PhD - Model order reduction for hybrid systems and application to power electronics

LAPLACE, groupe CODIASE (Toulouse)


Hybrid systems consist of finite collections of dynamical systems, indexed by a set of discrete modes, i.e. taking their value in a finite set. Each dynamic system is governed by a set of differential equations. The change from one mode to another can be externally imposed or depend on the value of the continuous state, and is orchestrated by a switching law.

In particular, switched affine systems are characterized by linear dynamic subsystems and the mode changes are controlled externally. This sub-category of hybrid systems is widely studied because, although it is the simplest kind of hybrid systems, it can be used to represent a wide range of applications, particularly in the field of electrical engineering (power converters in energy networks in particular).

Consequently, the analysis and control of these switched linear systems (SLS) are established topics. In order to apply these techniques, identification and model reduction of hybrid systems are the subject of an abundant literature. These techniques differ from traditional methods for model reduction or identification of LTI systems as they are not limited to obtaining continuous submodels, but take into account their complex interactions through the discrete modes.

Identification techniques for hybrid systems focus on obtaining structured input-output representations of a given order from noisy experimental data, but they are based on the identification and then fusion of linear subsystems, implying strong assumptions about the subsystems (same order and/or same basis in particular). The model reduction techniques developed for hybrid systems make it possible to obtain state-space representations and are naturally suited for the multivariable case. They also have the advantage of guiding the choice of the order of the reduced system, but they are based on knowledge of the underlying high-order model.


In this context, the main objective of this thesis is to propose an innovative approach combining system identification and model reduction to obtain SLS models from real data. This thesis will be based on a review of existing methods for hybrid systems, both in system identification and model reduction, highlighting their advantages and limitations.

This thesis has an important applicative objective as it should be applied in the field of power electronics, where obtaining reduced models is crucial for stability analysis in converter networks for instance. Indeed, the use of detailed models for all the components of such networks results in great numerical complexity, making it difficult to simulate and analyse long-term stability and to simulate complex systems. Model reduction is therefore a promising avenue for the stability analysis of energy networks dominated by converters. The method proposed during this thesis would make it possible to obtain finer models reflecting the fast dynamics due to switching. Indeed, fast dynamics have an impact on slow dynamic power loops, and neglecting them can lead to questionable results in  terms of control and analysis.

PhD organisation

The thesis will be carried out at LAPLACE, in the CODIASE group, located at ENSEEIHT in Toulouse. The thesis will be directed by Pauline Kergus and co-supervised by Zohra Kader.

Sought profile:

  • Candidates should hold a MSc or an engineering degree in automatic control or related field.

  • Backgroung in modelling, system identification, model order reduction or advanced control

  • Any experience with electrical engineering will be valued, as wells as research experience in general.

  • Proficient with Matlab

  • Excellent oral and written communication skills in english

  • Others : analytical and synthetical skills, autonomy, ability to work in team, scientific curiosity

To apply, please send a CV and a cover letter to and Please indicate one or two referees to contact for recommandation.