View Video Presentation: https://doi.org/10.2514/6.2023-1095.vid

This paper explores intrusive and non-intrusive methods that enable the inclusion of stochastic differential equations in design optimization of time-dependent systems. Using a gradient-based trajectory optimization formulation, pseudospectral integration, and proportional-integral controllers, uncertainties are introduced through distributed initial conditions, material properties, and performance coefficients, and are mitigated by changing open-loop control inputs or closed-loop controller gains. The examples include a linear system for uncertainty propagation and open-loop control optimization, and reproducible polyalphaolefin mixing chamber for optimal control gain selection. The linear system provides a fundamental baseline and the mixing chamber is simple enough for others to easily implement. The methods under investigation include Monte Carlo simulation, intrusive and non-intrusive generalized polynomial chaos, and unscented transform.