ترغب بنشر مسار تعليمي؟ اضغط هنا

Structure-Preserving Interpolation of Bilinear Control Systems

134   0   0.0 ( 0 )
 نشر من قبل Steffen W. R. Werner
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.



قيم البحث

اقرأ أيضاً

In this paper, we present an interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear sys tems, and then provide conditions on projection spaces for the interpolation of structured subsystem transfer functions such that the system structure and parameter dependencies are preserved in the reduced-order model. Two benchmark examples with different parameter dependencies are used to demonstrate the theoretical analysis.
Suppressing vibrations in mechanical models, usually described by second-order dynamical systems, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model order reduct ion to construct easy-to-evaluate surrogates for the original dynamical system having the same structure. In our work, we present an overview of our recently developed structure-preserving model reduction methods for second-order systems. These methods are based on modal and balanced truncation in different variants, as well as on rational interpolation. Numerical examples are used to illustrate the effectiveness of all described methods.
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional port-Hamiltoni an element is defined that enables a structure preserving discretization of the infinite dimensional model that inherits the Dirac structure, the underlying energy balance and matches the Hamiltonian function on any, possibly nonuniform mesh of the spatial geometry.
125 - Yu Cao , Jianfeng Lu 2021
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations, and carry out detailed error analysis and absolute stability analysis. Both error and absolute stability analysis are validated by numerical examples.
163 - Qing Cheng , Jie Shen 2021
We propose a new Lagrange multiplier approach to construct positivity preserving schemes for parabolic type equations. The new approach introduces a space-time Lagrange multiplier to enforce the positivity with the Karush-Kuhn-Tucker (KKT) conditions . We then use a predictor-corrector approach to construct a class of positivity schemes: with a generic semi-implicit or implicit scheme as the prediction step, and the correction step, which enforces the positivity, can be implemented with negligible cost. We also present a modification which allows us to construct schemes which, in addition to positivity preserving, is also mass conserving. This new approach is not restricted to any particular spatial discretization and can be combined with various time discretization schemes. We establish stability results for our first- and second-order schemes under a general setting, and present ample numerical results to validate the new approach.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا