Lecture notes and recordings for ECE5570: Optimization for Systems and Control

To play any of the lecture recording files (below), QuickTime is required. This software may be downloaded (free) from http://www.apple.com/quicktime/download/. Each of the recordings is on the order of 20 to 30 minutes long, and between about 40 and 50 Mb in size.

If you are not registered at UCCS to take this course for credit, and if you wish to do so, please contact Dr. M. Scott Trimboli.

This course can be taken at the graduate level as part of the Masters of Science in Electrical Engineering option in Battery Controls. See the IDEATE web site for more details.

1. Optimization Methods for Systems & Control. [PDF]
   • 1.1: What is Optimization?
   • 1.2: Course Outline.
2. Math Review. [PDF]
   • 2.1: Matrix Algebra: Basics.
   • 2.2: Matrix Algebra: Linear Independence and Rank.
   • 2.3: Matrix Algebra: Eigenvalues/Eigenvectors.
   • 2.4: Matrix Algebra: Vector Calculus.
   • 2.5: Linear Systems: State Space.
   • 2.6: Linear Systems: Controllability/Observability.
3. 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.
4. 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.
5. 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.
6. 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.