Dynamical Systems

Exploiting nonlinearity and shaping dynamics in creative and deeply mathematical ways.

We apply dynamical systems theory in applications ranging from space probe trajectory optimization to elevator suspensions. We also develop fundamental theory and computational methods in fluid dynamics.

  • Researchers

  • News & Events

    •  TALK    [MERL Seminar Series 2022] Prof. Sebastien Gros presents talk titled RLMPC: An Ideal Combination of Formal Optimal Control and Reinforcement Learning?
      Date & Time: Tuesday, April 12, 2022; 11:00 AM EDT
      Speaker: Sebastien Gros, NTNU
      MERL Host: Rien Quirynen
      Research Areas: Control, Dynamical Systems, Optimization
      Abstract
      • Reinforcement Learning (RL), similarly to many AI-based techniques, is currently receiving a very high attention. RL is most commonly supported by classic Machine Learning techniques, i.e. typically Deep Neural Networks (DNNs). While there are good motivations for using DNNs in RL, there are also significant drawbacks. The lack of “explainability” of the resulting control policies, and the difficulty to provide guarantees on their closed-loop behavior (safety, stability) makes DNN-based policies problematic in many applications. In this talk, we will discuss an alternative approach to support RL, via formal optimal control tools based on Model Predictive Control (MPC). This approach alleviates the issues detailed above, but also presents some challenges. In this talk, we will discuss why MPC is a valid tool to support RL, and how MPC can be combined with RL (RLMPC). We will then discuss some recent results regarding this combination, the known challenges, and the kind of control applications where we believe that RLMPC will be a valuable approach.
    •  
    •  TALK    [MERL Seminar Series 2022] Albert Benveniste, Benoît Caillaud, and Mathias Malandain present talk titled Exact Structural Analysis of Multimode Modelica Models
      Date & Time: Tuesday, April 5, 2022; 11:00 AM EDT
      Speaker: Albert Benveniste, Benoît Caillaud, and Mathias Malandain, Inria
      MERL Host: Scott A. Bortoff
      Research Areas: Dynamical Systems, Multi-Physical Modeling
      Abstract
      • Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In our introduction, will briefly explain why and when the approximate structural analysis implemented in current Modelica tools leads to such errors. Then we will present our multimode Pryce Sigma-method for index reduction, in which the mode-dependent Sigma-matrix is represented in a dual form, by attaching, to every valuation of the sigma_ij entry of the Sigma matrix, the predicate characterizing the set of modes in which sigma_ij takes this value. We will illustrate this multimode analysis on example, by using our IsamDAE tool. In a second part, we will complement this multimode DAE structural analysis by a new structural analysis of mode changes (and, more generally, transient modes holding for zero time). Also, mode changes often give raise to impulsive behaviors: we will present a compile-time analysis identifying such behaviors. Our structural analysis of mode changes deeply relies on nonstandard analysis, which is a mathematical framework in which infinitesimals and infinities are first class citizens.
    •  

    See All News & Events for Dynamical Systems
  • Internships

    • CA1741: Learning for Connected Vehicles

      MERL is seeking a highly motivated intern to collaborate with the Control for Autonomy team in the development of learning technologies for Connected Vehicles. The intern will conduct research in the development of methods for learning/optimization of Advanced Driver Assistance Systems (ADAS) using data-sharing between connected vehicles and/or infrastructure. The ideal candidate has knowledge of at least one of machine learning, estimation, connected vehicles, and vehicle control systems. Knowledge of one or more traffic and/or multi-vehicle simulators (SUMO, Vissim, etc.) is a plus. Good programming skills in Matlab are required and knowledge in Python or C/C++ is a merit. PhD students in engineering, mathematics, or similar are encouraged to apply. The expected duration of the internship is 3-6 months. The start date is flexible.

    • CA1707: Autonomous vehicles guidance and control

      MERL is seeking a highly motivated and qualified intern to collaborate with the Control for Autonomy team in research on planning and control for autonomous vehicles. The research domain includes algorithms for path planning, vehicle control, high level decision making, sensor-based navigation, driver-vehicle interaction. The ideal candidate is expected to be working towards a PhD with strong emphasis in vehicle guidance and control, and to have interest and background in as many as possible of: vehicle dynamics modeling and control, predictive control algorithms linear and nonlinear systems, motion planning, convex, non-convex, and mixed -integer optimization, statistical estimation, cooperative control. Good programming skills in MATLAB, Python or C/C++ are required, knowledge of rapid prototyping systems, automatic code generation or ROS is a plus. The expected start of of the internship is in the late Spring/Early Summer 2022, for a duration of 3-6 months.

    • CI1733: ML for GNSS-based Applications

      MERL is seeking a highly motivated, qualified intern to work on machine learning for Global Navigation Satellite System (GNSS) applications. The ideal candidate is working towards a PhD and is expected to develop innovative machine learning technologies to increase accuracy and integrity of GNSS-based positioning systems. Candidates should have strong knowledge about as many as possible of GNSS signal processing for multipath mitigation, handling RINEX data, neural network and learning techniques, such as feature extraction, deep machine learning, reinforcement learning, domain adaptation, and distributed learning. Proficient programming skills with PyTorch, Matlab, and C++, and strong mathematical analysis will be additional assets to this position. Candidates in their junior or senior years of a Ph.D. program are encouraged to apply.


    See All Internships for Dynamical Systems
  • Recent Publications

    •  Berntorp, K., Greiff, M., Di Cairano, S., "Bayesian Sensor Fusion of GNSS and Camera With Outlier Adaptation for Vehicle Positioning", International Conference on Information Fusion (FUSION), July 2022.
      BibTeX TR2022-093 PDF
      • @inproceedings{Berntorp2022jul,
      • author = {Berntorp, Karl and Greiff, Marcus and Di Cairano, Stefano},
      • title = {Bayesian Sensor Fusion of GNSS and Camera With Outlier Adaptation for Vehicle Positioning},
      • booktitle = {International Conference on Information Fusion (FUSION)},
      • year = 2022,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2022-093}
      • }
    •  Greiff, M., Di Cairano, S., Berntorp, K., "Dynamic Clustering for GNSS Positioning with Multiple Receivers", International Conference on Information Fusion (FUSION), July 2022.
      BibTeX TR2022-094 PDF
      • @inproceedings{Greiff2022jul,
      • author = {Greiff, Marcus and Di Cairano, Stefano and Berntorp, Karl},
      • title = {Dynamic Clustering for GNSS Positioning with Multiple Receivers},
      • booktitle = {International Conference on Information Fusion (FUSION)},
      • year = 2022,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2022-094}
      • }
    •  Schperberg, A., Di Cairano, S., Menner, M., "Auto-Tuning of Controller and Online Trajectory Planner for Legged Robots", IEEE Robotics and Automation Letters, DOI: 10.1109/​LRA.2022.3185387, Vol. 7, No. 3, pp. 7802-7809, June 2022.
      BibTeX TR2022-085 PDF
      • @article{Schperberg2022jun,
      • author = {Schperberg, Alexander and Di Cairano, Stefano and Menner, Marcel},
      • title = {Auto-Tuning of Controller and Online Trajectory Planner for Legged Robots},
      • journal = {IEEE Robotics and Automation Letters},
      • year = 2022,
      • volume = 7,
      • number = 3,
      • pages = {7802--7809},
      • month = jun,
      • doi = {10.1109/LRA.2022.3185387},
      • url = {https://www.merl.com/publications/TR2022-085}
      • }
    •  Berntorp, K., Menner, M., "Online Constrained Bayesian Inference and Learning of Gaussian-Process State-Space Models", American Control Conference (ACC), June 2022.
      BibTeX TR2022-066 PDF
      • @inproceedings{Berntorp2022jun,
      • author = {Berntorp, Karl and Menner, Marcel},
      • title = {Online Constrained Bayesian Inference and Learning of Gaussian-Process State-Space Models},
      • booktitle = {American Control Conference (ACC)},
      • year = 2022,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2022-066}
      • }
    •  Bonzanini, A.D., Mesbah, A., Di Cairano, S., "Multi-stage Perception-aware Chance-constrained MPC with Applications to Automated Driving", American Control Conference (ACC), June 2022.
      BibTeX TR2022-062 PDF
      • @inproceedings{Bonzanini2022jun,
      • author = {Bonzanini, Angelo Domenico and Mesbah, Ali and Di Cairano, Stefano},
      • title = {Multi-stage Perception-aware Chance-constrained MPC with Applications to Automated Driving},
      • booktitle = {American Control Conference (ACC)},
      • year = 2022,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2022-062}
      • }
    •  Elango, P., Di Cairano, S., Kalabic, U., Weiss, A., "Local Eigenmotion Control for Near Rectilinear Halo Orbits", American Control Conference (ACC), June 2022.
      BibTeX TR2022-060 PDF
      • @inproceedings{Elango2022jun,
      • author = {Elango, Purnanand and Di Cairano, Stefano and Kalabic, Uros and Weiss, Avishai},
      • title = {Local Eigenmotion Control for Near Rectilinear Halo Orbits},
      • booktitle = {American Control Conference (ACC)},
      • year = 2022,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2022-060}
      • }
    •  Firoozi, R., Quirynen, R., Di Cairano, S., "Coordination of Autonomous Vehicles and Dynamic Traffic Rules in Mixed Automated/Manual Traffic", American Control Conference (ACC), June 2022.
      BibTeX TR2022-059 PDF
      • @inproceedings{Firoozi2022jun,
      • author = {Firoozi, Roya and Quirynen, Rien and Di Cairano, Stefano},
      • title = {Coordination of Autonomous Vehicles and Dynamic Traffic Rules in Mixed Automated/Manual Traffic},
      • booktitle = {American Control Conference (ACC)},
      • year = 2022,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2022-059}
      • }
    •  Vaskov, S., Quirynen, R., Menner, M., Berntorp, K., "Friction-Adaptive Stochastic Predictive Control for Trajectory Tracking of Autonomous Vehicles", American Control Conference (ACC), June 2022.
      BibTeX TR2022-065 PDF
      • @inproceedings{Vaskov2022jun,
      • author = {Vaskov, Sean and Quirynen, Rien and Menner, Marcel and Berntorp, Karl},
      • title = {Friction-Adaptive Stochastic Predictive Control for Trajectory Tracking of Autonomous Vehicles},
      • booktitle = {American Control Conference (ACC)},
      • year = 2022,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2022-065}
      • }
    See All Publications for Dynamical Systems
  • Videos