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

    • MS1838: Data-Driven Optimization for Building Energy Systems

      MERL is looking for a highly motivated and qualified candidate to work on data-driven, sample-efficient optimization with real-world applications in building energy systems. The ideal candidate will have a strong understanding machine learning or sampling-based optimization with expertise demonstrated via, e.g., publications, in at least one of: few-shot optimization, Bayesian methods, and/or learning for control/estimation of buildings and energy systems. Hands-on programming experience with standard ML toolkits such as PyTorch/Tensorflow is preferred; knowledge of additional, relevant tools (e.g., GPyTorch, Pyro) is a plus. PhD students are preferred, as an expected outcome of the internship is a publication in a high-tier venue. The minimum duration of the internship is 12 weeks; start time is flexible. This internship is preferred to be onsite at MERL, but may be done remotely where you live if the COVID pandemic makes it necessary.

    • DA1841: High-fidelity CFD for simulation and optimization

      The Data Analytics Group at MERL is seeking a highly motivated, qualified individual to join our internship program in the summer of 2022. The ideal candidate will be a Ph.D. student specializing in fluid dynamics, with solid background in turbulence modeling and computational fluid dynamics (CFD). Research exposure to one of the following is very desirable but not necessary: PDE-constrained optimization, model reduction techniques, and Physics-informed Neural Nets (PINNs). Ideal candidate is familiar with open-source CFD solvers such as OpenFOAM or SU2. Publication of results obtained during the internship is expected. The starting date is flexible and the internship will last about 12 weeks.

    • CA1728: Safe data-driven control of dynamical systems under uncertainty

      MERL is looking for a highly motivated individual to work on safe control of data-driven, uncertain, dynamical systems. The research will develop novel optimization and learning-based control algorithms to guarantee safety and performance in various industrial applications, including autonomous driving. The ideal candidate should have experience in either one or multiple of the following topics: optimal control under uncertainty, (robust and stochastic) model predictive control, (convex and non-convex) optimization, and (reinforcement and statistical) learning. Ph.D. students in engineering or mathematics with a focus on control, optimization, and learning are encouraged to apply. A successful internship will result in submission of relevant results to peer-reviewed conference proceedings and journals, and development of well-documented (Python/MATLAB) code for MERL. The expected duration of the internship is 3-6 months, and the start date is Summer 2022.


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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