改进的动态规划算法可全局收敛求解带约束的最优控制问题。
Global Convergence of a Line-Search Filter Differential Dynamic Programming Method
- 用反向递推与前向仿真构造迭代步，替代传统牛顿法。
- 在特定约束条件下，算法保证全局收敛性。
- 适合需要稳定求解复杂控制问题的研究者。
本文建立了FilterDDP算法的全局收敛性，该算法将早期离散时间微分动态规划（DDP）扩展至处理状态和控制变量的非线性约束。与一般非线性规划中采用阻尼牛顿步不同，FilterDDP通过反向递推和前向仿真计算试步点。我们证明，在一类约束最优控制问题下，该反向-前向过程具备与牛顿步等效的性质，从而延续Wächter与Biegler（SIAM J. Optim., 2005）关于线搜索滤波法全局收敛分析的框架，确保算法整体收敛。
原文摘要 · Abstract (English)
In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in addition to the dynamics. FilterDDP adopts a line-search filter procedure for step acceptance. However, instead of a damped Newton step applied in the general nonlinear programming setting, the computation of a trial point involves applying a backward recursion and a forward simulation. We establish the global convergence of FilterDDP by showing that for a subset of constrained optimal control problems, the this backward-forward procedure satisfies the same properties as a Newton step for the purpose of establishing global convergence of a line-search filter method, following the analysis of Wächter and Biegler [\emph{SIAM Journal on Optimization}, 16 (2005), pp. 1-31].
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