Multidisciplinary System Modeling and Optimization

All-At-Once formulation integrating pseudo-spectral optimal control for launch vehicle design and uncertainty quantification

“…Consequently, the optimization problem to solve is composed of 16 optimization variables, three inequality constraints and one equality constraint. To perform the optimization, the system-level optimizer is based on the Covariance Matrix Adaptation -Evolution Strategy [52], that proved to be efficient to solve such a problem [53,54]. In MDF with direct single shooting method, an evolutionary algorithm is used instead of a gradient-based optimizer as the propagation of gradient through the trajectory integration (e.g., using Runge-Kutta integrator in direct single shooting method) is challenging as a small modification of control law parameters may lead to a large modification of the launch vehicle states at the end of the trajectory.…”