ECE Course Outline
Numerical Methods for Optimization and Optimal Control (3-0-3)
- ECE 3084 Signals and Systems OR ECE 3550 Feedback Control Systems
- Catalog Description
- Algorithms for numerical optimization and optimal control, Gradient-descent techniques, linear programming, numerical linear system solvers, second-order methods for optimizing performance of dynamical systems.
- No Textbook Specified.
- Course Objectives - As part of this course, students:
- To teach students the elements of numerical and computational methods for optimization and optimal control.
- Students will become familiar with static optimization methods such as gradient descent and Newton?s method, and with optimization of dynamical system
- Course Outcomes - Upon successful completion of this course, students should be able to:
- Students will be able to write computer code to implement linear system constructs learned in prior S+C courses.
- Students will understand the types of errors than can arise in these implementations, and how to quantify them.
- Students will be able to construct computer algorithms to solve other problems which don't benefit from closed form constructs acquired in previous
- Students will know which types of models should be paired with which types of numerical optimization algorithms based on properties such as convexi
- In cases were multiple choices of numerical optimization algorithms are suitable for a given problem, students will understand the relative advanta
- Topical Outline
I. Numerical Methods I.1 Review of numerical issues when using machine number systems I.2 Direct Linear systems solvers (LU, Cholesky, iterative refinement) I.3 Scalar nonlinear equation solvers (bisection, Newton, secant method) I.4 Numerical differentiation and Integration II. Optimization II.1. Introduction to nonlinear programming II.2. Optimality conditions for constrained and unconstrained problems II.3. Algorithms: gradient descent, Newton-Rhapson, conjugate-gradient techniques II.4. Least-square problems and algorithms II.5. Optimization problems with equality and inequality constraints III. Algorithms for optimal control problems III.1. Discrete-time optimal control: necessary optimality conditions III.2. Continuous-time optimal control: the Hamiltonian III.3. The linear-quadratic optimal control problem and feedback-based solution III.4. The Pontryagin?s Maximum principle III.5. Examples: minimum-time problems and minimal-path problems
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