基于Krotov方法的Markov跳变双线性系统最优跟踪控制及应用  

Optimal tracking control of Markov jump bilinear system based on Krotov’s method and its application

作　　者：刘越 周平 孙霄阳 Yue LIU;Ping ZHOU;Xiaoyang SUN(State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学流程工业综合自动化国家重点实验室,沈阳110819

出　　处：《中国科学:信息科学》2025年第3期582-600,共19页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:U22A2049);国家重点研发计划(批准号:2022YFB3304903)资助项目。

摘　　要：Markov跳变双线性系统由于具有不同模态下的双线性动力学,且系统模态跳变转移由Markov链控制,因而其控制与优化是一个挑战性难题.针对该问题,提出一种基于Krotov方法的离散时间Markov跳变双线性系统最优跟踪控制方法,并将其用于高炉铁水质量的最优跟踪控制.首先,联立Markov跳变双线性系统状态方程和参考轨迹,构建增广系统,将最优跟踪控制问题转化为最优二次调节问题;同时,设计一个适用于Markov跳变双线性系统的改进函数,以实现对容许过程的迭代更新;其次,迭代优化所建立的性能指标,并将满足收敛条件的最后一次迭代所求得的控制器作为最终的最优跟踪控制器;最后,基于数值仿真验证所提方法的有效性,并将所提方法应用于高炉铁水质量控制,取得了满意的跟踪控制效果.The control and optimization of the Markov jump bilinear system(MJBLS)are challenging due to the bilinear dynamics in different modes and the mode-switching controlled by a Markov chain.To address this,an optimal tracking control method for discrete-time MJBLS based on Krotov’s method is proposed and applied to the optimal tracking control of blast furnace molten iron quality.First,the state equation of the MJBLS and the reference trajectory are combined to construct an augmented system,transforming the optimal tracking control problem into an optimal quadratic regulation problem.Concurrently,an improving function suitable for MJBLS is designed to update the admissible process iteratively.Then,the established performance index is iteratively optimized,and the result obtained in thefinal iteration,which meets the convergence condition,is employed as the optimal controller.Finally,the effectiveness of the proposed method is verified through numerical simulation,and its application to blast furnace molten iron quality control achieves satisfactory tracking control results.

关 键 词：Markov跳变双线系统 最优跟踪控制 Krotov方法 高炉炼铁 铁水质量 

分 类 号：O211.62[理学—概率论与数理统计] O231[理学—数学]