A trust region method for optimal H<inf>2</inf> model reduction

Abstract

We present a trust-region approach for optimal H2 model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H2 error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with respect to H2 error criteria. Unlike existing H2 descent methods, the method does not require solving any Lyapunov equations and is both numerically stable and computationally tractable even for very large order systems. This method appears to be the first descent approach that uses Hessian information for optimal H2 model reduction of MIMO dynamical systems.

An iterative SVD-tangential interpolation method for medium-scale MIMO systems approximation with application on flexible aircraft

“…With reference to Table I, it appears that our implementation of the MIMO IRKA (also denoted ITIA) is good. Indeed, for r = 2, results are very similar, and, for r = 20, even better than the one provided in [12]. Note that this is may be caused by the initial shift selection.…”

“…Later, in [12], authors extended it to MIMO systems, with a complex Trust Region algorithm, which guarantees convergence and preserves stability.…”

“…As the previous one, this procedure shows to be effective in many classical benchmark [4] but does not preserve stability, a priori. The contribution of [12] is to propose a guaranteed descent algorithm.…”

“…Table I also illustrates that ISTIA, even if theoretically less optimal in the H 2 sense, is very close to the optimal value (indeed, here it provides the same results as the ITIA). Since no illustration of MIMO cases are available in [12], next experiments will focus on a MIMO benchmark without comparing with [12] but simply our implementation of the MIMO IRKA (denoted ITIA).…”

“…To compare with respect to the complex but very powerful approach presented in [12] (namely MIMO IRKA or ITIA), the SISO subsystem of ISS-1R Module (n = 270) is considered. With reference to Table I, it appears that our implementation of the MIMO IRKA (also denoted ITIA) is good.…”