Model order reduction for bilinear control systems with inhomogeneous initial conditions

Abstract

This work focuses on the model order reduction problem for bilinear control systems with nonzero initial conditions. Based on the Volterra series analysis, the system response can be decomposed into three parts. The first two parts are the zero input response and zero initial condition response of the system. The third part describes the response which couples the effect of the nonzero initial condition and the nonzero input.The system corresponding to the third part is a bilinear control system with a special time-varying input coefficient matrix. We show that such a system is equivalent to a time-invariant bilinear control system, and conventional model reduction methods can be applied to reduce it. We propose to reduce each of the component responses independently and then combine them to approximate the full system response. This method is of high flexibility and shows promising results. ARTICLE HISTORY

Model reduction for second-order systems with inhomogeneous initial conditions

“…where R T SO , R T x0 , R T v0 and S SO are the corresponding lowrank factors of P T SO , P T x0 , P T v0 and Q SO . Applying balanced truncation for second-order systems based on the low-rank factors of the combined Gramains P c and Q c from equation (10) results in a reduced-order system that takes into account the input to state and the initial conditions to state mappings.…”

“…Proposition 5.1. The position controllability Gramian of the first order system (4) with B as in equation ( 11) is equal to the Gramian P c in equation (10).…”

“…This superposition is used to reduce these two systems, separately. Extensions of the proposed methodology for the class of bilinear systems is proposed in [10] and [22] based on different splittings.…”

Simulation and Automated Modeling of Microwave Circuits: State-of-the-Art and Emerging Trends

“…These approaches, although mostly developed and applied in domains remotely related to nonlinear microwave devices and RF circuits, hold significant potentials for advancing the simulation and modeling for those circuits. For example, the recent work in [104] shows the relation of some of those approaches to the Volterra series of nonlinear systems which are known to model distortion effects of nonlinear circuits.…”

Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds

“…The above splitting was considered in [16], where the authors discuss a balancing approach to produce reduced order models (ROMs). Additionally, MOR of (1) based on a different splitting was proposed in [9]. However, theoretical questions remain open for this approaches such as the error analysis.…”