• 作者： Lin, Jeng-Shiaw; Hwang, Chyi
• 中文摘要： 基於將控制變數視為階段化操作,將狀態與控制變數格點化,並在每次迭代過程中收縮格點尺寸等技巧,吾人可以使用迭代式動態規劃法(IDP)以求解非線性動態系統的最佳化控制問題。在應用後向演算的迭代式動態規劃法( backward IDP)計算最佳控制變數的過程中,必需在時間區間,〔ti,tf〕內對每一個起始狀態格點使用動態系統方程式作積分運算,其中ti為時間區段的起始時間,tf為系統的終值時間。當某些狀態格點,對於給定的起始狀態變數值與可行的控制變數格點的條件下為無法到達的狀態格點時,此種處理方式將浪費可觀的計算時間。為了克服後向演算迭代式動態規劃法的這種缺失,本文中將提出一種前向演算策略的迭代式動態規劃法。使用此種前向演算技術,IDP演算法將可以藉由省略無法到達的狀態格點的積分計算與避免對所有狀態格點為了求取最佳控制變數而積分至終值時間的積分運算,而節省可觀的計算時間。
• 英文摘要： The use of iterative dynamic programming (IDP) for optimal control of nonlinear dynamic systems is based on treating the control as a stagewise operation, gridding the state and control variables, and contracting the grid size iteratively. In applying the backward IDP to obtain the optimal control, it is required to integrate dynamic system equations over the interval [ ti, tf ] with each allowable control, where ti is the beginning time of a stage, and tf is the final time. This will result in wasting considerable computation time in those state grids that are inaccessible from the specified initial condition by using allowable controls. To overcome such a drawback of the backward IDP, a forward IDP technique is proposed in this paper. Due to its forward operation, the proposed IDP provides substantial savings in computation time by eliminating the time integrations for inaccessible state grids and avoiding integrations up to the final time in evaluating the optimal control for each state grid point.
• 中文關鍵字： 動態規劃; 最適控制; 非線性動態系統; 前向; 後向
• 英文關鍵字： Dynamic Programming; Optimal Control; Nonlinear Dynamic System; Forward; Backward