Picture of Grand Isle team

This page describes my research on mathematical methods for controlling marine robots. It includes faculty and undergraduate and graduate student research. It began as a collaboration with Professor Fumin Zhang from the Georgia Tech School of Electrical and Computer Engineering, and currently involves Dr. Corina Barbalata from the LSU College of Engineering and Zhong-Ping Jiang from NYU. It includes mathematical control theory, numerical simulations, and real time experimental field work using actual marine robots. The long term objectives are to develop marine robotic methods that are adaptive, fault tolerant, repeatable, robust to uncertainty, and scalable to heterogeneous fleets of autonomous underwater vehicles. Marine robots are useful because of the hazards and high costs associated with conventional human-based marine surveys. The methods from my projects retrieved water and sediment samples, to help monitor the long term impacts of environment disasters, hazards, and stresses.

The projects began in September 2010, in response to the Deepwater Horizon oil spill disaster in the Gulf of Mexico. This included 3 weeks of field work at Grand Isle, Louisiana during the summer of 2011, in a region that was heavily polluted by the oil spill. A total of 14 students worked on the project, including 9 undergraduates. Ten were members of the Georgia Tech Savannah Robotics Team, 3 were from the College of William and Mary, and 1 was from LSU. The field work used several robotic vehicles, including 2 that were built by the Georgia Tech team. Georgia Tech used their surface vehicle Victoria, and their underwater vehicle ROV Beta. Mark Patterson from the Virginia Institute of Marine Science used two versions of his underwater vehicle Fetch. The water and sediment samples from Grand Isle were checked for contaminants by Prof. Ed Overton from the LSU School of the Coast and Environment, and the research produced crude oil concentration maps.

The students benefited from hands on training involving cutting edge control research that would not otherwise have been available. Our current work aims to better understand how to compensate for communication constraints and delays, which result from unfriendly sea conditions. Our techniques involve Lyapunov-Krasovskii functionals, nonlinear tracking controllers, input constraints, robust forward invariance, and event-triggered control. Event-triggered control differs from standard control methods because it calls for only changing control values when a significant event occurs. Our current work studies the benefits of replacing traditional event trigger mechanisms by novel mechanisms that use interval observers and linear Lyapunov functions. These benefits include reduced need to change control values without adversely affecting overshoots, undershoots, or settling times. The research can help protect marine ecosystems by improving responses to hazards such as oil spills, and can help with industrial and military applications that call for remotely operated or autonomous marine vehicles. Here are the vehicles used in the Grand Isle field work:

Picture of Grand Isle team

From left to right, they are VIMS Fetch 3.5, the YSI Ecomapper (a commercial vehicle), ASV-Victoria, ROV-Beta, and VIMS Fetch 1. Click here for an enlarged photo of the vehicles. Here is a crude oil concentration map that was generated by the projects:

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Here are publications that were sponsored in part by our projects. The people whose names are underlined were students when the paper was written. Clicking on their titles links to downloadable versions from the publishers' websites.
  1. Alyahia, S., C. Barbalata, M. Malisoff, and F. Mazenc, "Dynamic event-triggered control of linear continuous-time systems using a positive systems approach," Nonlinear Analysis: Hybrid Systems, Volume 54, November 2024, Article 101508.
  2. Malisoff, M., F. Mazenc, and C. Barbalata, "Event-triggered control under unknown input and unknown measurement delays using interval observers,'' IEEE Control Systems Letters, Volume 7, 2023, pp. 823-828.
  3. Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Subpredictor approach for event-triggered control of discrete-time systems with input delays," European Journal of Control, 2022, Article 100664.
  4. Zuo, W., A. Chakravarthy, M. Malisoff, and Z. Chen, "Event-triggered control of robotic fish with reduced communication rate," IEEE Robotics and Automation Letters, Volume 7, Issue 4, 2022, pp. 9405-9412.
  5. Mazenc, F., M. Malisoff, and C. Barbalata, "Event-triggered prediction-based delay compensation approach," IEEE Control Systems Letters, Volume 6, 2022, pp. 2515-2520.
  6. Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Event-triggered control for time-varying systems using a positive systems approach," Systems and Control Letters, Volume 161, March 2022, Paper 105131.
  7. Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Event-triggered control for discrete-time systems using a positive systems approach," IEEE Control Systems Letters, Volume 6, 2022, pp. 1843-1848.
  8. Mazenc, F., M. Malisoff, and C. Barbalata, "Event-triggered control for continuous-time linear systems with a delay in the input," Systems and Control Letters, Volume 159, January 2022, Paper 105075.
  9. Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Event-triggered control for systems with state delays using a positive systems approach," in Proceedings of the 60th IEEE Conference on Decision and Control, 2021, pp. 552-557.
  10. Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Event-triggered control using a positive systems approach," European Journal of Control, Volume 62, 2021, pp. 63-68.
  11. Malisoff, M., R. Sizemore, and F. Zhang, "Adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature," Automatica, Volume 75, 2017, pp. 133-143.
  12. Malisoff, M., R. Sizemore, and F. Zhang, "Robustness of adaptive control for three-dimensional curve tracking under state constraints: effects of scaling control terms," in Proceedings of the 55th IEEE Conference on Decision and Control (Las Vegas, NV, 12-14 December 2016), pp. 3825-3830.
  13. Malisoff, M., and F. Zhang, "Adaptive planar curve tracking control with unknown curvature," in Proceedings of the 2016 American Control Conference (Boston, MA, 6-8 July 2016), pp. 1608-1612.
  14. Malisoff, M., and F. Zhang, "Robustness of adaptive control under time delays for three-dimensional curve tracking,'' SIAM Journal on Control and Optimization, Volume 53, Number 4, 2015, pp. 2203-2236.
  15. Mukhopadhyay, S., C. Wang, M. Patterson, M. Malisoff, and F. Zhang, "Collaborative autonomous surveys in marine environments affected by oil spills," in Cooperative Robots and Sensor Networks 2014, A. Koubaa and A. Khelil, Eds., Studies in Computational Intelligence Series Vol. 554, Springer, New York, 2014, pp. 87-113.
  16. Malisoff, M., and F. Zhang, "An adaptive control design for 3D curve tracking based on robust forward invariance," in Proceedings of the 52nd IEEE Conference on Decision and Control (Florence, Italy, 10-13 December 2013), pp. 4473-4478.
  17. Malisoff, M., and F. Zhang, "Robustness of a class of three-dimensional curve tracking control laws under time delays and polygonal state constraints,'' in Proceedings of the American Control Conference (Washington, DC, 17-19 June 2013), pp. 5690-5695.
  18. Malisoff, M., and F. Zhang, "Adaptive control for planar curve tracking under controller uncertainty,'' Automatica, Volume 49, Issue 5, May 2013, pp. 1411-1418.
  19. Malisoff, M., and F. Zhang, "Adaptive controllers and robustness analysis for curve tracking with unknown control gains," in Proceedings of the 2012 American Control Conference (Montreal, Canada, 27-29 June 2012), pp. 344-349.
  20. Malisoff, M., F. Mazenc, and F. Zhang, "Stability and robustness analysis for curve tracking control using input-to-state stability," IEEE Transactions on Automatic Control, Volume 57, Issue 5, May 2012, pp. 1320-1326.
  21. Malisoff, M., F. Mazenc, and F. Zhang, "Input-to-state stability for curve tracking control: A constructive approach," in Proceedings of the 2011 American Control Conference (San Francisco, CA, 29 June-1 July 2011), pp. 1984-1989.
The preceding works were sponsored in part by the US National Science Foundation Division of Electrical, Communications and Cyber Systems Energy, Power, and Adaptive Systems Program and Division of Mathematical Sciences Applied Mathematics Program under grants 1056253, 1056255, 1102348, 2009644, or 2009659. Here are links to home pages for some of the project participants and their co-authors:
  1. Valerie Bazie
  2. Steve Bradshaw
  3. Lisa Hicks
  4. Michael Malisoff
  5. Shayok Mukhopadhyay
  6. Mark Patterson
  7. Chuanfeng Wang
  8. Fumin Zhang
Three MS students (Lisa Hicks, Valerie Bazie, and Steve Bradshaw) and one undergraduate (Michael Bunch) who worked on the projects went on to work for Toyota or General Motors. Here are links to news reports about the projects and its participants:
  1. May 31, 2023 Fumin Zhang Semi-Plenary
  2. April 2011 Poster
  3. One Minute YouTube Video
  4. Six Minute YouTube Video
  5. LSU Gold Article
  6. LSU College of Science News
  7. Georgia Tech ECE Report
  8. January 2012 Baton Rouge Advocate Article
  9. LSU Mathematics News
  10. WSB Report
  11. WOKV Report
  12. WJAC-TV Report
  13. Times Union Article
  14. Vicksburg Post Article
  15. Houston Chronicle Article
  16. Beaumont Enterprise Article
  17. San Antonio Express-News Article
  18. Mashable Article
  19. April 2012 Pursuit Article
  20. April 2012 APEGGA Peg Article
  21. LSU College of Science Strategic Plan
  22. February 2013 LSU Media Center News
  23. May 2013 Pursuit Article
  24. June 2013 SEE Innovation Research.gov Report
  25. March 2014 Rainmaker Award
  26. April 2014 College of Science E-News
  27. ASV-Victoria "Robots For Good" Poster
  28. Summer 2014 LSU Alumni Magazine
  29. August 2014 CMMI and EPCN Announcement
  30. Fall 2014 LSU ORED Magazine Article
  31. September 24, 2020 NYU Tandon News Report
  32. 2020 Linkedin Research Grant Announcement
  33. September 27, 2021 LSU Reveille Article and Tweet
  34. Issuu Version of September 27, 2021 Reveille Article
  35. 2021 LSU College of Science Annual Report Pursuit Article
  36. January 2022 LSU Mathematics Research Announcement
  37. February 2022 LSU College of Engineering Research Announcement
  38. March 2022 LSU College of Engineering Underwater Exploration Article
  39. WCMU Radio Article about Field Work in Great Lakes
  40. WBKB TV Article about Field Work
Thank you for your interest in our projects!


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