Optimal Control Lecture 8 : Dynamic Programming October 19 , 2015

This global viewpoint is in contrast to the calculus of variations approach where we typically look at local variations of trajectories in the vicinity of a given initial path x(·) often starting from a given state x(0) = x0. The DP principle is based on the idea that once an optimal path x∗(t) for t ∈ [t0, tf ] is computed then any segment of this path is optimal, i.e. x∗(t) for t ∈ [t1, tf ] is the optimal path from x(t1) to x(tf ).