Tudor Ionescu

The University of Sheffield, Automatic Control and Systems Engineering, Post-Doc

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Tudor C. Ionescu received the M.Sc. in Systems and Control Engineering from the Politehnica University of Bucharest, Romania (2004) and the Ph.D. in Applied Mathematics from the University of Groningen, the Netherlands (2009). During his Ph.D. he was a visiting researcher at Supelec, Paris, France (2005 and 2007) and at Nagoya University, Japan (2008). He was a Research Associate at Imperial College London, UK (2009-2013) and at the University of Sheffield, UK (2013-2015). During his post-doctoral years he has been awarded the Dutch Science Foundation (NWO) Visitor Grant at the University of Groningen, the Netherlands (2011 and 2015). Currently, he is a full-time Associate Professor at the Department of Automatic Control and Systems Engineering, Politehnica University of Bucharest, Romania. He is also a part-time Scientific Researcher at the "Gheorghe Mihoc - Caius Iacob" Institute for Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania. His research interests include modelling and control of nonlinear systems with focus on modelling and model order reduction with preservation of physical structure, as well as model reduction based finite-dimensional approximation of time-delay and distributed-parameter systems.
Address: University of Shefield, Mappin St., Sheffield S1 3JD, United Kingdom

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Papers by Tudor Ionescu

Moment matching for linear port Hamiltonian systems

IEEE Conference on Decision and Control and European Control Conference, 2011

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$Research paper thumbnail of Parameter selection for best $H_{2}$ moment matching-based model approximation through gradient optimization$

Parameter selection for best $H_{2}$ moment matching-based model approximation through gradient optimization

2019 18th European Control Conference (ECC), 2019

In this paper we compute a family of reduced order models, parameterized in a matrix of free para... more In this paper we compute a family of reduced order models, parameterized in a matrix of free parameters, that match a prescribed set of $\nu$ moments of a highly dimensional linear time-invariant system. Based on the parametrization and using as objective function the $H_{2}$-norm of the approximation error, we propose a non-convex optimization problem, which, for a fixed set of interpolation points, is seeking the optimal free parameters yielding the minimal $H_{2}$-norm error. Furthermore, we write the necessary first-order optimality conditions explicitly in terms of the controllability and the observability Gramians of a minimal realization of the error system. Based on the optimality conditions we propose a gradient method-based solution, accompanied by mathematical guarantees about its convergence. We illustrate the efficiency of our results on the test example of a CD player.

On moment matching with preservation of passivity and stability

Conference on Decision and Control, 2010

In this paper, the problem of moment matching with (preservation of) certain properties is tackle... more In this paper, the problem of moment matching with (preservation of) certain properties is tackled. Based on a new approach to linear and nonlinear matching we discuss the choices of interpolation (matching) points such that the resulting families of models have certain properties, namely passivity and stability, useful for modeling and analysis.

Singular Value Analysis Of Nonlinear Symmetric Systems

IEEE Transactions on Automatic Control, 2011

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Model reduction by moment matching: case study of a FIR system

2019 18th European Control Conference (ECC), 2019

We present two moment matching-based solutions to the problem of rational approximations of a fin... more We present two moment matching-based solutions to the problem of rational approximations of a finite-impulse response (FIR) system: a direct moment matching approximation performed on the FIR system and a sequential moment matching approximation performed on a block split model of a FIR system. Imposing moment matching conditions yields families of parametrized, low-order, rational approximations of the FIR filters, with guaranteed low frequency behavior. We show that the block rational implementation from [1], [2] is a particular case of the sequential moment matching result. The theory is illustrated with an example of a FIR system, where we select the free parameters such that the approximations are stable and more accurate. We compare the proposed approximations with existing rational implementations of the FIR system as well as with Loewner matrices-based approximations.

A moment matching approach for systems of delayed differential equations

2018 European Control Conference (ECC), 2018

Inthis paper we propose a moment matching ap-proach for approximating time-delay systems with del... more Inthis paper we propose a moment matching ap-proach for approximating time-delay systems with delays in the states. This approach is based on the unique solution of an associated Sylvester-like equation. It results in a family of parametrized, finite-dimensional, reduced order models that match a set of prescribed moments of the given delay-system. We show that, by properly choosing the free parameters, we obtain a finite-dimensional approximation that achieves moment matching at both the zero and first order derivatives of the transfer function of the given delay-system. This approach does not require the explicit computation of the transfer function and its derivatives. We illustrate the potential of this method with a simple example of a state delay-system. The constructed reduced order model for this delay-system is more accurate than approximations obtained using the well-known Padé approximation.

Optimal H2 moment matching-based model reduction for linear systems by (non)convex optimization

arXiv: Optimization and Control, 2018

In this paper we compute families of reduced order models that match a prescribed set of moments ... more In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free parameters, and then we fix the set of interpolation points and parametrize the models only in the free parameters. Based on these two parametrizations and using as objective function the H2-norm of the error approximation we derive non-convex optimization problems, i.e., we search for the optimal free parameters and even the interpolation points to determine the approximation model yielding the minimal H2-norm error. Further, we provide the necessary first-order optimality conditions for these optimization problems given explicitly in terms of the controllability and the observability Gramians of a minimal realization of the error system. Using the optimality conditions, we propose gradient type methods for solving the corresponding optimization proble...

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Balanced truncation for dissipative and symmetric nonlinear systems

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On moment matching of transfer functions and their derivatives

2015 European Control Conference (ECC), 2015

In this paper we study the problem of computing the (family of) reduced order model(s) that satis... more In this paper we study the problem of computing the (family of) reduced order model(s) that satisfy the following properties the systems match the moments of the given to be reduced system and the same property holds for the first order derivatives of the corresponding transfer functions. We prove that such a model exists and compute it. We also study the problem of moment matching for the state-space representations of the first order derivatives of rational transfer functions. Finally, we show that the model that matches the moment of both the given system and its first order derivative is a member of the family of reduced order models whose first order derivatives achieve moment matching.

Two-Sided Time-Domain Moment Matching for Linear Systems

IEEE Transactions on Automatic Control, 2015

In this technical note we study the problem of computing reduced order models of order ν that mat... more In this technical note we study the problem of computing reduced order models of order ν that match 2ν moments of the given to-be-reduced system at two sets of ν interpolation points, called two-sided moment matching, in the time-domain framework. We also study the time-domain moment matching problem of the state-space representations of the first order derivative of a transfer function. Based on this, we show that the solution of the two-sided time-domain moment matching problem at non-distinct (ν) interpolation points yields a unique ν order model that satisfies the following properties: the model matches the moments of the given system at the interpolation points and the same property holds for the first order derivatives of the corresponding transfer functions.

On an approximation with prescribed zeros of SISO abstract boundary control systems

Moment matching with prescribed poles and zeros for infinite-dimensional systems

2012 American Control Conference (ACC), 2012

Moment matching based controller reduction for linear systems

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Families of reduced order models that achieve nonlinear moment matching

2013 American Control Conference, 2013

Passivity preserving model order reduction for the SMIB

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Families of moment matching based, low order approximations for linear systems

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Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

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Singular Value Analysis Of Nonlinear Symmetric Systems

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Passivity preserving model order reduction for the SMIB

We apply (linear) positive real balancing to the model of a single machine connected to an infini... more We apply (linear) positive real balancing to the model of a single machine connected to an infinite bus. For that we compute the available storage and the required supply using Taylor approximation and define axis positive real singular value functions. Furthermore, we apply linear positive real balancing to the nonlinear model and analyze the results.

Nonlinear Cross Gramians

We study the notion of cross Gramians for nonlinear gradient systems, using the characterization ... more We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.