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Adaptive Control, Filtering, and Signal Processing pp 271–298Cite as

Potential Self-Tuning Analysis of Stochastic Adaptive Control

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 74))

Abstract

In this paper we present the first stage of a unified two-stage approach to analyzing stochastic adaptive control. In the first stage, we study the issue of potential self-tuning where we ask the question whether a certainty-equivalence adaptive control scheme achieves the same control objective as the ideal control design at the potential convergence points of the estimation algorithm. We exploit the fact that this important property can be analyzed independent of the estimation method that is used, without restoring to complicated convergence analysis. For linear time-invariant systems, this reduces to simply studying two identifiability equations; the Identifiability Equation for Internal Excitation (IEIE) and the Identifiability Equation for External Excitation (IE3) whose solutions determine the potential convergence points of the parameter estimates. Sufficient conditions and necessary conditions are then derived for potential self-tuning and identifiability of general control schemes. Applications of these general results to specific adaptive control policies then show that regardless of the external excitation, the certainty-equivalence adaptive control based on generalized Minimum-Variance, generalized predictive, and pole-placement control are potentially self-tuning. On the other hand, the LQG feedforward and feedback control designs are shown to require sufficient external excitation. In the next stage, we will show how to proceed from potential self-tuning to asymptotic self-tuning.

This research has been supported by the NSF grant FD92-11025-REN.

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Authors and Affiliations

  1. EECS Dept., University of California at Berkeley, Berkeley, CA, 94720, USA

    Karim Nassiri-Toussi & Wei Ren

Authors
  1. Karim Nassiri-Toussi
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  2. Wei Ren
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Editor information

Editors and Affiliations

  1. Department of Automatic Control, Lund Institute of Technology, Lund, Sweden

    K. J. Åström

  2. Department of Electrical Engineering and Computer Science, The University of Newcastle, Rankin Drive, Newcastle, NSW, 2308, Australia

    G. C. Goodwin

  3. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 West Main Street, Urbana, IL, 61801-2307, USA

    P. R. Kumar

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© 1995 Springer Science+Business Media New York

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Nassiri-Toussi, K., Ren, W. (1995). Potential Self-Tuning Analysis of Stochastic Adaptive Control. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_12

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  • DOI: https://doi.org/10.1007/978-1-4419-8568-2_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6439-2

  • Online ISBN: 978-1-4419-8568-2

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