西安电子科技大学学报 ›› 2022, Vol. 49 ›› Issue (6): 164-176.doi: 10.19665/j.issn1001-2400.2022.06.019

• 计算机科学与技术 & 人工智能 • 上一篇    

准最小最大优化动态输出反馈鲁棒MPC

平续斌(),刘思伟(),吴宗原(),刘鼎(),李志武()   

  1. 西安电子科技大学 机电工程学院,陕西 西安 710071
  • 收稿日期:2021-12-20 出版日期:2022-12-20 发布日期:2023-02-09
  • 作者简介:平续斌(1982—),男,副教授,博士,E-mail:pingxubin@126.com|刘思伟(1993—),男,西安电子科技大学硕士研究生,E-mail:siweiliu0116@163.com|吴宗原(1998—),男,西安电子科技大学硕士研究生,E-mail:wuzongyuan@stu.xidian.edu.cn|刘 鼎(1981—),男,副教授,博士,E-mail:dliu@xidian.edu.cn|李志武(1967—),男,教授,博士,E-mail:zhwli@xidian.edu.cn
  • 基金资助:
    陕西省自然科学基金(面上)项目(2020JM190)

Quasi-min-max optimization of dynamic output feedback robust MPC

PING Xubin(),LIU Siwei(),WU Zongyuan(),LIU Ding(),LI Zhiwu()   

  1. School of Electro-Mechanical Engineering,Xidian University,Xi’an 710071,China
  • Received:2021-12-20 Online:2022-12-20 Published:2023-02-09

摘要:

针对包含有界干扰的约束线性参数变化系统中未知系统状态情况,设计了一种基于准最小最大鲁棒优化的动态输出反馈鲁棒模型预测控制方法。在优化控制问题中,动态输出反馈控制器采取参数依赖形式,从而可以借助线性矩阵不等式技术将优化控制问题转化为凸优化。在准最小最大鲁棒优化控制问题中,通过约束当前和预测的闭环系统状态在不同的鲁棒正不变集合之内,并且考虑当前采样时刻模型参数精确已知情况,降低了动态输出反馈控制器参数设计保守性。此外,实时估计误差集合更新采用预测的闭环系统状态在鲁棒正不变集合内的不变性进行,从而避免了通常输出反馈鲁棒模型预测控制算法中辅助优化更新估计误差集合的要求。所提出的算法不仅提升了控制性能和确保优化控制问题递归可行性,而且可降低优化控制问题求解在线计算量。当标称闭环系统收敛到平衡点时,包含有界干扰的不确定性系统稳定在平衡点附近有界集合之内,从而确保了被控系统的鲁棒稳定性。通过仿真算例验证了该方法的有效性。

关键词: 模型预测控制, 输出反馈, 鲁棒控制, 线性参数变化系统

Abstract:

For unknown system states in constrained linear parameter varying systems with bounded disturbances,a dynamic output feedback robust model predictive control approach via quasi-min-max robust optimization is designed.In the optimization problem,the dynamic output feedback controller takes a parameter-dependent form,and the optimization control problem can be formulated as convex optimization by the techniques of linear matrix inequalities.In the quasi-min-max robust optimization control problem,by constraining the current and predicted closed-loop system states to be within different robust positively invariant sets,and considering the exactly known model parameters at the current sampling time,the conservativeness of the designed dynamic output feedback controller parameters is reduced.Furthermore,the updates on real-time estimation error sets are performed by considering the invariance of the predicted closed-loop system states in the robust positively invariant set,which avoids the requirement of an auxiliary optimization to update estimation error sets in common output feedback robust model predictive control algorithms.The proposed algorithm not only improves the control performance and guarantees recursive feasibility of the optimization control problem,but also reduces the online computational burden on solving the optimization control problem.When the nominal closed-loop system is steered to the origin,the closed-loop system with bounded disturbances is stabilized within a region in the neighborhood of the origin.A simulation example is given to verify the effectiveness of the algorithm.

Key words: model predictive control, output feedback, robust control, linear parameter varying system

中图分类号: 

  • TL361