Probability-one homotopy algorithms for full- and reduced-order H2/H∞ controller synthesis

✍ Scribed by Yuzhen Ge; Layne T. Watson; Emmanuel G. Collins Jr; Dennis S. Bernstein

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 883 KB
• Volume: 17
• Category: Article
• ISSN: 0143-2087
• DOI: 10.1002/(sici)1099-1514(199607/09)17:3<187::aid-oca572>3.0.co;2-o

✦ Synopsis

Homotopy algorithms for both full-and reduced-order LQG controller design problems with an H" constraint on disturbance attenuation are developed. The H" constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H 2 performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H 2 performance. The algorithms are based on two minimal parameter formulations: Ly, Bryson and Cannon's 2 x 2 block parametrization and the input normal Riccati form parametrization. An overparametrization 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 H2/H' synthesis. The nonmonotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.