Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control

TL;DR

This paper provides a comprehensive theoretical analysis of Sequential Convex Programming (SCP) for continuous-time optimal control, offering convergence guarantees and practical insights for handling manifold constraints and improving computational efficiency.

Contribution

It presents the first unified theoretical framework for continuous-time SCP, including convergence proofs and novel methods for manifold constraints and acceleration techniques.

Findings

Established convergence guarantees for continuous-time SCP.

Demonstrated easier handling of manifold constraints in optimal control.

Proposed methods to accelerate SCP using indirect optimal control techniques.

Abstract

Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.