论文标题
基于异位的动态编程，用于解决无限的地平线最佳控制问题
IsoCost-Based Dynamic Programming for Solving Infinite Horizon Optimal Control Problems
论文作者
论文摘要
本文使用Isocost-Hypersurface（ICHS）概念介绍了用于解决无限 - 马的最佳控制问题的创新数值算法。在最佳控制系统的状态空间中，ICHS定义为具有一定数量成本值的一组状态点。在本文中，事实证明，对于一定的成本量，由无限 - 水手最佳控制解决方案产生的ICH围绕着由非最佳控制策略造成的所有其他ICHS。关于这种几何特征，引入了新型等cost动态编程（IDP）算法来搜索最佳控制解决方案。作为引入ICHS概念的说明，并证明了提出的IDP算法的有效性，提出了几个模拟示例。将结果与常规DP的结果进行比较。这些比较表明，与DP算法相比，所提出的算法具有更好的相对最佳性，该算法通过比较了两种具有随机初始条件的非线性系统的闭环控制的结果，而累积成本值降低了18％。更重要的是，与DP算法相比，IDP能够通过在使用较少的内存时减少执行时间来提高计算性能。
An innovative numerical algorithm for solving infinite-horizon optimal control problems is introduced in this paper, using the IsoCost-HyperSurface (ICHS) concept. In the state space of an optimal control system, an ICHS is defined as a set of state points having a certain amount of the cost value. In this paper, it is proved that for a certain cost amount, the ICHS resulting from the infinite-horizon optimal control solution, surrounds all other ICHSs resulting from non-optimal control strategies. Regarding this geometric feature, the novel Isocost Dynamic Programming (IDP) algorithm is introduced to search for optimal control solutions. As an illustration of the introduced ICHS concepts and to demonstrate the effectiveness of the proposed IDP algorithm, several simulated examples are presented. The results are compared with those of conventional DP. These comparisons demonstrate that the proposed algorithm has better relative optimality compared to the DP algorithm with 18% lower cumulative cost value, by comparing results from the closed-loop control of two nonlinear systems with random initial conditions. More significantly, when compared to the DP algorithm, the IDP was able to enhance computational performance by reducing the execution time by 21 % while using less memory.
