On the Uses of Linear-Quadratic Methods in Solving Nonlinear Dynamic Optimization Problems With Direct Transcription

Solving nonlinear dynamic optimization (NLDO) and optimal control problems can be quite challenging, but the need for effective methods is ever increasing as more engineered systems become more dynamic and integrated. In this article, we will explore the various uses of linear-quadratic dynamic optimization (LQDO) in the direct transcription-based solution strategies for NLDO. Three general LQDO-based strategies are discussed, including direct incorporation, two-level optimization, and quasi-linearization. Connections are made between a variety of existing approaches, including sequential quadratic programming. The case studies are solved with the various methods using a publicly available, MATLAB-based tool. Results indicate that the LQDO-based strategies can improve existing solvers and be effective solution strategies. However, there are robustness issues and problem derivative requirements that must be considered.