Successive Convexification of Non-convex Optimal Control Problems: Theory and Applications

Abstract

The topic of this dissertation centers around Successive Convexification, a family of iterative algorithms designed to solve non-convex constrained optimal control problems. This document begins with an introduction to optimal control and finite-dimensional optimization in Chapter 2. It then presents the main algorithm within the Successive Convexification framework, SCvx, in Chapter 3. SCvx is a general-purpose solver that can handle problems with nonlinear system dynamics and non-convex state and control constraints. Analytical and numerical results are presented to demonstrate its convergence properties, including global convergence, strong convergence and superlinear convergence rate. SCvx-fast, a specialized version of SCvx is introduced next in Chapter 4 to handle systems with simpler dynamics and convex keep-out zones type of constraints commonly seen in quadrotor obstacle avoidance problems. It has new features such as a project-and-convexify step, removes the smoothness assumption, and does not rely on the trust-region updating mechanism. As a result, more aggressive steps can be taken and thus convergence occurs in much fewer iterations.With SCvx or SCvx-fast as the central pillar for on-board trajectory planning, we can build a fully autonomous system by further integrating i) a computer-vision-based perception unit and ii) Signal-Temporal-Logic (STL)-based mission specifications. Chapter 5 explores these directions as aerospace applications of Successive Convexification.