Petar Mlinarić

Petar Mlinarić
Virginia Tech | VT · Department of Mathematics

PhD

About

21
Publications
1,487
Reads
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112
Citations
Additional affiliations
January 2020 - present
Max Planck Institute for Dynamics of Complex Technical Systems
Position
  • PostDoc Position
September 2014 - January 2020
Max Planck Institute for Dynamics of Complex Technical Systems
Position
  • Research Assistant
Education
October 2014 - September 2019
Otto-von-Guericke University Magdeburg
Field of study
  • Applied Mathematics
September 2012 - July 2014
University of Zagreb
Field of study
  • Applied Mathematics

Publications

Publications (21)
Article
The iterative rational Krylov algorithm (IRKA) is a commonly used fixed point iteration developed to minimize the ${\mathcal {H}}_{2}$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed step size over the manifold of rational functions having fixed degree. This interpretation motivates t...
Preprint
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally covers the well-known interpolatory necessary conditions for $\mathcal{H}_2$-optimal model order reduction and lead...
Preprint
Full-text available
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive the gradients of the $\mathcal{L}_2$ cost function with respect to the reduced matrices, which then allows a non...
Chapter
pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector and operator interfaces, which allows a direct integration of pyMOR’s algorithms with a wide array of external PDE solvers. In this contribution, we give a brief overview o...
Chapter
Clustering by projection has been proposed as a way to preserve network structure in linear multi-agent systems. Here, we extend this approach to a class of nonlinear network systems. Additionally, we generalize our clustering method which restores the network structure in an arbitrary reduced-order model obtained by projection. We demonstrate this...
Preprint
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality conditions for a class of structured reduced-order models, and then building on those, propose a stability-preserv...
Preprint
Clustering by projection has been proposed as a way to preserve network structure in linear multi-agent systems. Here, we extend this approach to a class of nonlinear network systems. Additionally, we generalize our clustering method which restores the network structure in an arbitrary reduced-order model obtained by projection. We demonstrate this...
Preprint
pyMOR is a free software library for model order reduction that includes both reduced basis and system-theoretic methods. All methods are implemented in terms of abstract vector and operator interfaces, which allows direct integration of pyMOR's algorithms with a wide array of external PDE solvers. In this contribution, we give a brief overview of...
Article
Full-text available
This paper shows recent developments in pyMOR, in particular the addition of system‐theoretic methods. All methods are implemented using pyMOR's abstract interfaces, which allows the application to partial differential equation (PDE) models implemented with third‐party libraries. We demonstrate this by applying balanced truncation to a PDE model di...
Article
So far, ℋ2 ⊗ ℒ2‐optimal model order reduction (MOR) of linear time‐invariant systems, preserving the affine parameter dependence, was only considered for special cases by Baur et al in 2011. In this contribution, we present necessary conditions for an ℋ2 ⊗ ℒ2‐optimal parametric reduced order model, for general affine parametric systems resembling t...
Article
Full-text available
We study nonlinear power systems consisting of generators, generator buses, and non-generator buses. First, looking at a generator and its bus' variables jointly, we introduce a synchronization concept for a pair of such joint generators and buses. We show that this concept is related to graph symmetry. Next, we extend, in two ways, the synchroniza...
Article
Full-text available
In the recent paper (Monshizadeh et al. in IEEE Trans Control Netw Syst 1(2):145–154, 2014. https://doi.org/10.1109/TCNS.2014.2311883), model reduction of leader–follower multi-agent networks by clustering was studied. For such multi-agent networks, a reduced order network is obtained by partitioning the set of nodes in the graph into disjoint sets...
Article
We develop a stability preserving model reduction method for linearly coupled linear time-invariant (LTI) systems. The method extends the work of Monshizadeh et al. for multi-agent systems with identical LTI agents. They propose using Bounded Real Balanced Truncation to preserve a sufficient condition for stability of the coupled system. Here, we e...
Article
Full-text available
In this paper, we study a model reduction technique for leader-follower networked multi-agent systems defined on weighted, undirected graphs with arbitrary linear multivariable agent dynamics. In the network graph of this network, nodes represent the agents and edges represent communication links between the agents. Only the leaders in the network...
Conference Paper
Full-text available
In this paper, we extend our clustering-based model order reduction method for multi-agent systems with single-integrator agents to the case where the agents have identical general linear time-invariant dynamics. The method consists of the Iterative Rational Krylov Algorithm, for finding a good reduced order model, and the QR decomposition-based cl...

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