An Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions

Authors

  • Gabriel Pedro Ramos Maciel Escola Politécnicada Universidade de São Paulo
  • Roberto Spinola Barbosa Escola Politécnica da Universidade de São Paulo

DOI:

https://doi.org/10.5540/tema.2018.019.02.197

Keywords:

model reduction, dynamical systems, error bound

Abstract

In recent years, a great effort has been taken focused on the development of reduced order modeling techniques of dynamical systems. This necessity is pushed by the requirement for efficient numerical techniques for simulations of dynamical systems arising from structural dynamics, controller design, circuit simulation, fluid dynamics and micro electromechanical systems.

We introduce a method to calculate the minimum upper $\mathcal{L}_2$ error bound of a linear time invaritant reduced order model considering any possible unitary initial conditions (IC). As a consequence, the proposed method calculates the unitary IC vector which leads to the maximum $\mathcal{L}_2$ norm of the error. Based on this error bound, it is discussed the capacity of a reduced order system to approximate the free transient response in the worst case scenario.

Author Biographies

Gabriel Pedro Ramos Maciel, Escola Politécnicada Universidade de São Paulo

Escola Politécnica da Universidade de São Paulo

Roberto Spinola Barbosa, Escola Politécnica da Universidade de São Paulo

Prof. Dr. at Escola Politécnica da Universidade de São Paulo

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Published

2018-09-12

How to Cite

Maciel, G. P. R., & Barbosa, R. S. (2018). An Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions. Trends in Computational and Applied Mathematics, 19(2), 197. https://doi.org/10.5540/tema.2018.019.02.197

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Original Article