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shimodatakaki / mypy

mypy, an useful toolbox for control engineers
GNU General Public License v3.0
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On Fractional Constraints #5

Open shimodatakaki opened 6 years ago

shimodatakaki commented 6 years ago

Fractional constraints (a0.T xn+b0)/(c0.T xd + d0) < l0 can be transformed into ⇔ a0.T xn+b0 < l0(c0.T xd + d0) ⇔ a0.T xn - l0 c0.T xd < l0 d0 - b0 ⇔ [a0.T, - l0 c0.T] [ xn, xd ].T < l0d0 - b0 This means fractional constraints are equivalent to linear/quadratic constraints under some assumptions. ( c0.T xd + d0 > 0)

For now the controller C is defined as (a0.T xn+b0)/ (Const.), but we can let controller C = (a0.T xn+b0)/(c0.T xd + d0) to optimize both numerator and denominator coefficients.

shimodatakaki commented 6 years ago

This idea seemed good, but now is found to take much computation cost (since it uses SOCP). I added almost exact Fractional Controller Design (SOCP), but also added pseudo one that needs much less computation (using LP) @ 5581ffec1bf1eba2020ae79ff0a270890c923456 .

shimodatakaki commented 6 years ago

SDP Relaxation seemed another possibility, but SDR takes so much memory and time! Is LP best???