spectral factorization.
    American Control Conference (ACC), 2011; 08/2011
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    Erik Johannesson, Anders Rantzer, Bo Bernhardsson
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    ABSTRACT: We present a framework for the solution of control and estimation problems under a signal-to-noise (SNR) ratio constraint. The framework can be used to design optimal linear controllers, based on output feedback, with two degrees of freedom: One part of the controller is placed before the communication channel and represents sensing and encoding operations. The other part represents decoding and issuing of the control signal. The framework includes a generalized plant model that can be used to represent problem instances covered in previous papers [12], [11] as special cases. It is shown that the design problem can be solved by minimization of a convex functional depending on the 1- and 2-norms of the Youla parameter, followed by a spectral factorization.
    9th IEEE International Conference on Control and Automation, ICCA 2011, Santiago, Chile, December 19-21, 2011; 01/2011
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    ABSTRACT: In this paper, we study the joint design of optimal linear encoders and decoders for filtering and transmission of a signal over an additive Gaussian noise channel subject to a real-time constraint. The objective is to minimize the variance of the estimation error at the receiving end. The design problem is nonconvex, but it is shown that a global optimum can be found by solving a related two-stage problem. The first stage consists of a mixed H<sub>2</sub> and H<sub>1</sub> norm minimization problem, where the H<sub>2</sub> norm corresponds to the error variance in a corresponding Wiener-Kolmogorov filtering problem and the H<sub>1</sub> norm is induced by the channel noise. The second stage consists of a spectral factorization. The results are illustrated by a numerical example.
    American Control Conference (ACC), 2010; 08/2010
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    Anton Cervin, Erik Johannesson
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    ABSTRACT: Event-triggered control is a promising alternative to time-triggered control, espe- cially for severely resource-constrained networked embedded systems. Previous work has shown that event-triggered control can reduce both the output variance and the average control rate in scalar linear stochastic systems compared to time-triggered control. It has also been shown how a minimum inter-control interval can be imposed, hence the term "sporadic control". In this work we extend the analysis of event-triggered impulse control of first-order linear stochastic systems to handle general sampling intervals and minimum inter-control intervals, control delay and control jitter, and measurement noise. The results show that the advantage of sporadic control remains also in these cases.
    07/2008;
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    Toivo Henningsson, Erik Johannesson, Anton Cervin
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    ABSTRACT: The standard approach in computer-controlled systems is to sample and control periodically. In certain applications, such as networked control systems or energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic event-based control of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results show that sporadic control can give better performance than periodic control in terms of both reduced process state variance and reduced control action frequency.
    Automatica 01/2008; · 2.92 Impact Factor
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    Erik Johannesson, Toivo Henningsson, Anton Cervin
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    ABSTRACT: The standard approach in feedback control systems is to sample and control periodically. For some applications, such as networked control systems or severely energy-constrained systems, it could be advantageous to instead use event-based control schemes. Aperiodic control (that is, event-based control with no specified minimum inter-event time) of first-order stochastic systems has been investigated in previous work. In any real implementation, however, it is necessary to have a well-defined minimum inter-event time. In this paper, we explore two such sporadic control schemes for first-order linear stochastic systems and compare the achievable performance to both periodic and aperiodic control. The results indicate that sporadic control can give better performance than periodic control in terms of reduced process state variance and control action frequency.
    05/2007: pages 301-314;
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    Erik Johannesson, Toivo Henningsson, Anton Cervin
    Hybrid Systems: Computation and Control, 10th International Workshop, HSCC 2007, Pisa, Italy, April 3-5, 2007, Proceedings; 01/2007