论文标题
用于输入 - 植入动力学的快速近似动态编程
Fast Approximate Dynamic Programming for Input-Affine Dynamics
论文作者
论文摘要
我们提出了两种新型的数值方案，以近似与有限 - 摩尼子有关的动态编程〜（DP）操作的实现，这是对具有输入型动力学的离散时间系统的最佳控制。所提出的算法涉及状态和输入空间的离散化，并基于解决与DP操作相对应的双重问题的替代路径。我们为提出的算法提供了误差界，以及对其计算复杂性的详细分析。特别是，对于在州和输入变量中具有可分离数据的特定类别的问题，所提出的方法可以将DP操作的典型时间复杂性从$ O（XU）$降低到$ O（X+U）$，其中$ X $和$ u $分别表示离散状态和输入空间的大小。通过将DP操作中的最小化算法转换到通过离散共轭的添加到添加的算法转换来实现这种降低。
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms involve discretization of the state and input spaces and are based on an alternative path that solves the dual problem corresponding to the DP operation. We provide error bounds for the proposed algorithms, along with a detailed analysis of their computational complexity. In particular, for a specific class of problems with separable data in the state and input variables, the proposed approach can reduce the typical time complexity of the DP operation from $O(XU)$ to $O (X+U)$, where $X$ and $U$ denote the size of the discrete state and input spaces, respectively. This reduction is achieved by an algorithmic transformation of the minimization in the DP operation to an addition via discrete conjugation.
