A passivation algorithm for linear time-invariant systems

10/29/2020
by   Antonio Fazzi, et al.
0

We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest'), and also a closely related algorithm for computing the structured distance of a given passive system to non-passivity. Both problems are addressed by solving eigenvalue optimization problems for Hamiltonian matrices that are constructed from perturbed system matrices. The proposed algorithms are two-level methods that optimize the Hamiltonian eigenvalue of smallest positive real part over perturbations of a fixed size in the inner iteration, using a constrained gradient flow, and optimize over the perturbation size in the outer iteration. For large systems, we propose a variant of the algorithm that takes advantage of the inherent low-rank structure of the problem. Numerical experiments illustrate the behavior of the proposed algorithms.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/19/2022

Rank-1 matrix differential equations for structured eigenvalue optimization

A new approach to solving eigenvalue optimization problems for large str...
research
01/14/2022

Port-Hamiltonian Realizations of Linear Time Invariant Systems

The question when a general linear time invariant control system is equi...
research
05/17/2020

A decoupled form of the structure-preserving doubling algorithm with low-rank structures

The structure-preserving doubling algorithm (SDA) is a fairly efficient ...
research
09/13/2021

Computation of the nearest structured matrix triplet with common null space

We study computational methods for computing the distance to singularity...
research
08/18/2018

Exact Passive-Aggressive Algorithms for Learning to Rank Using Interval Labels

In this paper, we propose exact passive-aggressive (PA) online algorithm...
research
01/30/2021

A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems

We propose a flexible power method for computing the leftmost, i.e., alg...
research
02/05/2022

Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization

In these lectures notes, we review our recent works addressing various p...

Please sign up or login with your details

Forgot password? Click here to reset