Michael Malisoff

Roy P. Daniels Professor
Louisiana State University Department of Mathematics
malisoff@lsu.edu

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.

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.
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.
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.
Mazenc, F., M. Malisoff, and C. Barbalata, "Event-triggered prediction-based delay compensation approach," IEEE Control Systems Letters, Volume 6, 2022, pp. 2515-2520.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Malisoff, M., and F. Zhang, "Adaptive control for planar curve tracking under controller uncertainty,'' Automatica, Volume 49, Issue 5, May 2013, pp. 1411-1418.
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.
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.
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:

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:

Thank you for your interest in our projects!

Department of Mathematics | 392 Lockett Hall | Baton Rouge, LA 70803
www.math.lsu.edu | malisoff@lsu.edu | (225) 578-6714

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