AE-807 Flight Control System Design II 

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Course Objective

Principles of optimal control, optimal spacecraft trajectories including high-thrust and low-thrust transfers, optimization of powered and unpowered atmospheric flights, numerical methods including both direct and indirect optimization schemes, trajectory optimization for multi-air and space vehicle systems. 

Topics Covered (Tentative) 

Introduction (Number of Lectures=4) 

  • Overview of aerospace optimal control problems
  • Dynamics of air and space flight 
  • Mathematical background: minimization of functions with constraints
  • Parameter optimization: aircraft climb, orbital transfer 

Optimal Control Theory (Number of Lectures=10)

  • Minimization of functionals and Euler-Lagrange equations
  • Examples: aircraft loop trajectory, continuous thrust transfer 
  • Minimum time problems 
  • Constraints in aerospace trajectory optimization problems 
  • Pontryagin’s minimum principle and applications to aerospace systems  

Optimal Feedback Control (Number of Lectures=8)

  • Hamilton-Jacobi-Bellman equation and dynamic programming
  • Example: optimal thrust steering for spacecraft rendezvous 
  • Linear systems with quadratic criterion, matrix Riccati differential equation  
  • Terminal controllers and regulators 
  • Example: attitude regulator for a missile, aircraft autopilot design 

Numerical Methods (Number of Lectures=6)

  • Overview of indirect optimization techniques
  • Direct optimization technique
  • Example: Optimal patterns of dynamic soaring 
  • Numerical methods for solving H-J-B equations 


Grading Policy 

• Assignments – 10%
• Midterm 1 – 30%
• Midterm 2 – 30%
• Team project (in lieu of final exam) – 30% (project duration: 6 weeks approximately) 


Bryson, Ho, “Applied Optimal Control,” Taylor and Francis.