Newton Raphson Rule Tuning

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Newton Raphson Rule Tuning
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Rules

• Consider a rule base with
• M rules, rth rule has the form
• IF x1 is Tr,1 AND AND xn is Tr,n THEN y is yr
  (or y is yr other stuff)
• TSK fuzzy system has mathematical form

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Scalar Newton-Raphson iteration
Example p2-50, p?

• Why?
• Consider pdp, ignore dp2, solve for dp
• Taylor series expansion.

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• What is G(p)?
• How do we ENGINEER G(p)?
• TSK f(x,p) to G(p)
• What do we know about p?
• Previous value of p
• New data about p

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New p Old p
New data
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(No Transcript)
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Matrix Inverses

• Defining relationships
• MM-1 I M-1M
• Primary use
• If Mxb then M-1MxM-1b hence xM-1b
• Variety of techniques to compute M-1
• M-1 exists only if M is square and full rank

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Pseudo Inverses

• Defining relationships
• MMMM MMMM MM MM MMMM
• Primary use
• If Mxb then xMbI-MMz
• Many ways to compute M
• All matrices have pseudo inverses
• Two Applications of Pseudo Inverses
• pinv function

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Modified Newton-Raphson iteration
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Example

• yx2
• Tuning the TSK approximation
• NRtuning.lib
• main()