Orbital Mechanics (AERO-3310)
Introduction to space flight mechanics, transport theorem, the two-body problem, classification of orbits, time in orbit, orbital transfers, maneuvers and orbital analysis, interplanetary trajectories, and orbital perturbations.
Optimal Control of Aerospace Vehicles (AERO-7350)
calculus of variations, Formulation of optimal control problems, variational approach to optimal control problems, state variable representation of systems, performance measures, indirect optimization methods and two-point boundary-value problems, LQR problem, Pontryagin's Maximum Principle, homotopy and continuation methods, direct optimization methods, and transcription techniques (collocation approach, pseudo-spectral methods).
Advanced Trajectory Optimization
Dynamic programming, Hamilton-Jacobi-Bellman equation, function minimization problems, numerical methods and techniques for solving unconstrained minimization problems, constrained optimization (KKT conditions), meta-heuristic optimization methods (e.g., particle swarm optimization method), linear programming, mixed-integer programming, quadratic programming, model predictive control (MPC), differentially flat systems, minimum-snap motion planning for quad-copters, trajectory planning with collision avoidance and obstacle avoidance, convex optimization.