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.
翻译：最近,作为解决最佳控制问题的有效方法,SCP程序(SCP)最近获得显著的欢迎,并成功地应用于若干不同领域。然而,对SCP的理论分析受到的关注相对有限,而且往往限于独立时间的配方。在本文件中,我们对相当一般的SCP程序类别进行统一理论分析,以处理连续时间的最佳控制问题。除了在连续时间环境中产生趋同保证外,我们的分析还揭示了两种新的数字和实践见解。首先,我们展示了人们如何能够更容易地解释多种类型的限制,这是机械系统最佳控制的一个决定性特征。第二,我们展示了如何利用我们的理论分析来加速基于SCP的最佳控制方法,从间接最佳控制中引入技术。
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