Applied Optimal Control(04) - Continuous Optimal Optimization Basics (Euler-Lagrange / Control optimization / Transversality conditions)

Keypoints:

• Definitions of various variables such as $L$, $\phi$, $\psi$, $H$, $h$, $f$, $g$, $v$
• Solution methods: Euler-Lagrange / Control optimization / Transversality conditions
  • Hamiltonian conservation: $\partial_t H(x, u, \lambda, t) = 0$, then $H$ is a constant along the optimal trajectory. When $\partial_t \psi = 0$ and $\partial_t \phi = 0$, then $H(t) = 0$.
  • Minimum-time problem: $L = 1$, $\phi = 0$

Based on the lecture notes by Dr. Marin Kobilarov on “Applied Optimal Control (2021 Fall) at Johns Hopkins University