• Title/Summary/Keyword: dynamical systems

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On the Stability Theory in Dynamical Systems

  • Koo, Ki-Shik
    • Journal of the Chungcheong Mathematical Society
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    • v.7 no.1
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    • pp.211-216
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    • 1994
  • In this paper, we show that a continuous function $f:X{\rightarrow}X$ has regular coordinate then (X, f) has some properties which are similar to results following from a hypothesis of hyperbolicity.

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Global Synchronization of Two Different Chaotic Systems via Nonlinear Control

  • Emadzadeh, Amir Abbas;Haeri, Mohammad
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.985-989
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    • 2005
  • This paper presents chaos synchronization between two different chaotic systems using nonlinear control method. The proposed technique is applied to achieve chaos synchronization for the Lorenz and Rossler dynamical systems. Numerical simulations are also implemented to verify the results.

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Diagnosis of Linear Systems with Structured Uncertainties based on Guaranteed State Observation

  • Planchon, Philippe;Lunze, Jan
    • International Journal of Control, Automation, and Systems
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    • v.6 no.3
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    • pp.306-319
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    • 2008
  • Reaching fault tolerance in technological systems requires to detect malfunctions. This paper presents a diagnostic method that is robust with respect to unknown-but-bounded uncertainties of the dynamical model and the measurements. By using models of the faultless and the faulty behaviours, a state-set observer computes polyhedral sets from which the consistency of the models with the interval measurements is determined. The diagnostic result is proven to be complete, i.e., the set of faults obtained by the diagnostic algorithm includes the actual fault. The algorithm is illustrated by an application example.

Robust control of linear systems under structured nonlinear time-varying perturbations I - Analysis

  • Bambang, Riyanto-T.;Shimemura, Etsujiro
    • 제어로봇시스템학회:학술대회논문집
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    • 1993.10b
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    • pp.81-87
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    • 1993
  • In this paper robust stability conditions are obtained for linear dynamical systems under structured nonlinear time-varying perturbations, using absolute stability theory and the concept of dissipative systems. The conditions are expressed in terms of solutions to linear matrix inequality(LMI). Based on this result, a synthesis methodology is developed for robust feedback controllers with worst-case H$_{2}$ perforrmance via convex optimization and LMI formulation.

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Chaos in nonlinear control systems

  • Lee, Joon-Suh;Chang, Kun-Soo
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.758-762
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    • 1994
  • Complicated dynamical behavior can occur in model reference adaptive control systems when two external sinusoidal signals are introduced although the plant and reference model are stable linear first older systems. The phase portrait plot and the power spectral analysis indicate chaotic behavior. In the system treated, a positive Lyapuniov exponent and non-integer dimension clearly manifest chaotic nature of the system.

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Nonlinear Observers for Perspective Time-Varying Linear Systems

  • Itoh, Masahiko
    • 제어로봇시스템학회:학술대회논문집
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    • 2002.10a
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    • pp.83.5-83
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    • 2002
  • Perspective dynamical systems arise in machine vision, in which only perspective observation is available, and the essential problem is to estimate the state and /or unknown parameters for a moving rigid body based on the observed information. This paper proposes and studies a Luenberger-type observer for perspective tim e-varying linear systems. In particular, assuming a given perspective time-varying linear system to be Lyapunov stable and to satisfy some sort of observability condition, it is shown that the estimation error converges exponentially to zero. Finally, a simple numerical exam pie is presented to illustrate the result obtained.

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Composite Neural Networks for Controlling Semi-Linear Dynamical Systrms: Example from Inverted Pendulum Problem

  • Yamamoto, Yoshinobu;Anzai, Yuichiro
    • 제어로봇시스템학회:학술대회논문집
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    • 1989.10a
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    • pp.1129-1134
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    • 1989
  • In this paper, we propose a neural network for learning to control semi-linear dynamical systems. The network is a composite system of four three-layer backpropagation subnetworks, and is able to control inverted pendulums better than systems based on modern control theory at least in some ranges of parameters. Three of the four subnetworks in our network system process angles, velocities, and positions of a moving inverted pendulum, respectively. The outputs from those three subnetworks are input to the remaining subnetwork that makes control decisions. Each of the four subnetworks learns connection weights independently by backpropagation algorithms. Teaching signals are given by the human operator. Also, input signals are generated by the human operator, but they are converted by preprocessors to actual input data for the three subnetworks except for the network for control decisions. The whole system is implemented on both of 16 bit personal computers and 32 bit workstations. First, we briefly provide the research background and the inverted pendulum problem itself, followed by the description of our composite neural network model. Next, some results from the simulation are given, which are subsequently compared with the results from a control system based on modern control theory. Then, some discussions and conclusion follow.

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