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This year's course finished on 12 March 2013. 

Your initial state of knowledge was $W_0$, and has been brought to $W_{16}$. It is now your job to control the trajectory onwards. Information about certain unobservables will be revealed by variables $y_1,y_2,y_3$ in the Easter Term.

As you study and revise from the notes I would appreciate an email from you if you see any typos or grammatical mistakes, or find something that you recommend could be explained better. I try to tread a Goldilocks path in these notes of being neither too verbose nor too succinct. 

You can give the standard feedback on-line here. This is identical to the Faculty's paper form that I will handout on Thursday. It will be sent to my email anonymously. After reading the responses, I will forward them to the Faculty Office. The online form is easy to use and is particularly useful for anyone who is following the course from my notes and is not attending lectures.

Proof by Genie, continued

I am interested in collecting more examples of Proof by Genie, as mentioned in a previous post. If you come across an example of this, please let me know.

I've now remembered another example of proof by genie, actually from one of my own recent papers. Two people are trying to find each other on the vertices of a triangle. Initially they start at two different vertices and at each step $t=1,2,\dotsc$ each player stays or moves to another vertex, trying to minimize the expected number or steps until they meet. In working out the best symmetric rendezvous strategy it helps to assume that the players are given a common notion of what is "clockwise" on the triangle. However, once the optimal strategy is found it turns out that a common notion of clockwise is not needed to implement the optimal strategy. If you would like to learn more about this problem see 

R. R. Weber, Optimal symmetric rendezvous search on three locations, Math Oper Res., 37(1): 111-122, 2012.

or seminar slides. One of the slides begins with the words "Suppose the problem is made a bit easier: the players are provided with the same notion of clockwise. (We will see later that this does not actually help the players.)"

Broom balancing in the 21st century

Have a look at this link to see what optimal control can do when it is coupled to today's fast microprocessors and feedback controllers:

Quadrocopter pole acrobatics

Thanks to Felix Horns for finding this link.