# Semi-active $\mathcal{H}_{\infty}$ damping optimization by adaptive interpolation

@article{Tomljanovic2020SemiactiveD, title={Semi-active \$\mathcal\{H\}\_\{\infty\}\$ damping optimization by adaptive interpolation}, author={Zoran Tomljanovi'c and Matthias Voigt}, journal={arXiv: Numerical Analysis}, year={2020} }

In this work we consider the problem of semi-active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm of the transfer function from the exogenous inputs to the performance outputs. We make use of a new greedy method for computing the $\mathcal{H}_\infty$-norm of a transfer function based on rational interpolation. In this paper, this approach is adapted to parameter…

## References

SHOWING 1-10 OF 37 REFERENCES

### Damping optimization of parameter dependent mechanical systems by rational interpolation

- Computer ScienceAdv. Comput. Math.
- 2018

This work proposes an optimization approach that calculates ‘interpolatory’ reduced order models, allowing for significant acceleration of the optimization process, and maintains second-order structure through the use of modal coordinates, which allows for very efficient implementation.

### Fast Approximation of the HINFINITY Norm via Optimization over Spectral Value Sets

- MathematicsSIAM J. Matrix Anal. Appl.
- 2013

A Newton-bisection method is introduced to approximate the H_infty norm, for which each step requires optimization of the real part or the modulus over an $\varepsilon$-spectral value set.

### A structured pseudospectral method for $$\mathcal {H}_\infty $$H∞-norm computation of large-scale descriptor systems

- Computer Science, MathematicsMath. Control. Signals Syst.
- 2014

A new fast iterative scheme is used which is based on certain rank-1 perturbations of a matrix pencil to exploit the relationship between the H∞-norm and the structured complex stability radius of a corresponding matrix pencil.

### A BFGS-SQP method for nonsmooth, nonconvex, constrained optimization and its evaluation using relative minimization profiles

- Computer ScienceOptim. Methods Softw.
- 2017

The proposed algorithm is a sequential quadratic optimization method that employs Broyden-Fletcher-Goldfarb-Shanno quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy.

### Hybrid expansion–contraction: a robust scaleable method for approximating the H∞ norm

- Mathematics
- 2016

We present a new scaleable algorithm for approximating the H∞ norm, an important robust stability measure for linear dynamical systems with input and output. Our spectral-value-set-based method uses…

### FAST APPROXIMATION OF THE H∞ NORM VIA OPTIMIZATION OVER SPECTRAL VALUE SETS∗

- Mathematics, Computer Science
- 2012

This work extends an algorithm recently introduced by Guglielmi and Overton for approximating the maximal real part or modulus of points in a matrix pseudospectrum to spectral value sets and introduces a Newton-bisection method to approximate the H∞ norm.

### Dimension reduction for damping optimization in linear vibrating systems

- Computer Science, Mathematics
- 2011

The main problem considered in the paper is the construction of an efficient algorithm for calculating an optimal damping and an approximation of the solution of the structured Lyapunov equation and a corresponding error bound for the approximation.

### Constant and switching gains in semi-active damping of vibrating structures

- MathematicsInt. J. Control
- 2012

A state-switching feedback control strategy is proposed, which outperforms the constant damping approach with the optimal static gain performance as an upper bound, and a stochastic strategy based on a Markov-jump criterion is proposed.

### A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

- Computer Science, MathematicsSIAM J. Optim.
- 2005

A practical, robust algorithm to locally minimize such functions as f, a continuous function on $\Rl^n$, which is continuously differentiable on an open dense subset, based on gradient sampling is presented.

### Large-Scale Computation of ℒ∞-Norms by a Greedy Subspace Method

- MathematicsSIAM J. Matrix Anal. Appl.
- 2017

A subspace projection method is proposed to obtain approximations of the function H where the middle factor is of much smaller dimension and certain Hermite interpolation properties hold between the largest singular values of the original and the reduced function.