hinfsyn: very slow if stabilizing controller cannot be found

This

from control import ss, hinfsyn

# from control import tf, augw
# g = tf([1],[1,0.75])
# w1 = tf([1,1.25],[1.25,0.0125])
# p  = augw(g,w1)

p = ss([[-0.01, -0.992],
        [ 0.  ,  -0.75 ]],
       [[ 0.992,  0.   ],
        [ 0.   ,  1.   ]],
       [[ 1. , -0.8],
        [ 0. , -1. ]],
       [[ 0.8,  0. ],
        [ 1.,   0. ]])

k,n,gamma,rcond = hinfsyn(p,1,1)

takes very long to report that a stabilizing controller cannot be found (or so I assume: I gave up waiting). I changed the initial gamma in control.robust.hinfsyn from 1e100 (!!!) from 1e2, up to 1e5, and found execution time (best of 3 in each case):

gamma	time [s]
1e2	0.8
1e3	0.9
1e4	2.3
1e5	15.7

If I add "job=1" to the sb10ad argument list, the run-time drops back to 0.8s for initial gamma of 1e5, and also for 1e100.

The sb10ad SLICOT SB10AD comments say "job=3", the Slycot default, is the fastest. job=1 might be bisection search (I don't understand what the SLICOT docs say; Slycot help comment claims job=1 is bisection.)

I don't know what a good initial gamma value is; an old reference of mine says 1e6 is "very large"; this is Maciejowski, published in 1989.

So, possible fixes are to change the SB10AD search type via the job parameter, or to reduce the initial gamma value.

@murrayrm

Hello,

As you suggest, two approaches are possible to fix this problem. I have seen that @murrayrm asked for help on this topic.

Do you expect that changing the default job or the initial gamma will cause regressions in some cases?

I don't have the expertise to understand the implications. I don't think hinfsyn is used much, so I doubt regressions or backward compatibility are a concern.

Matlab's hinfsyn allows one to supply a particular gamma, or a search range of gamma values https://www.mathworks.com/help/robust/ref/hinfsyn.html

From a quick look at sb10ad I'm not sure if we can support those, but we could add an optional initial gamma value to pass to sb10ad.

The "h-infinite wait" seems to pose a problem on PowerPC: https://bugzilla.opensuse.org/show_bug.cgi?id=1172555

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hinfsyn: very slow if stabilizing controller cannot be found #152

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hinfsyn: very slow if stabilizing controller cannot be found #152

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don4get commented on Jan 5, 2019

roryyorke commented on Jan 6, 2019

bnavigator commented on Jun 9, 2020

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