Monique Chyba's main research area concerns the development of geometric methods to solve optimal control problems. One of her central objectives is to understand the role of singular extremals in optimal strategies for nonlinear control systems. More specifically, she has been lately focusing on using differential geometric techniques to exploit in the time optimal problem the particular structure of the Lie algebra formed by the vector fields describing a controlled mechanical system. Her research is oriented towards applications with a special emphasis on the motion planning problem for autonomous underwater vehicles.

Books

• Singular Trajectories and their Role in Control Theory (with B. Bonnard) Springer-Verlag, Series: Mathematics and Applications: Vol 40, 357 pgs (2003).

Journals and Conferences Proceedings

• (With T. Haberkorn, R.N. Smith, G.R. Wilkens) A Geometric Analysis of Trajectory Design for Underwater Vehicles. Discrete and Continuous Dynamical Systems-B. Submitted (October 2007).
• (With T. Haberkorn, R.N. Smith, S.K. Choi) Autonomous Underwater Vehicles: Development and Implementation of time and Energy Efficient Trajectories. Ship Technology Research. To appear, 2008.
• (With T. Haberkorn, R.N. Smith, S.K. Choi) Design and implementation of time efficient trajectories for an underwater vehicle. Journal of Ocean Engineering. To appear, 2008. (http://dx.doi.org/10.1016/j.oceaneng.2007.07.007)
• (With T. Haberkorn, R.N. Smith, S.K. Choi) Implementable Efficient Time and Energy Consumption Trajectories Design for an Autonomous UNderwater Vehicle. 6th International Conference on Computer Applications and Information Technology in the Maritime Industries (COMPIT), Italy (2007)
• (With T. Haberkorn, R.N. Smith, S. WeatherWax, S.K. Choi) Hydrodynamic and Thruster Model Validation for Autonomous Underwater Vehicles. 26th International Conference on Offshore Mechanics and Artic Engineering (OMAE), USA (2007)