Optimization of parameter dependent mechanical systems

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This project is financed by Croatian Science Foundation.  

 Project duration: 1. 7. 2015. – 30. 6. 2019.

 

PROJECT DESCRIPTION

This project is devoted to the second order mechanical systems described by a system of differential equations, whose coefficient matrices are large-scaled and dependent on one or more real parameters.

The majority of the research within this project will be focused on: optimization of active and passive damping and optimal control of parameter dependent mechanical systems with and without external force; describing the properties of eigenvalues and eigenvectors of the corresponding parameter-dependent quadratic or nonlinear problem.
Within the problem of active and passive damping optimization and optimal control of parameter dependent mechanical systems with and without external force, we will develop a general theoretical framework. These theoretical considerations will be related to the optimization of various damping parameters with respect to a several different optimization criteria. Furthermore, within the stated objectives we will solve many numerical demanding problems: mixed-integer nonlinear optimization problem, efficiently solving of large matrix equations (Lyapunov, Sylvester, Riccati), improving the optimization algorithms by dimension reduction. We will also consider theoretical and numerical aspects of optimization of semi-active damping problem and optimal control based on various criteria.

Within the problem of describing the behavior of eigenvalues and eigenvectors of the parameter-dependent nonlinear eigenvalue problems, we will develop perturbation theory for the corresponding quadratic problem separately for cases when the corresponding linearized pair is diagonalizable or definite. For both cases we will develop perturbation theory of absolute and relative type for the eigenvalues and associated eigenvectors i.e. subspaces.

The all mentioned problems are closely related, thus the insight into the behavior of eigenvalues and corresponding eigenvectors will allow better understanding of the behavior of mechanical systems and vice versa.

Key worlds: large-scaled mechanical systems, nonlinear eigenvalue problem, damping optimization, optimal control, matrix equations

PROJECT RESEARCHERS

 

Principal investigator: Prof. dr. sc. Ninoslav Truhar

Project partners: Prof. dr. sc. Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Prof. dr. sc. Ivan Slapničar, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split
Dr. sc. Nevena Jakovčević Stor, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split

Project members: prof. dr. sc. Ninoslav Truhar, izv. prof. dr. sc. Zoran Tomljanović, doc. dr. sc. Ivana Kuzmanović, dr. sc. Suzana Miodragović, Matea Puvača

ACTIVITIES

 

Open postdoc Position 

The Univeristy of Osijek, Department of Mathematics (https://www.mathos.unios.hr/index.php/en/) has an opening position for a postdoctoral researcher in Numerical Linear Algebra for 12 months. 

The postdoc holder will join the Department of Mathematics, starting from 1. March, 2018 within the project "Optimization of parameteer dependent mechanical systems" which has been fully financed by Croatian Science Foundation.

The candidates need to have PhD in mathematics, computer science, or some related area. Essential qualifications are a strong background in numerical linear algebra, control theory and especially Quadratic eigenvalue problems and basics in optimization methods. Part of the project involves programming in Matlab, (or some similar programs Maple or Mathematica) so experience in this direction is highly desirable.

Informal enquiries are encouraged; please contact Professor Ninoslav Truhar initially by e-mail: Ova e-mail adresa je zaštićena od spambota. Potrebno je omogućiti JavaScript da je vidite.

PUBLICATIONS

  1. N. Truhar, S. Miodragović, Relative perturbation theory for de nite matrix pairs and hyperbolic eigenvalue problem, Applied Numerical Mathematics 98 (2015), 106-121 
  2. I. Kuzmanović, Z. Tomljanović, N. Truhar, Damping optimization over the arbitrary time of the excited mechanical system, Journal of Computational and Applied Mathematics, 304 (2016), 120-129
  3. Z. Tomljanović, N. Truhar, K. Veselić, Damping optimization in mechanical systems with external force (poster), Publication date: 2015-09-01, DOI: 10.14293/S2199-1006.1.SOR-MATH.CLCIQMK.v1, Publisher: ScienceOpen url: https://www.scienceopen.com/collection/2015VM60  304 (2016), 120-129
  4. L. Grubišić, S. Miodragović, N. Truhar, Double Angle Theorems for Definite Matrix Pairs, Electronic Transactions of Numerical Analysis, 45 (2016), 33-57
  5. N. Truhar, Z. Tomljanović, M. Puvača, An Efficient Approximation for Optimal Damping in Mechanical Systems, International journal of numerical analysis and modeling (2017),  14 (2), 201–217
  6. Nevena Jakovčević Stor; Ivan Slapničar Forward stable computation of roots of real polynomials with only real distinct roots, Applied Mathematics & Information Sciences (2016), accepted for publication
  7. M. Essert, I. Kuzmanović, I. Vazler, T. Žilić, Theory of M-system, Logic Journal of the IGPL (2017), accepted for publication
  8. Z. Tomljanović, C. Beattie, S. Gugercin, Damping optimization of parameter dependent mechanical systems by rational interpolation, Advances in Computational Mathematics (2018), pp.1-24,  First Online: 11 April 2018
  9. C. Beattie, S. Gugercin, Z. Tomljanović, Sampling-free parametric model reduction of systems with structured parameter variation (poster), Publication date: 27 April 2018, DOI: 10.14293/P2199-8442.1.SOP-MATH.BBKSHV.v1, Journal: ScienceOpen Posters, Publisher: ScienceOpen, PDF

Technical reports

  1. Peter Benner, Xin Liang, Suzana Miodragović, Ninoslav Truhar, Relative Perturbation Theory for Quadratic Eigenvalue Problems. arXiv:1602.03420 [math.NA].
  2. N. Truhar, Z. Tomljanović, Dimension reduction approach for the parameter dependent quadratic eigenvalue problem (2017), submitted for publication.
  3. Y. Kanno, M.Puvača, Z. Tomljanović and N. Truhar, Optimization of damping positions in mechanical system, submitted for publication.
  4. N. Truhar, Z. Tomljanović, Eigensubspace perturbation bounds for quadratic eingenvalue problem (2017)

TALKS

Participation on conferences:

  • Zoran Tomljanović, Semi-active H-inf damping optimization by adaptive interpolation, 90th Annual Meeting GAMM 2019, Vienna, 18-22 February 2019
  • Ivan Slapničar i Nevena Jakovčević Stor, Fast Optimal Damping, International workshop on optimal control of dynamical systems and applications, June 20.-22. 2018., Osijek, Croatia
  • Ninoslav Truhar, Upper and lower bounds for sines of canonical angles between eigenspaces for regular Hermitian matrix pairs,  ALAMA 2018 Meeting,  May 30.-  June 1. 2018 Universities of Alicante, Alicante, Spain
  • Zoran Tomljanović, Upper and Lower Bounds for Sines of Canonical Angles, SIAM Conference on Applied Linear Algebra (SIAM-ALA18),  4-8 May 2018, Hong Kong Baptist University, Hong Kong
  • Suzana Miodragović, Relative Perturbation Bounds for Hyperbolic Quadratic Eigenvalue Problem, GAMM Annual Meeting, March 19-23, Munich, Germany
  • Matea Puvača, Perturbation Bounds for Parameter Dependent Quadratic Eigenvalue Problem, GAMM Annual Meeting, March 19-23, Munich, Germany
  • Zoran Tomljanović, Sampling-free parametric model reduction of systems with structured parameter variation (poster), Model Reduction of Parametrized Systems IV, 10-13 April 2018, Nantes, France
  • Ivana Kuzmanović, Parameter Dependent Generalized Sylvester and T-Sylvester Equations,  6th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2017), August 15-18, 2017, Budapest, Hungary.
  • Nevena Jakovčević Stor"27th Biennial Numerical Analysis Conference", 27-30 June 2017, University of Strathclyde, Glasgow (UK)
  • Ninoslav Truhar, Perturbation Bounds for the Quadratic Eigenvalue Problem, Householder Symposium XX, 19-23 June 2017, Blacksburg, Virginia
  • Zoran Tomljanović, Dimension reduction approach to the parameter dependent quadratic eigenvalue problem, 88th GAMM Annual Meeting, Weimar, Germany,  6-10 March 2017
  • Zoran Tomljanović, Damping optimization of parameter dependent mechanical systems by rational interpolation, 3rd Workshop on Model Reduction of Complex Dynamical Systems, Odense, Denmark, 11-13 January 2017 
  • Ivana Kuzmanović, Optimization of the solution of Sylvester and $T$-Sylvester equations with applications, 16th GAMM ANLA Workshop, September 15-16, 2016, Hamburg, Germany
  • Ivana Kuzmanović, Damping optimization over the arbitrary time of the excited mechanical systems, 6th Croatian MathematicalCongress, June 14-17, 2016, Zagreb, Croatia
  • Ninoslav Truhar, Optimal damping for vibrating systems,
    Kick-off meeting of the FWF project P27926 "Solution of large-scale Lyapunov differential
    equations". Department of Mathematics, University of Innsbruck May, 30-31 2016
  • Ninoslav Truhar, On Quadratic Eigenvalue Problem, Fourth Najman Conference on Spectral Problems for Operators and Matrices, Opatija, Croatia,  20-25, September, 2015.
  • Zoran Tomljanović, Optimization of semi-active damping and viscous damping in excited mechanical systems, Matrix Computation Seminar,   10 November 2015, Departments of Mathematics at Virginia Tech, USA
  • Zoran Tomljanović, Semi-active damping optimization using the parametric dominant pole algorithm, MatTriad'2015, Coimbra, Portugal, 7 - 11 September, 2015.
  • Suzana Miodragović, Relative Perturbation Theory for Definite Matrix Pairs and Hyperbolic Quadratic Eigenvalue Problem, Workshop on Matrix Equations and Tensor Techniques, September 21-22, Bologna, Italy
  • Suzana Miodragović, Relative Perturbation Theory for Definite Matrix Pairs, Joint Annual Meeting of GAMM and DMV, March 07-11, Braunschweig,  Germany