Presentation

The TRIPOP team is  a joint research team of Inria Grenoble Rhone-Alpes and of the Laboratoire Jean Kuntzmann (LJK). This new team is a follow up of the BIPOP team (2003–2017). The team is mainly concerned by the modeling, the mathematical analysis, the simulation and the control of nonsmooth dynamical systems. Nonsmooth dynamics concerns the study of the time evolution of systems that are not smooth in the mathematical sense, i.e., systems that are characterized by a lack of differentiability, either of the mappings in their formulations, or of their solutions with respect to time. In mechanics, the main instances of nonsmooth dynamical systems are multibody systems with Signorini unilateral contact, set-valued (Coulomb-like) friction and impacts. In Electronics, examples are found in switched electrical circuits withe ideal components (diodes, switches, transistors). In Control, nonsmooth systems arise in the sliding mode control theory and in optimal control. A lot of examples can also be found in cyber-physical systems (hybrid systems), in transportation sciences, in mathematical biology or in finance.

     

 

Research directions

  • Axis 1: Modeling and analysis
    1. Multibody vibro-impact systems
    2. Excitable systems
    3. Nonsmooth geomechanics and natural hazards assessment
    4. Cyber-physical systems (hybrid systems)
  • Axis 2: Numerical methods and simulation
    1. Geometric time–integration schemes for nonsmooth Initial Value Problem
    2. Stability and numerical continuation of invariants
    3. Numerical optimization for discrete nonsmooth problems
  • Axis 3: Automatic Control
    1. Discrete-time Sliding-Mode Control (SMC) and State Observers (SMSO)
    2. Optimal Control
    3. Control of nonsmooth discrete Lagrangian systems
    4. Switching LCS and DAEs, higher-order sweeping process (HOSwP)
    5. Control of Elastic (Visco-plastic) systems with contact, impact and friction

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