Time- and frequency-limited H2-optimal model order reduction of bilinear control systems

In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited H2-optimal model order reduction problem for bilinear control systems and derive first-order optimality conditions that a local optimum reduced-order model should satisfy. We then propose a heuristic algorithm that generates a reduced-order model, which tends to achieve these optimality conditions. The frequency-limited and the time-limited H2-pseudo-optimal model reduction problems are also considered wherein we restrict our focus on constructing a reduced-order model that satisfies a subset of the respective optimality conditions for the local optimum. Two new algorithms have been proposed that enforce two out of four optimality conditions on the reduced-order model upon convergence. The algorithms are tested on three numerical examples to validate the theoretical results presented in the paper. The numerical results confirm the efficacy of the proposed algorithms.Comment: International Journal of Systems Science (2021

Time-limited pseudo-optimal H2_2-model order reduction

A model order reduction algorithm is presented that generates a reduced-order model of the original high-order model, which ensures high-fidelity within the desired time interval. The reduced model satisfies a subset of the first-order optimality conditions for time-limited H$_2$-model reduction problem. The algorithm uses a computationally efficient Krylov subspace-based framework to generate the reduced model, and it is applicable to large-scale systems. The reduced-order model is parameterized to enforce a subset of the first-order optimality conditions in an iteration-free way. We also propose an adaptive framework of the algorithm, which ensures a monotonic decay in error irrespective of the choice of interpolation points and tangential directions. The efficacy of the algorithm is validated on benchmark model reduction problems.Comment: IET Control Theory & Applications (2020