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 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. They 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. The research can help protect marine ecosystems by improving responses to hazards such as oil spills. 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.

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, to appear.
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 (Austin, TX, 13-15 December 2021), to appear.
Mazenc, F., M. Malisoff, C. Barbalata, and Z.-P. Jiang, "Event-triggered control using a positive systems approach," in European Journal of Control, Volume 62, 2021, pp. 63-68.
Zhang, F., Cyber-Maritime Cycle: Autonomy of Marine Robots for Ocean Sensing, Now Publishers, Boston, MA, 2017.
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.
Szwaykowska, K., and F. Zhang, "Trend and bounds for error growth in controlled Lagrangian particle tracking," IEEE Transactions on Oceanic Engineering, Volume 39, Issue 1, January 2014, pp. 10-25.
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.
Wu, W., F. Zhang, and Y. Wardi, "Energy-information tradeoffs in motion and sensing for target localization," in Proceedings of the 2013 European Control Conference (Zurich, Switzerland, 17-19 July 2013), pp. 1250-1255.
Yang, H., C. Wang, and F. Zhang, "Robust geometric formation control of multiple autonomous underwater vehicles with time delays," in Proceedings of the American Control Conference (Washington, DC, 17-19 June 2013), pp. 1382-1387.
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.
Wu, W., and F. Zhang, "A switching strategy for target tracking by mobile sensing agents," Journal of Communications, Volume 8, Number 1, January 2013, pp. 47-54.
Wu, W., and F. Zhang, "Coherent steps of mobile sensing agents in Gaussian scalar fields," in Proceedings of the 51st IEEE Conference on Decision and Control (Maui, HI, 10-13 December 2012), pp. 2814-2819.
Mukhopadhyay, S., C. Wang, S. Bradshaw, V. Bazie, S. Maxon, L. Hicks, M. Patterson, and F. Zhang, "Controller performance of marine robots in reminiscent oil surveys," in Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (Vilamoura, Algarve, Portugal, 7-12 October 2012), pp. 1766-1771.
Wu, W., I. Couzin, and F. Zhang, "Bio-inspired source seeking with no explicit gradient estimation," in Proceedings of the 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (Santa Barbara, CA, 14-15 September 2012), pp. 240-245.
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.
Yang, H., and F. Zhang, "Robust control of formation dynamics for autonomous underwater vehicles in horizontal plane," Journal of Dynamic Systems, Measurement, and Control, Volume 134, Issue 3, Paper 031009.
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.
Wu, W., and F. Zhang, "Explorability of noisy scalar fields," in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (Orlando, FL, 12-15 December 2011), pp. 6439-6444.
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.
Yang, H., and F. Zhang, "Control of horizontal formation dynamics for autonomous underwater vehicles," in Proceedings of the 2011 IEEE International Conference on Robotics and Automation (Shanghai, China, 9-13 May 2011), pp. 3364-3369.

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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