On the H2-pseudo-optimal bilinear model reduction

For large-scale linear time-invariant systems, several well-established model reduction techniques are available. Among these, the interpolation-based Iterative Rational Krylov Algorithm (IRKA) has proven very successful in many applications, yielding – upon convergence – a reduced order model (ROM) and interpolation points (shifts) that locally minimize the H2-norm of the approximation error. The concept of H2-pseudo-optimality refers to global optimality within the subspace of ROMs with fixed reduced poles. Although only the Lagrangian interpolation condition (and not the Hermite one) is being satisfied in this framework, H2-pseudo-optimality yields a global minimizer for the H2 error norm in the respective subspace. What is more, this concept has a series of further nice properties and applications that we will discuss in the talk. Recently, H2-optimal model reduction and interpolatory optimality conditions have been developed for bilinear systems too. The iterative algorithm B-IRKA satisfies – upon convergence – those optimality conditions and yields a locally optimal ROM, which basically interpolates the original Volterra series with certain weights and interpolation points. Similar to the linear case, in the talk we will extend the concept of H2-pseudo-optimality to the bilinear setting and discuss the convexity of the optimization problem. Further properties and possible applications of this framework in the bilinear model reduction will also be reported.      «

For large-scale linear time-invariant systems, several well-established model reduction techniques are available. Among these, the interpolation-based Iterative Rational Krylov Algorithm (IRKA) has proven very successful in many applications, yielding – upon convergence – a reduced order model (ROM) and interpolation points (shifts) that locally minimize the H2-norm of the approximation error. The concept of H2-pseudo-optimality refers to global optimality within the subspace of ROMs with fixed...     »