• 张浩东、王宁、张书辉
  • 邓晓枫、李春洋、孙逸乐

Nonlinear Control of Transport PDE-ODE Interconnections

Nonlinear Control of Transport PDE-ODE Interconnections

  • 2018年3月21日上午10点
  • 浙江大学智能系统与控制研究所304教室

Nikolaos Bekiaris-Liberis
Marie Sklodowska-Curie Fellow
Dep. of Production Eng. & Managem.
Technical University of Crete
Chania, Greece 73100

Abstract: Numerous physical processes are described by transport PDE-ODE interconnections. LTI systems with constant input delays is perhaps the most elementary class in this category, where the transport speed is constant and the boundary of the spatial domain is fixed, besides the plant being linear. For this class of systems, predictor feedback is now a well-known delay-compensating control design tool. The situation becomes dramatically more complex when, in addition to the ODE being nonlinear, the speed of propagation or the boundary of the domain is a nonlinear function of the overall infinite-dimensional state (i.e., of the PDE or the ODE state) of the system. For such interconnections, I will present predictor-feedback design ideas, which I will then illustrate with several application examples, including, traffic systems (where the transport speed is a nonlinear function of the PDE state), extruders for 3D printing (giving rise to a system with ODE state-dependent moving boundary), and metal rolling (where the transport speed is a nonlinear function of the ODE state).

Nikolaos Bekiaris-Liberis received the Ph.D. degree in Aerospace Engineering from the University of California, San Diego, in 2013. From 2013 to 2014 he was a postdoctoral researcher at the University of California, Berkeley and from 2014 to 2017 he was a research associate and adjunct professor at Technical University of Crete, Greece. Dr. Bekiaris-Liberis is currently a Marie Sklodowska-Curie Fellow at the Dynamic Systems & Simulation Laboratory, Technical University of Crete. He has coauthored the SIAM book Nonlinear Control under Nonconstant Delays. His interests are in delay systems, distributed parameter systems, nonlinear control, and their applications.

Dr. Bekiaris-Liberis was a finalist for the student best paper award at the 2010 ASME Dynamic Systems and Control Conference and at the 2013 IEEE Conference on Decision and Control. He received the Chancellor’s Dissertation Medal in Engineering from the University of California, San Diego, in 2014. Dr. Bekiaris-Liberis received the best paper award in the 2015 International Conference on Mobile Ubiquitous Computing, Systems, Services and Technologies. He is the recipient of a 2017 Marie Sklodowska-Curie Individual Fellowship Grant.



  • 什么是最优控制问题
  • 最优控制有哪些应用
  • 最优控制的数学本质
  • 课程参考书籍与资料


  • 泛函极值问题的例子
  • 欧拉折线近似解法
  • 拉格朗日变分解法
  • 欧拉-拉格朗日方程


  • 广义坐标
  • 拉格朗日力学
  • 哈密顿力学


  • 回顾无约束最优化问题
  • 回顾带等式约束最优化问题
  • 带微分方程约束的泛函极值问题的变分方法


  • 最简单的最优控制问题
  • 带积分方程约束的泛函极值问题
  • 三类最优控制指标的分类与等价性


  • 终端时刻固定,终端状态自由
  • 终端时刻自由,终端状态固定


  • 终端时刻和状态自由且无关
  • 一般情况的横截条件
  • 光滑最优控制问题

第八讲:线性二次最优控制 I(2018年3月26日、28日-请假调课,2018年4月4日)

  • 无约束最优控制例子
  • 线性二次最优控制

第九讲:线性二次最优控制 II(2018年4月9日)

  • 最小能量控制问题(Robert L. Williams II and Douglas A. Lawrence, Linear State-Space Control Systems)
  • 线性系统的跟踪问题
  • 带终端约束的反馈控制


  • 内点约束问题
  • 内点条件推导
  • 小车折返问题

第十一讲:最大值原理及应用 (2018年4月16日)

  • 最大值原理的描述
  • 时间最优控制问题


  • 多级决策问题的最优性原理概述
  • Bellman方程
  • 运用动态规划求解离散系统最优控制


  • 遍历离散状态空间
  • 遍历离散状态空间与控制空间
  • 近似值函数
  • 维数灾难
  • 离散时间系统的策略迭代与值迭代方法


  • Hamilton-Jacobi-Bellman方程推导
  • 求解连续最优控制问题示例
  • 连续时间自适应动态规划(策略迭代方法)


  • 离散系统LQ问题
  • 连续系统LQ问题
  • 滚动时域优化控制



  • Desineni Subbaram Naidu, Optimal Control Systems, CRC Press
  • 张杰、王飞跃,最优控制,清华大学出版社
  • Mark Kot, A First Course in the Calculus of Variations, AMS
  • Robert L. Williams II and Douglas A. Lawrence, Linear State-Space Control Systems, John Wiley & Sons, INC.