Three bounded proofs for nonlinear multi-input multi-output approximate dynamic programming based on the Lyapunov stability theory
Three bounded proofs for nonlinear multi-input multi-output approximate dynamic programming based on the Lyapunov stability theory
复制标题
基于Lyapunov稳定性理论的非线性多输入多输出近似动态规划的三个有界证明
DOI：
10.1002/oca.2332
复制
发表时间：
2018
影响因子：
1.8
通讯作者：
Yuli Chen
中科院分区：
文献类型：
--
作者：
Zhijian Huang;Xuemei Xiong;Wentao Chen;Qin Zhang;Yihua Liu;Yuli Chen
近似动态规划是一种有效的最优控制方法，需要满足两个前提条件。首先，在应用前必须保证算法的稳定性和收敛性。其次，控制系统应主要是非线性多输入多输出形式。因此，本文引入了一个非线性多输入多输出近似动态规划，并证明了它在李雅普诺夫意义下是稳定的，因此它是收敛的。此外，还分析了李雅普诺夫函数的设计。这些证明是基于李雅普诺夫稳定性理论的形式的效用函数的二次，平方加权和，和绝对值。最后，给出了三个典型的非线性多输入多输出近似动态规划控制实例，说明了它们的应用和证明。该证明克服了复杂的推导过程，结果包含了3个实用的、系统的有界证明。首次从效用函数的角度对非线性多输入多输出近似动态规划进行了证明。此外，所得结果还可为非线性多输入多输出近似动态规划的效用函数设计和稳定性判据提供有效的分析和指导。
The approximate dynamic programming needs 2 prerequisites to be an effective optimal control method. Firstly, it must be assured to be stable and convergent before application. Secondly, the control system should mainly he a nonlinear multi-input multi-output form. Thus, this paper introduces a nonlinear multi-input multi-output approximate dynamic programming and proves that it is stable in Lyapunov sense, therefore it is convergent. Besides, the Lyapunov function design is also analyzed. These proofs are based on the Lyapunov stability theory in the form of the utility function of quadratic, square-weighted sum, and absolute value. Thereafter, 3 typical control examples of nonlinear multi-input multi-output approximate dynamic programming arc offered to show their applications and verify the proofs. The proof overcomes the complex derivation, and the results contain 3 practical and systematic bounded proofs. It is for the first time that the proof focuses on nonlinear multi-input multi-output approximate dynamic programming from the view of utility function. What is more, the results can also serve as an effective analysis and guide for the utility function design and the stability criterion of nonlinear multi-input multi-output approximate dynamic programming as well.