Wyniki wyszukiwania - Biblioteka Nauki

1

Delay Systems Synthesis using Multi-Layer Perceptron Network

100%

Plonis D. , Katkevičius A. , Urbanavičius V. , Miniotas D. , Serackis A. , Gurskas A.

Acta Physica Polonica A

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2018

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tom 133

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nr 5

1281-1286

EN

The aim of this paper is to accelerate development and investigation of the delay systems. The computational time for investigation of particular design of delay system may take from several minutes up to several days. To achieve the required constructional parameters of the system, the iterative calculations usually should be repeated many times. In this paper, an artificial neural network is proposed to be used as the universal approximator for solving mathematical problems of delay system investigation instead of usual analytical and numerical techniques. The application of a multi-layer perceptron is proposed for approximation of solution space with discrete estimates, which were initially received by application of numerical techniques. Different structures of the multi-layer perceptron were tested for approximation. The difference between delay systems synthesis, which was estimated using numerical techniques and trained multi-layer perceptron did not exceed 5% for any of the six design parameter values. The execution time for estimating single delay system was reduced from 240 s to 20 ms. Such fast estimation of design parameters enables performing delay system analysis and design in real time, preserving time for structure visualization in 3D or virtual reality environment.

2

On the constrained controllability of dynamical systems with multiple delays in the state

88%

Sikora B.

International Journal of Applied Mathematics and Computer Science

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2003

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tom 13

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nr 4

469-479

EN

Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllability with constrained controls for dynamical systems with delays in the state are established. Various types of constraints are considered. Numerical examples illustrate the theoretical analysis. An example of a real technical dynamical system is given to indicate one of possible practical applications of the theoretical results.

3

On-line parameter and delay estimation of continuous-time dynamic systems

75%

Kozłowski J. , Kowalczuk Z.

International Journal of Applied Mathematics and Computer Science

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2015

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tom 25

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nr 2

223-232

EN

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

4

Discrete-averaged mathematical models of neutral delay systems

75%

Kozera W.

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1998

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tom Vol. 7, no. 1/2

105-120

EN

This article presents a method of determining discrete-averaged mathematical models of multi-input multi-output (MIMO) linear time-invariant systems with constant commensurate delays characterized by a finite-dimensional subspace of antistable states. The proposed method generalizes the, presented in works [10 - 13], methods of determining models for retarded-delay systems to include systems of neutral type. The finite-dimensional approximation substantially facilitates analysis and enables designing the physically implemented control laws of the systems in question. To illustrate these problems, included are simple examples of determining unstable eigenvalues and of stabilization of the plant with a digital-analog (hybrid) compensator.

5

Motion planning, equivalence, infinite dimensional systems

75%

Rouchon P.

International Journal of Applied Mathematics and Computer Science

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2001

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tom 11

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nr 1

165-188

EN

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al. 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with -trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.

6

Motion Planning, Equivalence, Infinite Dimensional Systems

63%

Rouchon P.

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2001

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tom Vol. 11, no 1

165-188

EN

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.