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Identification and Adaptive Control of the Uncertain Lorenz System

[+] Author Affiliations
Hossein Nejat Pishkenari, Mohammad Shahrokhi

Sharif University of Technology

Paper No. IMECE2005-80393, pp. 1105-1111; 7 pages
doi:10.1115/IMECE2005-80393
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Dynamic Systems and Control, Parts A and B
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 0-7918-4216-9 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

In this paper an identification method which can estimate the unknown parameters of a general nonlinear system based on three techniques (gradient, least-squares and rapid identification) has been developed. The stability of the proposed schemes has been shown using the Lyapunov stability theorem. The properties of each identification technique have been discussed briefly. Open loop identification of the Lorenz chaotic system is presented to show the effectiveness of the proposed approach. To illustrate the efficiency of the identification method for control purposes, it has been applied for controlling the well-known Lorenz system. By exploiting the property of the system a novel singularity-free controller is proposed. The stability of controller has been shown by a Lyapunov function. The designed controller coupled with the proposed identification technique can stabilize the uncertain Lorenz system. The effectiveness of the approach has been shown through simulation.

Copyright © 2005 by ASME

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