# Optimal Control Systems

### From ANCS Wiki

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