Optimal Control Systems

This course serves as an introduction to optimal control theory for linear and nonlinear systems.

TEXT: “Optimal Control Theory, An Introduction,” by D.E. Kirk, Prentice-Hall, New York, NY, 1970.

• Optimal Control Examples
• Review of Function Optimization
  • Global Extremum
  • Little o and Big O Functions
  • Vector Calculus
  • Constraints and Lagrange Multipliers
• Calculus of Variations
  • Perturbations in Functions
  • Necessary Conditions
  • First Problem of Calculus of Variations
  • Boundary Condition Problems
  • Piece-Wise Smooth Extremals
  • Sufficient Conditions for Local Minima
• Hamiltonian Formulation
  • Euler-Lagrange Equations
  • Transversality Conditions
  • Maximum Principle
• Linear Quadratic Regulator
  • Matrix Riccati Equation
• Computational Techniques
  • Gradient Method
  • Shooting Methods

Years Taught: Spring '01