Sensitivity analysis of optimal control problems (Alen Alexanderian)

Prerequisites: Multivariable calculus, ordinary differential equations, and basic programming skills.

Outline: A common problem in the sciences and engineering is the design or control of systems governed by differential equations. Examples include finding optimal control strategies to combat an epidemic, computing an optimal navigation path for a ship moving in a body of water or optimal navigation of drones. We focus on systems governed by systems of ODEs. Such models often include Unknown/uncertain parameters, in addition to the control or design variables. The quality and effectiveness of the computed optimal control/design are influenced by the choice of these parameters. Therefore, understanding the sensitivity of the computed optimal control to uncertain model parameters is essential. This type of sensitivity analysis is called hyper-differential sensitivity analysis (HDSA) (1, 2).

Research objectives: We will explore HDSA in optimal control problems governed by ODEs with focus on navigation problems. The goal is to understand the sensitivity of the optimal navigation paths to additional parameters in the model.

Outcomes: Computational approach and results for understanding the sensitivity of optimal control problems under study. Results will provide tools for quickly determining which parameters in the model are most influential to the computed control strategy. Computer codes will be made publicly available to stimulate further research in this direction.

References:

• Hart J, van Bloemen Waanders B, Herzog R. Hyperdifferential sensitivity analysis of uncertain parameters in pdde-constrained optimization. Int J Uncertain Quant. 2020;10:225-248.
• Sunseri I, Hart J, van Bloemen Waanders B, Alexanderian A. Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations. Inverse Probl. 2020;36:125001.