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Probability‐one homotopy algorithms for full‐ and reduced‐order H 2 / H ∞ controller synthesis
Author(s) -
Ge Yuzhen,
Watson Layne T.,
Collins Jr Emmanuel G.,
Bernstein Dennis S.
Publication year - 1996
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199607/09)17:3<187::aid-oca572>3.0.co;2-o
Subject(s) - mathematics , homotopy analysis method , homotopy , parametrization (atmospheric modeling) , upper and lower bounds , riccati equation , norm (philosophy) , piecewise , algorithm , mathematical analysis , differential equation , pure mathematics , physics , quantum mechanics , political science , law , radiative transfer
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 × 2 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 2 / H ∞ synthesis. The non‐monotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.