Ja. Olkin et Pj. Titterton, USING SEMIDEFINITE PROGRAMMING FOR MULTI-CONSTRAINED H-2 CONTROLLER-DESIGN IN ACTIVE NOISE AND VIBRATION CONTROL, Journal of VLSI signal processing systems for signal, image, and video technology, 14(1), 1996, pp. 57-66
Citations number
13
Categorie Soggetti
Computer Sciences, Special Topics","Engineering, Eletrical & Electronic","Computer Science Information Systems
We consider the practical design of linear controllers to meet a given
set of H-2 specifications. The Q-parametrization reduces the problem
to a quadratic minimization subject to multiple quadratic constraints,
which we solve using semi-definite programming (SDP) methods. Each SD
P iteration requires calculating a primal and dual search direction an
d minimizing the cost function along the plane defined by these search
directions. The primal direction requires solving a least squares pro
blem whose normal equation matrix is composed of a block-Toeplitz port
ion plus other structured matrices. We make use of Kronecker products
and FFT's to greatly reduce the calculation. The dual search direction
and plane search are accelerated by low-rank representations of the S
DP structured matrices. As an example, we design controllers which exp
lore the optimal tradeoff between in-band residual and out-of-band enh
ancement of acoustic radiation from a (mathematically modeled) submerg
ed spherical shell, while simultaneously constraining two sensitivity
measures. For this example we show that significant reduction in out-o
f-band enhancement is possible with only minor in-band penalties.