Optimal modal truncation

@article{Vuillemin2021OptimalMT,
  title={Optimal modal truncation},
  author={Pierre Vuillemin and Adrien Maillard and Charles Poussot-Vassal},
  journal={Syst. Control. Lett.},
  year={2021},
  volume={156},
  pages={105011}
}
This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation problem. The latter is reformulated as an equivalent convex integer or mixed-integer program. Numerical examples highlight the concept and optimisation approach. 

Figures and Tables from this paper

References

SHOWING 1-10 OF 20 REFERENCES
Multiobjective output-feedback control via LMI optimization
TLDR
An overview of a linear matrix inequality (LMI) approach to the multiobjective synthesis of linear output-feedback controllers is presented and the validity of this approach is illustrated by a realistic design example. Expand
Poles residues descent algorithm for optimal frequency-limited ℋ2 model approximation
TLDR
A new formulation of the frequency-limited ℋ2 model approximation error is presented and its gradient derived and it is then used in a descent algorithm which does not require to solve any Lyapunov equations but one eigenvalue problem for the full-order model. Expand
Robust and optimal control
  • J. Doyle
  • Mathematics
  • Proceedings of 35th IEEE Conference on Decision and Control
  • 1996
This paper will very briefly review the history of the relationship between modern optimal control and robust control. The latter is commonly viewed as having arisen in reaction to certain perceivedExpand
Efficient Computation of Multivariable Transfer Function Dominant Poles Using Subspace Acceleration
This paper describes a new algorithm to compute the dominant poles of a high-order multiple-input multiple-output (MIMO) transfer function. The algorithm, called the Subspace Accelerated MIMOExpand
Convex Optimization
TLDR
A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency. Expand
Time-limited H2-optimal model order reduction
TLDR
It is illustrated that the newly proposed iterative method can lead to a better reduced-order models compared to the unrestricted iterative rational Krylov subspace algorithm in a finite time interval of interest. Expand
Advanced Structural Dynamics and Active Control of Structures
  • S. Joshi
  • IEEE Transactions on Automatic Control
  • 2005
Advances in control theory have often led to solutions of a variety of difficult practical problems. One such application is control of flexible structures, which are typically characterized by largeExpand
Approximation of Large-Scale Dynamical Systems
  • A. Antoulas
  • Mathematics, Computer Science
  • Advances in Design and Control
  • 2005
TLDR
This paper presents SVD-Krylov Methods and Case Studies, a monograph on model reduction using Krylov methods for linear dynamical systems, and some examples of such reduction schemes. Expand
Nineteen Dubious Ways to Compute the Exponential of a Matrix
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...
Low-rank methods for high-dimensional approximation and model order reduction
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit theExpand
...
1
2
...