Search

In this paper, we focus on the topic of model order reduction (MOR) for coupled systems. At first, an approximation via Laguerre polynomials expansions to controllability and observability gramians for such systems are presented, which provides a low-rank decomposition form whose factors are constructed from a recurrence formula instead of Lyapunov equations. Then, in combination of balanced truncation and dominant subspace projection method, a series of MOR algorithms are proposed that preserve the coupled structures. What's more, some main properties of reduced-order models, such as stability preservation, are well discussed. Finally, three numerical simulations are provided to illustrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a series of structure-preserving model order reduction algorithms for K-power bilinear systems via Laguerre functions. The method first aims to rewritten the K-power bilinear system as a general bilinear system and calculate the approximate low-rank factors of the cross Gramian of the bilinear system by combining the idea of Laguerre functions expansion of the matrix exponential function. After that, the approximate balanced system of the K-power bilinear system is constructed by the corresponding projection transformation of each subsystem. In order to achieve the purpose of model order reduction, the states with smaller singular values are then truncated, so as to further obtain the reduced order model. For this approach, there is a disadvantage that unstable systems may be generated although the original one is stable. To alleviate the inadequacies of this approach, we have improved the model reduction procedure, which is based upon the dominant subspace projection method. In addition, we also carried out a correlation analysis on the stability of improved algorithms. Finally, numerical experiments are employed to substantiate the effectiveness of the presented algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model order reduction (MOR) method based on general orthogonal polynomials for K-power bilinear systems in the time domain. Constructing proper projection matrices by solving a series of linear equations, a reduced K-power bilinear system is produced, which preserves the original coupled structure. It can match several expansion coefficients of the original output. Then the error bound of our algorithm is also investigated. Moreover, the stability of the reduced system is discussed as well. Finally, two numerical examples are provided to illustrate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

The cross Gramian is a useful tool in model order reduction but only applicable to square dynamical systems. Throughout this paper, time-limited cross Gramians is firstly extended to square bilinear systems that satisfies a generalized Sylvester equation, and then concepts from decentralized control are used to approximate a cross Gramian for non-square bilinear systems. In order to illustrate these cross Gramians, they are calculated efficiently based on shifted Legendre polynomials and applied to dimension reduction, which leads to a lower dimensional model by truncating the states that are associated with smaller approximate generalized Hankel singular values. In combination of the dominant subspace projection method, our reduction procedure is modified to produce a bounded-input bounded-output stable-preserved reduced model under some certain conditions. At last, the performance of numerical experiments indicates the validity of our reduction methods. [ABSTRACT FROM AUTHOR]