[Quote] Abstract – There are none.
From Guaranteed Margins for LQG Regulartors J.C. Doyle (1978) IEEE Transactions on Automatic Control 23(4), pp. 756- 757
The abstract has one sentence: There are none and the first paragraph of this short paper explains the uniqueness of the abstract:
Considerable attention has been given lately to the issue of robustness of linear-quadratic (LQ) regulators. The recent work by Safonov and Athans[1] has extended to the multivariable case the now well-known guarantee of 60(deg) phase and 6dB gain margin for such controllers. However, for even the single-input, single-output case there has remained the question of whether there exist any guaranteed margins for the full LQG (Kalman filter in the loop) regulator. By counterexample, this note answers that question; there are none.
Quoting the whole abstract is an intention of little entertainment, whereas the content may not be of any interests to astronomers and statisticians. There is a long winding evolutionary history in Automatic Control, which has dragged many mathematicians, applied mathematicians, and statisticians (The earlier versions of Kalman filter, AIC, and MDL appeared in this journal).
- M.G. Safonov and M. Athans (1977), IEEE Transactions on Automatic Control, 22 (Apr.), pp. 173-179[↩]
hlee:
I think I have to correct about Kalman filter. The first publication of Kalman filter was not accepted for this journal and eventually the paper was published in a Chilean journal.
01-10-2008, 10:28 pm