不确定时间延迟下RMPC的保代价区域优化研究

Analyzing Regions of Guaranteed Cost in RMPC under Uncertain Time Delay

在控制系统中,时间延迟的不确定性往往会影响控制策略的准确性.为了进一步分析时间延迟对系统性能的影响,该文在传统RMPC(Robust Model based Predictive Control)的基础上引入了不确定时间延迟,分析了不确定时间延迟下系统的保代价区域.首先,介绍了线性矩阵不等式约束下的RMPC,并分析了相应的保代价区域.接下来,在RMPC中引入不确定时间延迟,通过对系统状态空间进行放大,使其包含了更多的历史状态信息.最后,依据最大时间延迟分析了不确定性对控制系统性能的影响,并分析了相应的保代价区域.仿真实验表明,控制系统的保代价区域随着时间延迟的增加而逐渐减小,并且时间延迟的不确定性范围越大系统的保代价区域越小.

In control system, the uncertainty of time delay influences the accuracy of the control strategy in the system. In order to further analyze the effect of time delay on the performance of the system, this pa- per introduces uncertain time delay into the control system, and analyzes the regions of guaranteed cost of the system under uncertain time delay. Firstly, we introduced the RMPC under linear matrix inequality con- straints, and analyzed its corresponding regions of guaranteed cost. Secondly, we introduced uncertain time delay into RMPC, augmented the status space with more history status information. Finally, we analyzed the effect of uncertainty of uncertain time delay on the performance of the system based on maximal time de- lay, and analyzed its corresponding regions of guaranteed cost. The numerical experiment shows that, the size of regions of guaranteed cost increases with the decreasing of time delay, and the more uncertainty of time delay, the smaller regions of guaranteed cost is.