Numerical simulation of large-scale dynamical systems plays a fundamental role in studying
a wide range of complex physical phenomena; however, the inherent large-scale nature of …

In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and
wide applicability for simulating large-scale mathematical models in engineering and the …

Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical
benchmark for reinforcement learning-based control of complex dynamical systems with …

A tensor decomposition approach for the solution of high-dimensional, fully nonlinear
Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear …

Dynamical systems are at the core of computational models for a wide range of complex
phenomena and, as a consequence, the simulation of dynamical systems has become a …

Efficient numerical algorithms for the solution of large and sparse matrix Riccati and
Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have …

In this paper, we will discuss the problem of optimal model order reduction of bilinear control
systems with respect to the generalization of the well-known \calH_2-norm for linear …

We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB)
control systems. Our contributions are threefold. First, we discuss the variational analysis …

The Loewner framework for model reduction is extended to the class of bilinear systems.
The main advantage of this framework over existing ones is that the Loewner pencil …