Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

Trentelman, Harry L.; Minh, Ha Binh; Rapisarda, Paolo

doi:10.1007/s00498-009-0043-6

Cited by 15 publications

(2 citation statements)

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“…In a balanced state representation the matrices corresponding to the maximal and the minimal storage function are diagonal and the inverse of each other; for passive systems and for bounded-real systems, this definition coincides with the classical one (see Desai and Pal (1984) and Opdenacker and Jonckheere (1988) a system, which we consider in the last part of this work. Structurepreserving model reduction is usually considered starting from a given state representation; recently, some authors (see Antoulas (2005), Antoulas (2004), Gugerçin and Antoulas (2004), Polyuga and van der Schaft (2010), Sorensen (2005), and Trentelman, Ha, and Rapisarda (2009)) have investigated the computation of reduced-order models from data. However, the data considered in these works are often of a special type, e.g.…”

Section: Introductionmentioning

confidence: 99%

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Rapisarda

Trentelman

2011

Automatica

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a b s t r a c tWe illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.

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Section: Introductionmentioning

confidence: 99%

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Rapisarda

Trentelman

2011

Automatica

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“…Further, a nonlinear extension of the positive and bounded real balanced truncation is provided in [98], where a generalization to dissipativity-preserving balancing is also presented. Moreover, a behavioral perspective on dissipativity-preserving model reduction is proposed in [173]. Appealingly, this method forms a generalization for passivity-preserving model reduction methods in the interpolatory and the balancing frameworks in [8] and [168], respectively.…”

Section: Balanced Truncationmentioning

confidence: 99%

From data to reduced-order models of complex dynamical systems

Burohman¹

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It is not possible to recall/mention all those whose support has made the completion of this thesis possible. I would like to thank all of them.Finally, I would like to express my deepest gratitude to my lovely family. Thank you very much for all your unconditional understanding, support, and prayers to my mother-in-law Ibu Sugiyah (Mbah Sugi) and family in Kalipalet. I am very grateful to be part of such a supportive family. I know it is not easy for you to allow your only daughter and granddaughter to be thousands of kilometers away to accompany me pursuing my dream abroad. Thank you for your patience and for believing in us. InsyaAllah, we will reunite soon.To my father and mother, Bapak Khotib Ma'mun and Ibu Suyati, thank you so much for your endless love and continuous prayers. Semoga kelulusan ini menjadi berkah untuk keluarga. To my brother, Om Aldi, thanks for looking after our parents when I could not be there. I am glad you are taking mathematics for your bachelor's study; I am also delighted to know you are very active in your higher education. Keep trying, learning, and praying for whatever you are dreaming of.To my dearest wife, Aidina Anisa, I am incredibly grateful to have you by my side on this journey. Thank you for never stop encouraging me and believing in me, especially when I felt inferior in facing challenges. Thank you for your patience when I was distracted and not able to take care of Haura or even take care of the family. You are my sunshine. I dedicate this success to you. The last year was a tough one, but how lucky I am to have you who understood and struggled with me to deal with the situation. Thank you for the countless moments we shared, and I look forward to what the future will bring us. To my beloved little daughter, Aliza Haura Syauqina, I cannot say anything but I love you so much! Thank you for your genuine love for me. Watching you grow during this PhD study has become my source of strength. Jadi anak solehah ya Haura.

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Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros

Freitas,

Rommes,

Martins

2022

Realization and Model Reduction of Dynamical Systems

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Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

Cited by 15 publications

References 25 publications

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

From data to reduced-order models of complex dynamical systems

Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros

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