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Minimal state-space realization in linear system theory: an overview

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期121卷 331-354页

作者： De Schutter, B Delft Univ Technol Fac Informat Technol & Syst Control Lab NL-2600 GA Delft Netherlands

We give a survey of the results in connection with the minimal state-space realization problem for linear time-invariant systems. We start with a brief historical overview and a short introduction to linear system theory. Next we present some of the basic algorithms for the reduction of nonminimal state-space realizations and for the minimal state-space realization of infinite or finite sequences of Markov parameters of linear time-invariant systems. Finally, we discuss some extensions of this problem to other classes of systems and point out some related problems. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： minimal realization linear system theory state-space models

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A simple and scalable particle swarm optimization structure based on linear system theory

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MEMETIC COMPUTING 2024年第2期16卷 219-231页

作者： Zhu, Jian Liu, Jianhua Fujian Univ Technol Sch Comp Sci & Math Fuzhou 350118 Peoples R China Fujian Prov Key Lab Big Data Min & Applicat Fuzhou 350118 Peoples R China

Since it was first presented, particle swarm optimization (PSO) has experienced numerous improvements as a traditional optimization approach. PSO becomes more complex as a result of the majority of improvement strategies, which use learning model replacement or parameter adjustment to enhance PSO's performance. Based on linear system theory, this study proposes a simple and scalable framework for restructuring particle swarm optimization (RPSO) and provides a new example of the RPSO algorithm framework, Q-RPSO. The RPSO framework adopts a single position updating formula instead of the original position and velocity updating formulas, which are unrelated to the PSO's velocity and the current position. The experiments were carried out to compare with the standard PSO and six PSO variants based on CEC 2013 benchmark functions. The experimental results demonstrate that, whether in terms of global exploration capability or convergence accuracy, Q-RPSO outperforms all competitor algorithms.

关键词： PSO linear system theory RPSO Q-RPSO

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CONFIRMATION OF linear-system theory PREDICTION - CHANGES IN HERRNSTEIN-K AS A FUNCTION OF CHANGES IN REINFORCER MAGNITUDE

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JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 1984年第2期41卷 183-192页

作者： MCDOWELL, JJ WOOD, HM EMORY UNIV DEPT PSYCHOL ATLANTA GA 30322 USA

Human subjects (8) pressed a lever on a range of variable-interval schedules for ***. to ***. per reinforcement. Herrnstein''s hyperbola described 7 of the 8 subjects response-rate data well. For all subjects, the .gamma.-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory;they contradict formal properties of Herrnstein''s account and of 6 other mathematical accounts of single-alternative responding.

关键词： linear system theory Herrnstein\'s equation quantitative law of effect choice reinforcer magnitude variable‐interval schedules lever press humans

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Analysis of tracer transit in rat brain after carotid artery and femoral vein administrations using linear system theory

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MAGNETIC RESONANCE IMAGING 1997年第5期15卷 551-558页

作者： Rudin, M Beckmann, N Sauter, A Core Technology Area Novartis Pharma Ltd. Basel Switzerland Nervous System Department Novartis Pharma Ltd. Basel Switzerland

Determination of tissue perfusion rates by MRI bolus tracking methods relies on the central volume principle which states that tissue blood flow is given by the tissue blood volume divided by the mean tracer transit time (MTT). Accurate determination of the MTT requires knowledge of the arterial input function which in MRI experiments is usually not known, especially when using small animals. The problem of unknown arterial input can be circumvented in animal experiments by directly injecting the contrast agent into a feeding artery of the tissue of interest. In the present article the passage of magnetite nanoparticles through the rat cerebral cortex is analyzed after injection into the internal carotid artery. The results are discussed in the framework of linear system theory using a one-compartment model for brain tissue and by using the well characterized gamma-variate function to describe the tissue concentration profile of the contrast agent. The results obtained from the intra-arterial tracer administration experiments are then compared with the commonly used intra-venous injection of the contrast agent in order to estimate the contribution of the peripheral circulation to the MTT values in the latter case. The experiments were analyzed using a two-compartment model and the gamma-variate function. As an application perfusion rates in normal and ischemic cerebral cortex of hypertensive rats were estimated in a model of focal cerebral ischemia. The results indicate that peripheral circulation has a significant influence on the MTT values and thus on the perfusion rates, which cannot be neglected. (C) 1997 Elsevier Science Inc.

关键词： magnetic resonance imaging cerebral perfusion superparamagnetic iron oxide nanoparticles dynamic susceptibility contrast linear system theory

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CONFIRMATION OF linear-system theory PREDICTION - RATE OF CHANGE OF HERRNSTEIN K AS A FUNCTION OF RESPONSE-FORCE REQUIREMENT

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JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 1985年第1期43卷 61-73页

作者： MCDOWELL, JJ WOOD, HM EMORY UNIV DEPT PSYCHOL ATLANTA GA 30322 USA

Four human subjects worked on all combinations of 5 variable-interval schedules and 5 reinforcer magnitudes (.cents./reinforcer) in each of 2 phases of the experiment. In 1 phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein''s k were obtained at each reinforcer magnitude. The results follow. Response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement. k increased from the beginning to the end of the magnitude range for all subjects at both force requirements. The reciprocal of k was a linear function of the reciprocal of reinforcer magnitude for 7 of the 8 data sets. The rate of change of k was greater at the high than at the low force requirement by an order of magnitude or more. The 2nd and 3rd findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell et Wood, 1984). The 4th finding confirms a further prediction of the theory and supports the theory''s interpretation of conflicting data on the constancy of Herrnstein''s k.

关键词： linear system theory Herrnstein"s equation reinforcer value reinforcer magnitude response force variable-interval schedules lever press humans

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Restructuring Particle Swarm Optimization algorithm based on linear system theory

Restructuring Particle Swarm Optimization algorithm based on...

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IEEE Congress on Evolutionary Computation (CEC)

作者： Zhu, Jian Liu, Jianhua Wang, Zihang Chen, Yuxiang Fujian Univ Technol Sch Comp Sci & Math Fuzhou Peoples R China

ISBN: (数字)9781665467087

ISBN: (纸本)9781665467087

The original Particle Swarm Optimization (PSO) used two formulas to describe updating of particle's position and velocity, respectively, based on simulating the foraging behavior of bird swarm. The general improving methods on PSO are to adjust and optimize its parameters or combine new learning strategy to update velocity formula for the better performance. But these methods lack of theoretical analysis and make the algorithm more complex. This paper proposes a new formulation to restructure the particles' position updating behaviors based on linear system theory, and obtain a Restructuring PSO algorithm (RPSO). Compared with the conventional PSO algorithm, RPSO only uses one particle position updating formula, without velocity updating formula, and takes fewer parameters. In order to verify the effectiveness of RPSO, experiments on the CEC 2013 benchmark functions have been conducted to compare with four algorithms, and the final results show that proposed algorithm has a certain degree of competition.

关键词： PSO Restructuring PSO linear system theory

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A Study of Reform in linear system theory Teaching

A Study of Reform in Linear System Theory Teaching

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第三届教学管理与课程建设学术会议

作者： Bingji XU 1 , Hui CHENG 1,2 1 Schoole of Information Engineering, China University of Geosciences, Beijing ,China 2 Schoole of Mechanical and Electronic Engineering, Chizhou University, Chizhou, Anhui, China

The linear system theory is a professional course in the control science and engineering field and the course has a strong theoretical and abstraction, how can we let the students to grasp this course more easily and learn to use the knowledge to solve the problem in the control areas is the original intention of this teaching reform in the linear system theory. Analysis by the features of the course and the students' learning ability, our electrical and automation laboratory decided to bring in the linear triple stage inverted pendulum as the experimental platform for teaching reform, through design, discussion, testing and summary the control scheme of the experimental platform to help the student understand the course more easily, at the same time also stimulate the students' independent innovation thinking.

关键词： linear system theory Education Reform linear Triple Stage Inverted Pendulum

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An explanation for the logarithmic connection between linear and morphological system theory

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INTERNATIONAL JOURNAL OF COMPUTER VISION 2005年第2-3期64卷 157-169页

作者： Burgeth, B Weickert, J Univ Saarland Fac Math & Comp Sci Math Image Anal Grp D-66041 Saarbrucken Germany

Dorst/van den Boomgaard and Maragos introduced the slope transform as the morphological equivalent of the Fourier transform. Generalising the conjugacy operation from convex analysis it formed the basis of a morphological system theory that bears an almost logarithmic relation to linear system theory;a connection that has not been fully understood so far. Our article provides an explanation by disclosing that morphology in essence is linear system theory in specific algebras. While linear system theory uses the standard plus-prod algebra, morphological system theory is based on the max-plus algebra and the min-plus algebra. We identify the nonlinear operations of erosion and dilation as linear convolutions in the latter algebras. The logarithmic Laplace transform makes a natural appearance as it corresponds to the conjugacy operation in the max-plus algebra. Its conjugate is given by the so-called Cramer transform. Originating from stochastics, the Cramer transform maps Gaussians to quadratic functions and relates standard convolution to erosion. This fundamental transform relies on the logarithm and constitutes the direct link between linear and morphological system theory. Many numerical examples are presented that illustrate the convexifying and smoothing properties of the Cramer transform.

关键词： linear system theory morphology convex analysis max-plus algebra min-plus algebra slope transform Cramer transform

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An explanation for the logarithmic connection between linear and morphological system theory

An explanation for the logarithmic connection between linear...

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4th International Conference on Scale Space Methods in Computer Vision

作者： Burgeth, B Weickert, J Univ Saarland Fac Math & Comp Sci Math Image Anal Grp D-66041 Saarbrucken Germany

ISBN: (纸本)354040368X

关键词： linear system theory morphology convex analysis max-plus algebra min-plus algebra slope transform Cramer transform

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Frequency Domain Thermal Analysis of Future Spacecraft and systems

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 2025年第2期39卷 326-336页

作者： Harpole, George M. Arenberg, Jonathan W. Petach, Michael B. Northrop Grumman Corp Thermal Prop & Cryocooler Syst Dept Redondo Beach CA 90278 USA Northrop Grumman Corp Sci & Robot Explorat Redondo Beach CA 90278 USA

Future space telescopes require tight thermomechanical stability. The thermal analysis may be based on a nonlinear steady solution with a superimposed linear transient perturbation. This linearity allows frequency domain (FD) thermal solutions that retain high resolution when scaled. linearity allows generality through superposition. linear superelements can represent subsystems and thereby simplify interfaces. The (rare) prior spacecraft FD thermal analyses have been with NxN system matrices, converting lumped parameter (LP) time domain models to FD. This paper includes continuously distributed resistance and capacitance elements. Exact distributed element results differ greatly from LP renditions at higher frequency. Two FD methods are used together: a 2x2 matrix method with a bridge to an NxN matrix method. The 2x2 method allows the combination of elements in series/parallel configurations into overall elements. The 2x2 matrices can then be used in an NxN system matrix formulation. This paper includes FD analysis and programming methods, FD testing methods, and model to data comparisons. A thermal signal generator was developed for FD testing.

关键词： Thermal Modeling and Analysis Space Telescopes Spacecraft system Heat Transfer Coefficients Non Fourier Heat Conduction Frequency Domain linear system theory Superelement Control theory Distributed Parameter system

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