IngentaConnect Using Semi-Definite Programming for Multi-Constrained H

Authors: Olkin J.A.¹; Titterton Jr. P.J.¹

Source: The Journal of VLSI Signal Processing, Volume 14, Number 1, 1996 , pp. 57-66(10)

Publisher: Springer

Abstract:

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 SDP iteration requires calculating a primal and dual search direction and minimizing the cost function along the plane defined by these search directions. The primal direction requires solving a least squares problem whose normal equation matrix is composed of a block-Toeplitz portion 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 SDP structured matrices.

As an example, we design controllers which explore the optimal tradeoff between in-band residual and out-of-band enhancement of acoustic radiation from a (mathematically modeled) submerged spherical shell, while simultaneously constraining two sensitivity measures. For this example we show that significant reduction in out-of-band enhancement is possible with only minor in-band penalties.

Language: English

Document Type: Regular paper

Affiliations: 1: Applied Control and Signal Processing Group, SRI International, Menlo Park, CA 94025

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$47.00 plus tax Refund Policy

Using Semi-Definite Programming for Multi-Constrained H_2Controller Design in Active Noise and Vibration Control