Optimal Control Parametrization Strategies for MPC with Application to On-Orbit Servicing

Kurzfassung

This thesis aims to identify the most performant optimal control parametrization for Model Predictive Control (MPC) setups. The work begins with a systematic investigation of various explicit and implicit optimal control methods based on a generic multi-body benchmark example. A detailed validation is done on the real-time performance capabilities of the methods, their closed-loop performance, and open-loop versus closed-loop behavior. The optimal control strategies are evaluated along the nonlinear program solvers FATROP, IPOPT and SQP. Among the approaches considered, combining FATROP with a MS method or an adapted local LGR-LOC* pseudospectral method proves in simulations to be the most effective. Further, MS and LGR-LOC* are compared and evaluated in the context of a tracking and escape maneuver for On-Orbit Servicing (OOS). The MS method is identified to be the computationally most efficient solution, while the LGR-LOC* method achieved minimally improved closed-loop performance. The final section of the thesis proposes a universal Bayesian Optimization (BO) framework for identifying the most suitable optimal control method and parametrization for a respective MPC control problem. The developed LGR-LOC* incorporates explicit multiple shooting and implicit low- and high-order collocation methods in one formulation. This leverages the BO algorithm to determine the optimal parametrization, eliminating the need to implement each control method individually. This approach decreases the computational cost of MPC for OOS by 45 %, while simultaneously improving the closed-loop performance by 8-43 %, depending on the maneuver.