2021-03758 - PhD Position F/M Self-sustained oscillations in nonsmooth dynamical systems
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

A propos du centre ou de la direction fonctionnelle

Grenoble Rhône-Alpes Research Center groups together a few less than 650 people in 37 research teams and 8 research support departments.

Staff is localized on 5 campuses in Grenoble and Lyon, in close collaboration with labs, research and higher education institutions in Grenoble and Lyon, but also with the economic players in these areas.

Present in the fields of software, high-performance computing, Internet of things, image and data, but also simulation in oceanography and biology, it participates at the best level of international scientific achievements and collaborations in both Europe and the rest of the world.


Contexte et atouts du poste

TRIPOP (Inria Grenoble Rhône-Alpes ; Laboratoire Jean Kuntzmann) team is mainly concerned by the modeling, the simulation and the control of nonsmooth dynamical systems. Regrding control, the main instances of nonsmooth dynamical systems are complementarity systems, relay feedback systems, differential inclusions, dynamics variational inequalities, etc. Such systems appear in the modeling of electrical circuits, mechanical systems with unilateral constraints, models from mathematical biology to name afew. The members of the team have a long experience of nonsmooth dynamics modeling and control together with the development of simulation software.

Mission confiée

Oscillations are fundamental for life and computing. Any living organism has internal clocks regulating its behavior and any computer has clocks to process instructions, without their internal clocks none of them can persist. However, despite of its clear importance, oscillations are most of the time regarded as something that must be avoided in control synthesis problems. This is mainly because most of control problems are regarded as problems of regulation towards equilibrium. That is indeed one of the main reasons why there are very few control methods for building oscillators, compared to the vast theory on methods for reaching a state of equilibrium. Nevertheless, the acknowledge of feedback as the essential modulator of the behavior, at both, local and global scales, situates control theory in an exceptional position in the delegation of approaches for understanding oscillatory systems.

In this context the emphasis on nonsmooth methods is motivated by several properties. Namely, in the case of regulation towards equilibrium, nonsmooth controllers show robustness properties that are not shared by their smooth counterparts, making them an attractive scheme in environments with uncertainty. Second, nonsmooth maps facilitate the modeling stage, abstracting the important features of the process. Third, nonsmooth systems can be used as a tool for modulating the resolution of the model, (for instance, via a piecewise linear approach) with the end of alleviating the computational load of the original model. Fourth, the strong links between convex analysis and monotone set-valued maps makes nonsmooth set-valued controllers attractive from a numerical viewpoint, leading to accurate and efficient simulation results.

Principales activités

The selected candidate will develop novel tools for the analysis and synthesis of self-sustained oscillations in nonsmooth dynamical systems, as for instance, linear complementarity systems (LCS) and relay feedback systems. Recent extensions of dissipativity theory and nonsmooth bifurcation methods will be used for the analysis and synthesis of control laws that guarantee an oscillatory behavior. Applications are found in electrical circuits with non-smooth components (like ideal diodes), mathematical models of gene regulatory networks in systems biology, and circuit pattern generators for motion coordination in robotics, to name a few.


Name of Co-supervisors:

Félix A. Miranda-Villatoro (TRIPOP team, INRIA Grenoble Rhône-Alpes)

Francesco Ferrante (GIPSA-Lab, Université Grenoble Alpes)

Bernard Brogliato (TRIPOP team, INRIA Grenoble Rhône-Alpes)




Technical skills and level required : Master in Automatic control, applied mathematics, or a related area.

Languages : English, French.

Other valued appreciated : Programming skills in Python, C++.


  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (90 days / year) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage


1st and 2nd year: 1 982 euros gross salary /month

3rd year: 2 085 euros gross salary / month