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
