# Sensitivity analysis of optimal control problems

**Faculty Mentors:**

- Alen Alexanderian (Mathematics, NCSU)
- Joseph Hart (Sandia National Laboratory)

**Prerequisites:** Calculus, differential equations, some programming.

**Outline:** A common problem in the sciences and engineering is the control of systems governed by differential equations. Examples include finding optimal control strategies to fight 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 typically include several uncertain parameters in addition to the control variables. The effectiveness of the computed optimal control is influenced by the choice of these uncertain 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); see [1].

**Objectives: **Exploring HDSA in optimal control problems governed by ODEs with focus on navigation problems. To understand the sensitivity of the optimal navigation paths to additional model parameters.

**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:**

*Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations.*Inverse Probl, 2020. 36: p. 125001.