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Lattice point sets for state sampling in approximate dynamic programming

机译：近似动态规划中的状态采样的格子点集

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摘要

This paper investigates the use of lattice point sets as an efficient method to sample uniformly the state space of discrete-time dynamic systems for the solution of finite-horizon optimal control problems using approximate dynamic programming. Lattice point sets are a kind of discretization method, commonly employed for efficient numerical integration, providing a regular and balanced sampling of the state space based on the repetition of elementary unit cells. A convergence analysis of the approximate solution of the control problem to the optimal one is provided, pointing out that such sampling schemes allow one to efficiently exploit possible regularities of the cost-to-go functions. Furthermore, it is shown that a higher accuracy may be obtained through suitable transformations of the state vector of the dynamic system. Another advantage of lattice point sets over other sampling schemes is the possibility of evaluating a priori the goodness of a given set over another through the explicit computation of a specific parameter. Simulation results concerning the optimal control of a water reservoirs system are presented to show the effectiveness of the proposed approach.
机译：本文调查了使用晶格点集作为一种均匀地样本的有效方法，用于使用近似动态规划解决有限地平线最佳控制问题的离散时间动态系统的状态空间。格子点集是一种离散化方法，通常用于有效的数字积分，基于基于基本单元电池的重复提供状态空间的规则和平衡的采样。提供了对最佳方法的控制问题的近似解的收敛性分析，指出这种采样方案允许人们有效地利用成本到去功能的可能正规。此外，示出了通过动态系统的状态向量的合适变换来获得更高的精度。格子点集的另一个优点在于其他采样方案是通过显式计算特定参数的显式计算来评估先验的给定集合的优点。提出了关于水库系统的最佳控制的仿真结果，以显示了所提出的方法的有效性。

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