# Probability-One Homotopy Algorithms for Full and Reduced Order H-squared/H-to Infinity Controller Synthesis

1994) Probability-One Homotopy Algorithms for Full and Reduced Order H-squared/H-to Infinity Controller Synthesis. Technical Report ncstrl.vatech_cs//TR-94-01, Computer Science, Virginia Polytechnic Institute and State University. (

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## Abstract

Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H-to infinity constraint on disturbance attenuation are developed. The H-to infinity constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper boundary on H-squared performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H-squared performance. The algorithms are based on two minimal parameter formulations: Ly, Bryson, and Cannon's 2X2 block parametrization and the input normal Riccati form parametrization. An over-parametrization formulation is also proposed. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H-squared/H-to infinity synthesis. The nonmonocity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated that standard continuation are necessary.

Item Type: | Departmental Technical Report |
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Subjects: | Computer Science > Historical Collection(Till Dec 2001) |

ID Code: | 383 |

Deposited By: | User autouser |

Deposited On: | 05 December 2001 |

Alternative Locations: | URL:ftp://ei.cs.vt.edu/pub/TechnicalReports/1994/TR-94-01.ps.gz, URL:http://historical.ncstrl.org/tr/ps/vatech_cs/TR-94-01.ps |