Abstract

The paper presents a proof of stability of model reference adaptive control systems using direct control. The structure of the adaptive system is similar to that considered by Monopoli [1] and Narendra and Valavani [2] but contains an additional feedback term which ensures that the time derivative of the parameter error vector belongs to the L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> space. The output of the plant is shown to be bounded by expressing the plant feedback loop as an exponentially stable system with a time-varying gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{\phi}(\cdot)\in L^{2}</tex> in the feedback path.

Keywords

Bounded functionStability (learning theory)Controller (irrigation)Control theory (sociology)Adaptive controlDerivative (finance)Term (time)MathematicsComputer scienceDiscrete mathematicsControl (management)Mathematical analysisPhysicsArtificial intelligence

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1964 IEEE Transactions on Information Theory 508 citations

Publication Info

Year
1980
Type
article
Volume
25
Issue
3
Pages
440-448
Citations
605
Access
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Kumpati S. Narendra, Yuan-Hao Lin, L. Valavani (1980). Stable adaptive controller design, part II: Proof of stability. IEEE Transactions on Automatic Control , 25 (3) , 440-448. https://doi.org/10.1109/tac.1980.1102362

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DOI
10.1109/tac.1980.1102362