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.
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    •  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.
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  • Internships

    • CA1795: Path Planning and Control for Autonomous Articulated Vehicles

      MERL is seeking a highly motivated and qualified intern to collaborate with multiple researchers on the implementation and experimental validation of algorithms for path/motion planning, optimal control and reference tracking in autonomous articulated vehicles. The ideal candidate has a background in either path planning or model predictive control (MPC) for autonomous (articulated) vehicles, and the candidate should be familiar with optimal control, vehicle dynamics, A* search, Matlab and Simulink, and C/C++ code generation. Any experience with dSPACE (e.g., MicroAutoBox or Scalexio) is a plus. MS or PhD students in control, robotics, electrical and mechanical, or related areas, are encouraged to apply. Start date for this internship is as soon as possible, and the expected duration is about 3-6 months.

    • 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.

    • 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.


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  • Recent Publications

    •  Mowlavi, S., Benosman, M., Nabi, S., "Reinforcement Learning State Estimation for High-Dimensional Nonlinear Systems", International Conference on Learning Representations (ICLR) Workshop, April 2022.
      BibTeX TR2022-042 PDF
      • @inproceedings{Mowlavi2022apr,
      • author = {Mowlavi, Saviz and Benosman, Mouhacine and Nabi, Saleh},
      • title = {Reinforcement Learning State Estimation for High-Dimensional Nonlinear Systems},
      • booktitle = {International Conference on Learning Representations (ICLR) Workshop},
      • year = 2022,
      • month = apr,
      • url = {https://www.merl.com/publications/TR2022-042}
      • }
    •  Vijayshankar, S., Chakrabarty, A., Grover, P., Nabi, S., "Co-Design of Reduced-Order Models and Observers from Thermo-Fluid Data", IFAC Journal of Systems and Control, DOI: 10.1016/​j.ifacsc.2021.100181, Vol. 19, pp. 100181, January 2022.
      BibTeX TR2022-009 PDF
      • @article{Vijayshankar2022jan,
      • author = {Vijayshankar, Sanjana and Chakrabarty, Ankush and Grover, Piyush and Nabi, Saleh},
      • title = {Co-Design of Reduced-Order Models and Observers from Thermo-Fluid Data},
      • journal = {IFAC Journal of Systems and Control},
      • year = 2022,
      • volume = 19,
      • pages = 100181,
      • month = jan,
      • doi = {10.1016/j.ifacsc.2021.100181},
      • url = {https://www.merl.com/publications/TR2022-009}
      • }
    •  Berntorp, K., Chakrabarty, A., Di Cairano, S., "Vehicle Rollover Avoidance by Parameter-Adaptive Reference Governor", IEEE Annual Conference on Decision and Control (CDC), DOI: 10.1109/​CDC45484.2021.9683770, December 2021, pp. 635-640.
      BibTeX TR2021-151 PDF
      • @inproceedings{Berntorp2021dec,
      • author = {Berntorp, Karl and Chakrabarty, Ankush and Di Cairano, Stefano},
      • title = {Vehicle Rollover Avoidance by Parameter-Adaptive Reference Governor},
      • booktitle = {IEEE Annual Conference on Decision and Control (CDC)},
      • year = 2021,
      • pages = {635--640},
      • month = dec,
      • doi = {10.1109/CDC45484.2021.9683770},
      • url = {https://www.merl.com/publications/TR2021-151}
      • }
    •  Quirynen, R., Di Cairano, S., "Sequential Quadratic Programming Algorithm for Real-Time Mixed-Integer Nonlinear MPC", IEEE Conference on Decision and Control (CDC), DOI: 10.1109/​CDC45484.2021.9683714, December 2021, pp. 993-999.
      BibTeX TR2021-147 PDF
      • @inproceedings{Quirynen2021dec,
      • author = {Quirynen, Rien and Di Cairano, Stefano},
      • title = {Sequential Quadratic Programming Algorithm for Real-Time Mixed-Integer Nonlinear MPC},
      • booktitle = {IEEE Conference on Decision and Control (CDC)},
      • year = 2021,
      • pages = {993--999},
      • month = dec,
      • doi = {10.1109/CDC45484.2021.9683714},
      • url = {https://www.merl.com/publications/TR2021-147}
      • }
    •  Vinod, A.P., Weiss, A., Di Cairano, S., "Abort-safe spacecraft rendezvous under stochastic actuation and navigation uncertainty", IEEE Annual Conference on Decision and Control (CDC), DOI: 10.1109/​CDC45484.2021.9683322, December 2021, pp. 6620-6625.
      BibTeX TR2021-148 PDF
      • @inproceedings{Vinod2021dec,
      • author = {Vinod, Abraham P. and Weiss, Avishai and Di Cairano, Stefano},
      • title = {Abort-safe spacecraft rendezvous under stochastic actuation and navigation uncertainty},
      • booktitle = {IEEE Annual Conference on Decision and Control (CDC)},
      • year = 2021,
      • pages = {6620--6625},
      • month = dec,
      • doi = {10.1109/CDC45484.2021.9683322},
      • url = {https://www.merl.com/publications/TR2021-148}
      • }
    •  Bonzanini, A.D., Mesbah, A., Di Cairano, S., "On the Stability Properties of Perception-aware Chance-constrained MPC in Uncertain Environments", IEEE Conference on Decision and Control (CDC), DOI: 10.1109/​CDC45484.2021.9682990, December 2021.
      BibTeX TR2021-145 PDF
      • @inproceedings{Bonzanini2021dec,
      • author = {Bonzanini, Angelo Domenico and Mesbah, Ali and Di Cairano, Stefano},
      • title = {On the Stability Properties of Perception-aware Chance-constrained MPC in Uncertain Environments},
      • booktitle = {IEEE Conference on Decision and Control (CDC)},
      • year = 2021,
      • month = dec,
      • doi = {10.1109/CDC45484.2021.9682990},
      • url = {https://www.merl.com/publications/TR2021-145}
      • }
    •  Johnson, R.S., Di Cairano, S., Sanfelice, R., "Parameter Estimation using Hybrid Gradient Descent", IEEE Conference on Decision and Control (CDC), DOI: 10.1109/​CDC45484.2021.9682794, December 2021.
      BibTeX TR2021-146 PDF
      • @inproceedings{Johnson2021dec,
      • author = {Johnson, Ryan S. and Di Cairano, Stefano and Sanfelice, Ricardo},
      • title = {Parameter Estimation using Hybrid Gradient Descent},
      • booktitle = {IEEE Conference on Decision and Control (CDC)},
      • year = 2021,
      • month = dec,
      • doi = {10.1109/CDC45484.2021.9682794},
      • url = {https://www.merl.com/publications/TR2021-146}
      • }
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  • Videos