Applied Optimal Control(03) - Trajectory Optimization Basics (Euler-Lagrange equation, boundary conditions)

Keypoints:

• Euler-Lagrange equation:
  • Fixed boundary conditions
  • Free boundary conditions:
    • $x(t_f)$ is free
    • $t_f$ is free
• Differential constraints
• General boundary constraints

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