H2 order-reduction for bilinear systems based on Grassmann manifold

Xu, Kang-Li; Jiang, Yao‐Lin; Yang, Zhixia

doi:10.1016/j.jfranklin.2015.06.022

Cited by 8 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the matrices C i , G i are given in (5), and x i (0) = x i0 is the initial condition of (22). The transfer function is given by…”

Section: ε-Embedding Technique Of Subsystemsmentioning

confidence: 99%

“…Its goal is to replace the original large‐scale system by a small one such that the computation cost is significantly reduced and the efficiency of the simulation is obviously improved. Notice that these coupled systems are often described by differential equations [4, 5]. Thus, they can be solved by many iterative methods, such as waveform relaxation methods [6, 7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Balanced truncation with ε‐embedding for coupled dynamical systems

Jiang

Chen

Yang

2018

IET Circuits, Devices & Systems

View full text Add to dashboard Cite

The authors focus on exploring the ε-embedding balanced truncation method of coupled systems. First, the coupled system is converted into a closed-loop system. Then, the ε-embedding technique and the Cholesky factor-alternating direction implicit algorithm are introduced to establish the balanced truncation method. The error bound and the stability of the resulting reduced-order system are discussed. Furthermore, the proposed method is applied to reduce the order of each subsystem such that the original interconnected structure is preserved. The error bound and the stability of the corresponding reduced-order system are also investigated. Finally, two numerical examples are employed to demonstrate the efficiency of the proposed method.

show abstract

“…where the matrices C i , G i are given in (5), and x i (0) = x i0 is the initial condition of (22). The transfer function is given by…”

Section: ε-Embedding Technique Of Subsystemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Balanced truncation with ε‐embedding for coupled dynamical systems

Jiang

Chen

Yang

2018

IET Circuits, Devices & Systems

View full text Add to dashboard Cite

show abstract

“…Prior work To the best of our knowledge, the contribution of the paper is new. Model reduction of bilinear systems is an established topic, without claiming completeness, we mention Bai and Skoogh (2006); Zhang and Lam (2002); Wang and Jiang (2012); Xu et al (2015); Breiten and Damm (2010); Benner and Breiten (2015); Flagg and Gugercin (2015); Feng and Benner (2007); Lin et al (2007); Flagg (2012). In particular, moment matching methods for bilinear systems were proposed in Bai and Skoogh (2006); Feng and Benner (2007); Lin et al (2007); Flagg (2012); Breiten and Damm (2010); Benner and Breiten (2015); Flagg and Gugercin (2015); Wang and Jiang (2012) and for general non-linear systems in Astolfi (2010).…”

Section: Problem Formulationmentioning

confidence: 99%

Moment matching for bilinear systems with nice selections

Petreczky

Wiśniewski

Leth³

2016

IFAC-PapersOnLine

View full text Add to dashboard Cite

The paper develops a method for model reduction of bilinear control systems. It leans upon the observation that the input-output map of a bilinear system has a particularly simple Fliess series expansion. Subsequently, a model reduction algorithm is formulated such that the coefficients of Fliess series expansion for the original and reduced systems match up to certain predefined sets -nice selections. Algorithms for computing matrix representations of unobservability and reachability spaces complying with a nice selection are provided. Subsequently, they are used for calculating a partial realization of a given input-output map.Prior work To the best of our knowledge, the contribution of the paper is new. Model reduction of bilinear systems is an established topic, without claiming completeness, we mention Bai and Skoogh (2006); Zhang and Lam (2002); Wang and Jiang (2012); Xu et al. (2015); Breiten and Damm (2010); Benner and Breiten (2015); Flagg and Gugercin (2015); Feng and Benner (2007); Lin et al. (2007); Flagg (2012). In particular, moment matching methods for bilinear systems were proposed in Bai and Skoogh (2006); Feng and Benner (2007); Lin et al. (2007); Flagg (2012); Breiten and Damm (2010); Benner and Breiten (2015); Flagg and Gugercin (2015); Wang and Jiang (2012) and for general non-linear systems in Astolfi (2010). The current paper represents another version of moment matching for bilinear systems. In Flagg (2012); Breiten and Damm (2010); Benner and Breiten (2015) the concept of moment matching at some frequencies σ 1 , . . . , σ k was defined. The papers Bai and Skoogh (2006); Feng and Benner (2007); Lin et al. (2007) correspond to moment matching at zero frequency (σ = 0). The cur-arXiv:1605.04414v1 [math.OC]

show abstract

“…In [25], H 2 optimal MOR problems were investigated for the socalled K-power systems as a special class of bilinear systems. Xu et al showed that the H 2 optimal MOR problem of the bilinear system could be considered as the unconstrained minimization problem on the Grassmann manifold by using Gramians of controllability and observability [26] and cross Gramians of the bilinear system [27]. Since the H 2 optimization problem existed on the Grassmann manifold, the algorithm was reliable and could quickly converge to the minimal solution.…”

Section: Introductionmentioning

confidence: 99%

H₂model order reduction of bilinear systems via linear matrix inequality approach

Soloklo

Bigdeli

2023

IET Control Theory & Appl

View full text Add to dashboard Cite

This paper proposes an H2‐optimal model order reduction (MOR) method for bilinear systems based on the linear matrix inequality (LMI) approach. In this method, to reduce the computational complexity, at first, a reduced middle‐order approximation of the system is derived based on common bilinear MOR methods. Next, the H2 norm of the error system is minimized to obtain the reduced‐order bilinear model. Generalized Lyapunov equations are added to the optimization problem as LMI constraints to guarantee the specification of type II Gramians of the bilinear system to improve accuracy. Besides, two stability conditions are included to the optimization problem as its constraints to preserve stability of reduced‐order bilinear model. One of advantages of the proposed method is the need for only one of the Gramians of controllability or observability. Since the proposed H2‐optimal MOR problem is a polynomial matrix inequality (PMI) problem, an iterative method is used to convert the PMI to the LMI problems and solve the optimization problem. Three bilinear test systems are considered to show the proposed method's efficiency, while its performance is compared with some classical methods. Results show that the proposed methods lead to a more accurate reduced‐order model than other MOR methods.

show abstract

H2 order-reduction for bilinear systems based on Grassmann manifold

Cited by 8 publications

References 14 publications

Balanced truncation with ε‐embedding for coupled dynamical systems

Balanced truncation with ε‐embedding for coupled dynamical systems

Moment matching for bilinear systems with nice selections

H₂model order reduction of bilinear systems via linear matrix inequality approach

Contact Info

Product

Resources

About

H2 order-reduction for bilinear systems based on Grassmann manifold

Cited by 8 publications

References 14 publications

Balanced truncation with ε‐embedding for coupled dynamical systems

Balanced truncation with ε‐embedding for coupled dynamical systems

Moment matching for bilinear systems with nice selections

H2model order reduction of bilinear systems via linear matrix inequality approach

Contact Info

Product

Resources

About

H₂model order reduction of bilinear systems via linear matrix inequality approach