Through the years, Sequential Convex Programming (SCP) has gained great interest as an efficient tool for non-convex optimal control. Despite the large number of existing algorithmic frameworks, only a few are accompanied by rigorous convergence analysis, which are often only tailored to discrete-time problem formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures which is applied to the original continuous-time formulation. Besides the extension of classical convergence guarantees to continuous-time settings, our analysis reveals two new features inherited by SCP-type methods. First, we show how one can more easily account for manifold-type constraints, which play a key role in the optimal control of mechanical systems. Second, we demonstrate how the theoretical analysis may be leveraged to devise an accelerated implementation of SCP based on indirect methods. Detailed numerical experiments are provided to show the key benefits of a continuous-time analysis to improve performance.

中文翻译：

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连续时间最优控制的序贯凸规划的理论和数值特性分析

多年来，顺序凸规划 (SCP) 作为非凸最优控制的有效工具引起了极大的兴趣。尽管有大量现有的算法框架，但只有少数伴随着严格的收敛分析，这些分析通常只针对离散时间问题公式化。在本文中，我们对适用于原始连续时间公式的一类相当普遍的 SCP 程序进行了统一的理论分析。除了将经典收敛保证扩展到连续时间设置之外，我们的分析还揭示了 SCP 类型方法继承的两个新特征。首先，我们展示了如何更容易地解释流形类型的约束，这些约束在机械系统的优化控制中起着关键作用。第二，我们展示了如何利用理论分析来设计基于间接方法的 SCP 加速实施。提供了详细的数值实验，以显示连续时间分析在提高性能方面的主要优势。