Problem 3.
Note that the equation for the co-state lambda is solved backwards in time from the terminal condition, and thus you should get an equation for lambda(k) in terms of lambda(k+1).
Also note that we could equally well have defined the augmented cost with lambda(k) instead of lambda(k+1), the only difference being that we would then get an equation for lambda(k-1) in terms of lambda(k), and the boundary condition would be on lambda(N-1)... the choice of how to index lambda relative to x is arbitrary.
- DGM, 2009.01.19 10:30a