A second‐order optimization algorithm using quadric control updates for multistage optimal control problems

This paper describes a trajectory optimization algorithm that generates a quadric control update, which satisfies the constraints and necessary conditions to the second order. The algorithm is designed to solve multistage optimization problems. The algorithm is tested against a commercially available Sequential Quadratic Programming algorithm on problems with linear dynamics and linear and nonlinear constraints. This algorithm is a departure from previous methods because it explicitly satisfies the constraints to the second order.