Dear Professor He,
I am so sorry to disturb you again. The last message has some mistake in format. Thus I send message again. Please forgive me.
I am studying the optimal control recently. But there is a concept about conjugate point confused me. Fortunately, this concept is mentioned in your paper--“J.V. Breakwel and Ho Yu-Chi, “On the conjugate point condition for the control problem,” International Journal of Engineering Science,vol.2, issue. 6, pp. 565-579, Mar. 1965.\". However, I can not find the manuscript from the Internet. Could you please send me a copy of the manuscript? ?I would be very grateful. My e-mail address is Betty_Guoli@163.com. Best regards.
我的回复(2018-8-26 01:52)：Thank you for your interest. However, 45+years ago there were no Internet and/or electronic copies of paper. Thus, the best you can do is to write to the publisher and find out what library archive their journals. BTW, as I recall my conjugate point condition can be reinterpreted as the Riccati equation of the problem has finite escape time. Hope this helps. Good luck
Dear Professor He,
It is so sorry to disturb you. I am studying the optimal control recently. But there is a concept about conjugate point confused me. Fortunately, this concept is mentioned in your paper--“J.V. Breakwel and Ho Yu-Chi, “On the conjugate point condition for the control problem,” International Journal of Engineering Science,vol.2, issue. 6, pp. 565-579, Mar. 1965.\". However, I can not find the manuscript from the Internet. Could you please send a copy of the manuscript to me ? ?I would be very grateful. My e-mail address is Betty_ty_Guoli@163.com. Be. Best regards.
我的回复(2018-8-26 04:56)：Unfortunately after 40+ years, I no longer have a copy of the paper nor was electronic copy available then.
Dear Professor He, I used to follow your blog since ten years ago. It was like a window to look out, to imagine what it would be to do research in the U.S. I went to Brown University as a visiting scholar last year. Now when I read your former blogs again, I find so many familiar things. I am writing to say thank you. Thanks for keep writing blogs here. Thanks for providing so many new things to Chinese young researchers including me. Best regards.
我的回复(2018-5-25 18:13)：Comment like yours makes my day. Thank you.
Dear teacher, Hello, I am editor of WeChat public account platform (ID:penetratingview current user 1.60 million yen). Can we reprint "He Xiaoqi: A university professor living in the United States" article is very good, I hope to get The teacher's authorization, we will indicate the author and source, I wish the teacher is good, hope for recovery.
A Small friendly correction: You can aim for the best, say Tsinghua or Baida. These two university have: should be "two universities have. Great assay! Best wishes!
我的回复(2017-9-14 09:01)：Thanks. Some old Chinese language habit ( gender, polarity, et al) still slips through even after more than half a century of living and breathing English.
I am glad to read your message on sciencenet and thank you very much for your help.
Based on the definitions of the controllable region of the input-constrained systems[1], I propose a computing method on the volume of the region and a proportional relation theorem between the volume of the region and the size of the solution space of the control laws in the controller designing is proposed and proven. According to the theorem, the bigger the volume is, the bigger the size of the solution space, and then the better the performance of the closed-loop control systems designed by the conventional control methods are. So, I think, the volume of the region is a good measure on the control ability and efficiency of the input variables to the state space and, after deeply understanding on that, the better works on the application of the volume to the system analysis and control design can be developed and expected. My two questions are as follows.
1. Whether the same or similar works have been done after 1960's? In the control ability studying, some conclusions promoting the ability has been proposed in the earlier works, such as, the distribution of the eigenvalues of the system matrix A must be uniform, the angel between the eigenvectors and the vectors of the input matrix B must tend to be orthogonal, and so on. But, as a synthetical measure on the control ability, I doesn't find the same or similar works and the theorem on the relation between the volume of the controllable region and the solution space of the control laws maybe proposed firstly.
2. If my works on the control ability are with some innovation, how to name the new measure? Considered the relation to the solution space of the control laws, whether the new measure can be named as 'controllable abundance'?
Your are a key pioneer on the state controllability and your comments and suggestions are very important to me. Thank you for help.
Best regards.
Mingwang Zhao
Wuhan University of Science and Technology
July 25, 2017
References
[1] Hu, T., Lin, Z., & Qiu, L. (2002). An explicit description of the null controllable regions of linear systems with saturating actuators. Systems & Control Letters, 47, 65-78.
I am glad to read your message on sciencenet and thank you very much for your help. An email about my questions has been sent to your email box in Harvard Univ.
Prof. Ho, 我从读硕士开始一直学习您的最优控制、离散时间摄动分析等方面著作和文章，受益匪浅。现有一问题请教。对线性离散和连续系统，通过已有的定义能控域（即所有能控状态构成的几何体）的工作，我建立了计算任意N步（或有限时间T、无限时间等）能控域在n维空间的体积的方法，用此体积作为控制能力的一个测度，并证明这个体积与控制设计中控制律(control law)的解空间大小的正比关系。因此这个体积大，即控制设计的解空间大，设计控制器就可能达到更好的性能。我想把这个能控域的体积命名controllable abundance(控制丰富性或充裕性)，并进一步研究其在系统分析和控制中的应用。但由于能控性方面工作是上个世纪60年代的工作，许多文献查找不易。您是能控性工作的重要的开拓者，不知您能否告诉我是否已经有类似或相关工作？这个工作该如何进一步发展下去？打扰了，谢谢! 学生：赵明旺
我的回复(2017-7-22 09:13)：I have difficulty reading technical Chinese. Please write to me in English via an e- mail with your questions. I'll see if I can help
我的回复(2017-6-14 02:18)：Our current president seems to have no sense of shame. he tells a lie; he knows that it is a lie; he also knows that you know it is a lie; yet he goes on telling it.
我的回复(2017-4-5 11:07)：I am not sure what you wanted me to say. I believe I said everything on this topic in my blog article. Also I am not sure what you mean by "我的贴上" pardon my understanding oof current Chinese usage.
我的回复(2017-2-12 13:06)：Dear Prof. 吴中祥
Greetings. Unfortunately this is not my expertise area and I am not able to comment intelligently. Many thanks. YCHo