Today's lecture was about solving some problems using Pontryagin's Maximum Principle. Some personal experience of the power of PMP came in solving the problem in the paper
R. R. Weber. Optimal search for a randomly moving object. J. Appl. Prob. 23:708-717, 1986.
The problem that is solved in this paper in continuous time is still an open problem in discrete time. That shows the power of PMP, in that with it we can solve problems in discrete time that cannot be solved in discrete time.
I mentioned today in connection with section 15.5 (insects as optimizers) that zoologists have observed that in real-world choices of $t_{\text{switch}}$ some insect populations seem to do a good job of predicting $T$ (the time of the serious frost that ends the lives of the workers.)
R. R. Weber. Optimal search for a randomly moving object. J. Appl. Prob. 23:708-717, 1986.
The problem that is solved in this paper in continuous time is still an open problem in discrete time. That shows the power of PMP, in that with it we can solve problems in discrete time that cannot be solved in discrete time.
I mentioned today in connection with section 15.5 (insects as optimizers) that zoologists have observed that in real-world choices of $t_{\text{switch}}$ some insect populations seem to do a good job of predicting $T$ (the time of the serious frost that ends the lives of the workers.)
