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Journal ArticleDOI

State-Space Methods for Control Systems

01 May 1979-IEEE Transactions on Systems, Man, and Cybernetics (IEEE)-Vol. 9, Iss: 5, pp 314-315
About: This article is published in IEEE Transactions on Systems, Man, and Cybernetics.The article was published on 1979-05-01. It has received 16 citations till now. The article focuses on the topics: Automatic control & Instrumentation and control engineering.
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Book ChapterDOI
15 Sep 2009
TL;DR: This work presents a more sophisticated extension on the traditional way of characterizing the reservoir dynamics, by using the dynamic profile of the Jacobian of the reservoir instead of static, a priori measures such as the standard spectral radius.
Abstract: Reservoir Computing (RC) offers a computationally efficient and well performing technique for using the temporal processing power of Recurrent Neural Networks (RNNs), while avoiding the traditional long training times and stability problems. The method is both simple and elegant: a random RNN (called the reservoir) is constructed using only a few global parameters to tune the dynamics into a desirable regime, and the dynamic response of the reservoir is used to train a simple linear regression function called the readout function - the reservoir itself remains untrained. This technique has shown some experimentally very convincing results on a variety of tasks, but a thorough understanding of the importance of the dynamics for the performance is still lacking. This contribution aims to extend this understanding, by presenting a more sophisticated extension on the traditional way of characterizing the reservoir dynamics, by using the dynamic profile of the Jacobian of the reservoir instead of static, a priori measures such as the standard spectral radius. We show that this measure gives a more accurate description of the reservoir dynamics, and can serve as predictor for the performance. Additionally, due to the theoretical background from dynamical systems theory, this measure offers some insight into the underlying mechanisms of RC.

48 citations


Cites background from "State-Space Methods for Control Sys..."

  • ...It follows from linear system theory [2] that if the matrix A has all singular values smaller than 11, it is definitely stable, while if any absolute eigenvalue (i....

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Journal ArticleDOI
TL;DR: The properties of linearity and noninterference were reasonably well supported, but the property of time-invariance was violated in a complex manner, which corroborate previous findings by Busemeyer and Myung (1988) using more general “measurement free” tests.

10 citations

Journal ArticleDOI
TL;DR: The Class-E amplifier as mentioned in this paper is a tuned switching power amplifier with a linear drain amplitude modulation characteristic ideally suited for high-efficiency amplifier systems (e.g., Kahn-amplifiers).
Abstract: The Class-E amplifier is a highly efficient tuned switching power amplifier with a linear drain amplitude modulation characteristic ideally suited for high-efficiency amplifier systems (e.g., Kahn-amplifiers). This brief describes a design procedure to determine the circuit elements for optimum operation of the amplifier using state space methods. Finite feed inductance and quality factor of the resonant circuit are taken into account. It is shown that high efficiency can be sustained for a wide variety of element combinations, allowing relaxed demands on the output capacitance of the active device. This is especially useful for high-frequency amplifiers where the maximum operation frequency of a given device is often limited by its intrinsic drain-source capacitance.

9 citations


Cites background or methods from "State-Space Methods for Control Sys..."

  • ...[ 12 ] , “A study of phase noise in CMOS oscillators,” IEEE J. Solid-State...

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  • ...For numerical calculations, the explicit Laplace transform can be avoided making use of Sylverster’s expansion theorem [ 12 ]....

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Journal ArticleDOI
TL;DR: In this article, the authors apply control analysis techniques to study the response of two moving-boundary nodal models for the prediction of the time evolution of the boiling boundary in a heated channel.

8 citations

Journal ArticleDOI
TL;DR: The possible introduction of a prejudice free control - similar to the term for the modeling introduced by Rudi Kalman - is investigated and the application of the HEISENBERG-type uncertainty relationship in control is discussed, combining the robustness of control and quality of modeling.
Abstract: The paper discusses some interesting, mainly philosophical paradigms of the modeling and control areas, which are still partly unsolved and/or only partially studied. First the possible introduction of a prejudice free control - similar to the term for the modeling introduced by Rudi Kalman - is investigated. Next the real constraints in real control systems are discussed. It seems that these are the amplitude limit for the actuators in practical systems. Then the application of the HEISENBERG-type uncertainty relationship in control is discussed, combining the robustness of control and quality of modeling. Finally a special irregularity in the classical LQR control methodology is treated investing some unreachable poles in the anomaly. The paper constitutes a review of a few specific problems in the control theory. They are enumerated in keywords and discussed on the basis of the references. The authors aim at least to invite further authors to continue such a discussion.

4 citations


Cites background or methods from "State-Space Methods for Control Sys..."

  • ...It can be shown that the simpler dyadic factorization [7] Wx = g g T ; T 1 1 n n g , ,g ,g − =      g (61) can also be used....

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  • ...The LQR (Linear system - Quadratic criterion Regulator) problem This optimization paradigm was formulated by the general, quadratic criterion [7], [8]...

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  • ...The frequency domain condition of the minimum of (55) is called the KALMAN equation [7], [8] or sometimes it is named frequency domain identity wu 1+ k TΦ s ( )b 2 = wu + gTΦ s ( )b 2 (62)...

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