基于切换时刻参数化法的切换系统问题求解  

Optimal Control of Switched Systems Based on Parameterization of the Switching Instants

作　　者：赵瑞艳[1] 林旭梅[1] 李树荣[2] 

机构地区：[1]青岛理工大学自动化工程学院,山东青岛266520 [2]中国石油大学(华东)信息与控制工程学院,山东青岛266580

出　　处：《控制工程》2015年第4期737-741,共5页Control Engineering of China

基　　金：山东省教育厅基金项目(J13LN40)

摘　　要：研究了子系统切换次序固定的切换系统最优控制问题的数值解法。对于该类问题,主要是寻找最优切换时刻和最优控制策略使得性能指标最小。提出了切换时刻和控制向量同时参数化的方法,把该类问题转化成与之等价的非线性规划问题进行求解。为了优化切换时刻,引入一个新的标准化的时间变量,对时间段进行了标准化处理,然后用基于控制向量参数化的方法,把该切换系统最优控制问题转化成非线性规划问题,数值计算采用序列二次规划进行求解。最后对3个切换系统最优控制问题进行仿真,仿真结果证明该方法是有效的。A new approach for solving optimal control problems of switched systems with pre-specified order of the sequence of subsystems is studied in this paper. For such problems, both the optimal switching instants and the optimal continuous inputs are needed to seek. The proposed method transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and the control vectors. In order to search for the optimal switching instants, we introduce a new normalized time variable and do normalized treatment for the control arcs. Based on the control vector parameterization method, the optimal switching control problem is converted to a nonlinear programming problem. The numerical solution is obtained by using the sequential quadratic programming method. Three examples are solved using the proposed method so as to demonstrate the effectiveness of the proposed method.

关 键 词：切换系统 最优控制 非线性规划 序列二次规划 

分 类 号：TP29[自动化与计算机技术—检测技术与自动化装置]