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

  • Awards

    •  AWARD    Marcus Greiff receives Outstanding Student Paper Award at CCTA 2022
      Date: August 25, 2022
      Awarded to: Marcus Greiff
      MERL Contact: Marcus Greiff
      Research Areas: Control, Dynamical Systems, Robotics
      • Marcus Greiff, a Visiting Research Scientist at MERL, was awarded one of three outstanding student paper awards at the IEEE CCTA 2022 conference for his paper titled "Quadrotor Control on SU(2)xR3 with SLAM Integration". The award was given for originality, clarity, and potential impact on practical applications of control. The work presents a complete UAV control system design, facilitating autonomous supermarket inventorying without the need for external motion capture systems. A video of the experiments is on YouTube, including both simulations and real-time examples.

    See All Awards for MERL
  • News & Events

    •  NEWS    MERL researchers presenting workshop papers at NeurIPS 2022
      Date: December 2, 2022 - December 8, 2022
      MERL Contacts: Matthew Brand; Toshiaki Koike-Akino; Jing Liu; Saviz Mowlavi; Kieran Parsons; Ye Wang
      Research Areas: Artificial Intelligence, Control, Dynamical Systems, Machine Learning, Signal Processing
      • In addition to 5 papers in recent news (https://www.merl.com/news/news-20221129-1450), MERL researchers presented 2 papers at the NeurIPS Conference Workshop, which was held Dec. 2-8. NeurIPS is one of the most prestigious and competitive international conferences in machine learning.

        - “Optimal control of PDEs using physics-informed neural networks” by Saviz Mowlavi and Saleh Nabi

        Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a neural network-based surrogate model for the unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained optimal control problems, for which the governing PDE is fully known and the goal is to find a control variable that minimizes a desired cost objective. We validate the performance of the PINN framework by comparing it to state-of-the-art adjoint-based optimization, which performs gradient descent on the discretized control variable while satisfying the discretized PDE.

        - “Learning with noisy labels using low-dimensional model trajectory” by Vasu Singla, Shuchin Aeron, Toshiaki Koike-Akino, Matthew E. Brand, Kieran Parsons, Ye Wang

        Noisy annotations in real-world datasets pose a challenge for training deep neural networks (DNNs), detrimentally impacting generalization performance as incorrect labels may be memorized. In this work, we probe the observations that early stopping and low-dimensional subspace learning can help address this issue. First, we show that a prior method is sensitive to the early stopping hyper-parameter. Second, we investigate the effectiveness of PCA, for approximating the optimization trajectory under noisy label information. We propose to estimate the low-rank subspace through robust and structured variants of PCA, namely Robust PCA, and Sparse PCA. We find that the subspace estimated through these variants can be less sensitive to early stopping, and can outperform PCA to achieve better test error when trained on noisy labels.

        - In addition, new MERL researcher, Jing Liu, also presented a paper entitled “CoPur: Certifiably Robust Collaborative Inference via Feature Purification" based on his previous work before joining MERL. His paper was elected as a spotlight paper to be highlighted in lightening talks and featured paper panel.
    •  EVENT    MERL's Virtual Open House 2022
      Date & Time: Monday, December 12, 2022; 1:00pm-5:30pm ET
      Location: Mitsubishi Electric Research Laboratories (MERL)/Virtual
      Research Areas: Applied Physics, Artificial Intelligence, Communications, Computational Sensing, Computer Vision, Control, Data Analytics, Dynamical Systems, Electric Systems, Electronic and Photonic Devices, Machine Learning, Multi-Physical Modeling, Optimization, Robotics, Signal Processing, Speech & Audio, Digital Video
      • Join MERL's virtual open house on December 12th, 2022! Featuring a keynote, live sessions, research area booths, and opportunities to interact with our research team. Discover who we are and what we do, and learn about internship and employment opportunities.

    See All News & Events for Dynamical Systems
  • Internships

    • CA1940: Autonomous vehicle planning and contro in uncertain environments

      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 in uncertain surrounding environments. The research domain includes algorithms for path planning and control in environments that are uncertain and perceived by sensing and predicted according to models and data. 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, sensor uncertainty modeling, data-driven prediction, predictive control for uncertain systems, motion planning. Good programming skills in MATLAB, Python are required, knowledge of C/C++, rapid prototyping systems, automatic code generation, vehicle simulation packages (CarSim, CarMaker) or ROS are a plus. The expected start of of the internship is in the late Spring/Early Summer 2022, for a duration of 3-6 months.

    • MD1886: Co-design of robotic arm and control systems

      MERL is seeking a highly motivated and qualified individual to conduct research in model-based robotic system design. The ideal candidate should have solid backgrounds in robotic dynamics and simulation, motion planning and control, simulation-based optimization, surrogate modeling, and coding skills. Demonstrated experience on implementing robotic dynamics and simulation/optimization software such as Matlab is a necessity. Ph.D. students in mechanical engineering, robotics, computer science, and electrical engineering are encouraged to apply. Start date for this internship is flexible and the duration is about 3 months.

    • MS1957: Estimation and Model Structure Identification for Digital Twins

      MERL is looking for a highly motivated and qualified candidate to work on estimation and model structure identification for digital twins of multi-physical systems. The research will involve study and development of white-box and grey-box model calibration and identification methods suitable for large-scale systems. The ideal candidate will have a strong background in one or multiple of the following topics: nonlinear estimation, model identification, optimization, data-driven and reduced order modeling, and machine learning; with expertise demonstrated via, e.g., peer-reviewed publications. Prior programming experience in Julia/Modelica is a plus. Senior PhD students in mechanical, electrical, chemical engineering or related fields are encouraged to apply. The typical duration of internship is 3 months and start date is flexible.

    See All Internships for Dynamical Systems
  • Recent Publications

    •  Lin, C., "Magnetic Cooling with Thin Peltier Modules as Thermal Switches", Journal of Magnetism and Magnetic Materials, DOI: 10.1016/​j.jmmm.2023.170482, Vol. 570, pp. 170482, February 2023.
      BibTeX TR2023-006 PDF
      • @article{Lin2023feb,
      • author = {Lin, Chungwei},
      • title = {Magnetic Cooling with Thin Peltier Modules as Thermal Switches},
      • journal = {Journal of Magnetism and Magnetic Materials},
      • year = 2023,
      • volume = 570,
      • pages = 170482,
      • month = feb,
      • doi = {10.1016/j.jmmm.2023.170482},
      • issn = {0304-8853},
      • url = {https://www.merl.com/publications/TR2023-006}
      • }
    •  Garg, K., Baranwal, M., Gupta, R., Benosman, M., "Fixed-Time Stable Proximal Dynamical System for Solving MVIPs", IEEE Transactions on Automatic Control, December 2022.
      BibTeX TR2022-171 PDF
      • @article{Garg2022dec,
      • author = {Garg, Kunal and Baranwal, Mayank and Gupta, Rohit and Benosman, Mouhacine},
      • title = {Fixed-Time Stable Proximal Dynamical System for Solving MVIPs},
      • journal = {IEEE Transactions on Automatic Control},
      • year = 2022,
      • month = dec,
      • url = {https://www.merl.com/publications/TR2022-171}
      • }
    •  Mowlavi, S., Nabi, S., "Optimal Control of PDEs Using Physics-Informed Neural Networks", Advances in Neural Information Processing Systems (NeurIPS) workshop, December 2022.
      BibTeX TR2022-163 PDF
      • @inproceedings{Mowlavi2022dec,
      • author = {Mowlavi, Saviz and Nabi, Saleh},
      • title = {Optimal Control of PDEs Using Physics-Informed Neural Networks},
      • booktitle = {Advances in Neural Information Processing Systems (NeurIPS) workshop},
      • year = 2022,
      • month = dec,
      • url = {https://www.merl.com/publications/TR2022-163}
      • }
    •  Greiff, M., Berntorp, K., "Distributed Kalman Filtering: When to Share Measurements", IEEE Conference on Decision and Control (CDC), DOI: 10.1109/​CDC51059.2022.9993404, December 2022, pp. 5399-5404.
      BibTeX TR2022-158 PDF
      • @inproceedings{Greiff2022dec,
      • author = {Greiff, Marcus and Berntorp, Karl},
      • title = {Distributed Kalman Filtering: When to Share Measurements},
      • booktitle = {IEEE Conference on Decision and Control (CDC)},
      • year = 2022,
      • pages = {5399--5404},
      • month = dec,
      • publisher = {IEEE},
      • doi = {10.1109/CDC51059.2022.9993404},
      • issn = {2576-2370},
      • isbn = {978-1-6654-6761-2},
      • url = {https://www.merl.com/publications/TR2022-158}
      • }
    •  Tu, H., Wang, Y., Li, X., Fang, H., "Spatio-Temporal Thermal Monitoring for Lithium-Ion Batteries via Kriged Kalman Filtering", IEEE Conference on Decision and Control (CDC), DOI: 10.1109/​CDC51059.2022.9992543, December 2022.
      BibTeX TR2022-162 PDF
      • @inproceedings{Tu2022dec2,
      • author = {Tu, Hao and Wang, Yebin and Li, Xianglin and Fang, Huazhen},
      • title = {Spatio-Temporal Thermal Monitoring for Lithium-Ion Batteries via Kriged Kalman Filtering},
      • booktitle = {IEEE Conference on Decision and Control (CDC)},
      • year = 2022,
      • month = dec,
      • doi = {10.1109/CDC51059.2022.9992543},
      • url = {https://www.merl.com/publications/TR2022-162}
      • }
    •  Aguilar Marsillach, D., Di Cairano, S., Weiss, A., "Abort-Safe Spacecraft Rendezvous on Elliptic Orbits", IEEE Transactions on Control Systems Technology, November 2022.
      BibTeX TR2022-142 PDF
      • @article{AguilarMarsillach2022nov,
      • author = {Aguilar Marsillach, Daniel and Di Cairano, Stefano and Weiss, Avishai},
      • title = {Abort-Safe Spacecraft Rendezvous on Elliptic Orbits},
      • journal = {IEEE Transactions on Control Systems Technology},
      • year = 2022,
      • month = nov,
      • url = {https://www.merl.com/publications/TR2022-142}
      • }
    •  Mowlavi, S., Nabi, S., "Optimal control of PDEs using physics-informed neural networks", Journal of Computational Physics, October 2022.
      BibTeX TR2022-143 PDF
      • @article{Mowlavi2022oct,
      • author = {Mowlavi, Saviz and Nabi, Saleh},
      • title = {Optimal control of PDEs using physics-informed neural networks},
      • journal = {Journal of Computational Physics},
      • year = 2022,
      • month = oct,
      • url = {https://www.merl.com/publications/TR2022-143}
      • }
    •  Elango, P., Di Cairano, S., Berntorp, K., Weiss, A., "Sequential linearization-based station keeping with optical navigation for NRHO", AAS/AIAA Astrodynamics Specialist Conference, September 2022.
      BibTeX TR2022-114 PDF
      • @inproceedings{Elango2022sep,
      • author = {Elango, Purnanand and Di Cairano, Stefano and Berntorp, Karl and Weiss, Avishai},
      • title = {Sequential linearization-based station keeping with optical navigation for NRHO},
      • booktitle = {AAS/AIAA Astrodynamics Specialist Conference},
      • year = 2022,
      • month = sep,
      • url = {https://www.merl.com/publications/TR2022-114}
      • }
    See All Publications for Dynamical Systems
  • Videos