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Optimal Control and Other Complex Systems Paradigms in the Context of Turbulent Flows

  • T. Ritz
  • A. W. Hübler
Part of the International Centre for Mechanical Sciences book series (CISM, volume 369)

Abstract

Complex systems are high dimensional, nonlinear systems far from equilibrium. Turbulent fluids can therefore be considered as a typical example for complex systems. In these lectures, we present new principles and methodologies of complex systems research, that may help to understand and control the dynamics of turbulent flows. The dynamics of a high dimensional complex system can in many cases be estimated from simple models such as coupled maps dynamics, low dimensional systems of ODEs, singular motions, or genetic algorithms. The reduction of dimensionality means that a few order parameters govern the dynamics of the complex system.

While the mentioned models are simple, they still may contain a large number of parameters. These parameters can be determined from experiments if the experimental dynamics is complex, e.g. aperiodic or chaotic. However, if the experimental dynamics is simple, e.g. a fixed point dynamics, it is necessary to perturb it in order to reconstruct the model. Of course, perturbations are also necessary to control a system. The problem with these perturbations is that they may activate additional variables which are not included in the simple model. Thus, the simple model is in general no longer valid for the perturbed system. From the principle of the dynamical key, we derive a special class of aperiodic forcing functions, that overcome this problem and make it possible to investigate a complex system with spectroscopic methods based on the simple model. We study different methods of system identification and control of complex systems.

Finally, we assign a physical meaning to some of the attractors of the simple models. We formulate the physical meanings in terms of variation principles, including the principle of minimum resistance, the leadership and the simplification paradigm.

Keywords

Control Force Frequency Response Function Couple Oscillator Resonance Curve Unstable Periodic Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • T. Ritz
    • 1
  • A. W. Hübler
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA

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