基于勒贝格采样的非线性系统优化控制  

Optimal Control of Nonlinear Systems Based on Lebesgue Sampling

作　　者：朱萌萌 宋运忠[1] ZHU Mengmeng;SONG Yunzhong(School of Electrical Engineering and Automation,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学电气工程与自动化学院

出　　处：《复杂系统与复杂性科学》2019年第1期83-93,共11页Complex Systems and Complexity Science

基　　金：国家自然科学基金(61340041,61374079);河南省自然科学基金(182300410112)

摘　　要：为了解决非线性系统中的最优控制问题,在性能势理论的基础上,提出了一种基于勒贝格采样的新的事件触发控制策略。首先,根据最优控制理论,给出了基于勒贝格采样的非线性系统数学模型。然后,结合Markov决策过程中的时间集结法、解析法和策略迭代算法对搭建的数学模型进行Matlab仿真求解,得出了该系统的最优策略和最优性能。最后,将勒贝格采样系统与传统的周期采样系统作比较,深入分析了两种采样方案下的优化性能,比较了其优缺点,得出了勒贝格采样方法不仅能改善系统性能,解决了系统的“维数灾”问题,还能在某种程度上减小系统的资源消耗。In order to solve the optimal control problem in nonlinear systems,a new event-triggered control strategy based on Lebesgue sampling is proposed based on the performance potential theory. Firstly,according to the optimal control theory,a mathematical model of nonlinear system based on Lebesgue sampling is given. Then,combined with time aggregation method,analytical method and strategy iteration algorithm in Markov decision process,the mathematical model of the constructed mathematical model is solved by Matlab,and the optimal strategy and optimal performance of the system are obtained. Finally,the Lebesgue sampling system is compared with the traditional periodic sampling system. The optimization performance of the two sampling schemes is analyzed in depth,and its advantages and disadvantages of the sampling system are compared. It is concluded that the Lebesgue sampling method can not only improve the system performance,but also solve the "dimensionality disaster" problem of the system. It can reduce the resource consumption of the system to some extent.

关 键 词：非线性系统 勒贝格采样 时间集结 性能势 策略迭代算法 最优控制 

分 类 号：N945.15[自然科学总论—系统科学] TP273.1[自动化与计算机技术—检测技术与自动化装置]