Today's lecture was about solving some problems using Pontryagin's Maximum.
We touched only briefly on controlled diffusion processes. The continuous time model for noise is Brownian motion, $B(t)$. The effect is that the Hamilton-Jacobi-Bellman equation gains another term, in $F_{xx}$.
I mentioned today in connection with section 16.1 (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.) This example is from Luenberger, Introduction to Dynamic Systems, 1979, page 403.
We touched only briefly on controlled diffusion processes. The continuous time model for noise is Brownian motion, $B(t)$. The effect is that the Hamilton-Jacobi-Bellman equation gains another term, in $F_{xx}$.
I mentioned today in connection with section 16.1 (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.) This example is from Luenberger, Introduction to Dynamic Systems, 1979, page 403.
