Wang Fei-Yue, Jin Ning, Liu Derong, Wei Qinglai
Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.
IEEE Trans Neural Netw. 2011 Jan;22(1):24-36. doi: 10.1109/TNN.2010.2076370. Epub 2010 Sep 27.
In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.
在本文中，我们使用自适应动态规划（ADP）方法研究离散时间非线性系统的有限时域最优控制问题。其思路是使用一种迭代ADP算法来获得最优控制律，该控制律能使性能指标函数在ε误差范围内接近所有性能指标的最大下界。所提出的ADP算法还能得到最优控制步数。对所提出的ADP算法在性能指标函数和控制策略方面进行了收敛性分析。为便于迭代ADP算法的实现，使用神经网络来逼近性能指标函数、计算最优控制策略以及对非线性系统进行建模。最后，通过两个仿真例子来说明所提方法的适用性。
