**Optimization Methods for Systems & Control.**[PDF]**Math Review.**[PDF]**Parameter Optimization: Unconstrained**[PDF]- 3.1: Unconstrained Optimization: The Basics.
- 3.2: Unconstrained Optimization: One & Two Params.
- 3.3: Line Search Methods.
- 3.4: Line Search Algorithm: Bracketing.
- 3.5: Line Search Algorithm: Sectioning.
- 3.6: Descent Methods.
- 3.7: Newton's Method.
- 3.8: Modified Newton's Method.
- 3.9: Quasi-Newton Methods.

**Parameter Optimization: Constrained.**[PDF]- 4.1: Constrained Optimization: The Basics.
- 4.2: Equality Constraints: Two-Parameter.
- 4.3: Lagrange Multipliers: Two-Parameter Problem.
- 4.4: Lagrange Multipliers: Multi-Parameter Problem.
- 4.5: Equality Constraints: Examples.
- 4.6: Numerical Algorithms.
- 4.7: Inequality Constraints: Scalar Parameter.
- 4.8: Inequality Constraints: Vector Parameter.
- 4.9: Linear Programming.
- 4.10: Linear Programming: Simplex Algorithm.
- 4.11: Quadratic Programming.
- 4.12: Quadratic Programming: Lagrange Multipliers.
- 4.13: Quadratic Programing: Inequality Constraints.
- 4.14: Primal-Dual Method.
- 4.15: Hildreth's QP Algorithm.

**Dynamic Systems Optimization.**[PDF]- 5.1: Discrete-Time: Single-Stage.
- 5.2: Discrete-Time: Multi-Stage.
- 5.3: Example: Discrete-Time Brachistochrone Problem.
- 5.4: Solution Methods: 2-Pt Boundary Value Problems.
- 5.5: Continuous: Fixed-Time, No Terminal Constraints.
- 5.6: Example: Min Energy Room Temperature.
- 5.7: Continuous: Fixed-Time, Terminal Constraints.
- 5.8: Example: Fixed-Time, Terminal Constraints.
- 5.9: Continuous-Time: Free Time Problems.
- 5.10: Example: Free Time Problem.
- 5.11: Continuous-Time: Minimum Time.
- 5.12: Example: Zermelo's Problem.
- 5.13: Discrete-Time: Minimum Time.
- 5.14: Continuous-Time: Equality Path Constraints.
- 5.15: Example: Dido's Problem.
- 5.16: Control-Only Equality Constraints.
- 5.17: Continuous-Time: Inequality Constraints.
- 5.18: Continuous-Time: Linear Constraints.

**Linear Quadratic Optimal Control.**[PDF]- 6.1: Introduction to Linear Quadratic Control.
- 6.2: Dynamic Programming.
- 6.3: Linear Quadratic Control Problem.
- 6.4: Linear Quadratic Control Problem Example.
- 6.5: Feedback Form of the LQ Control Problem.
- 6.6: Linear Regulator Problem.
- 6.7: Linear Regulator Problem: Example.
- 6.8: SISO Systems: Symmetric Root Locus.
- 6.9: MIMO Systems: Eigenvector Analysis.
- 6.10: Zero Terminal Error Controller.
- 6.11: Tracking Controller.