Optimal Control and Optimization


CMPE Degree: This course is Not Applicable for the CMPE degree.

EE Degree: This course is Not Applicable for the EE degree.

Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.

Technical Interest Group(s) / Course Type(s): Systems and Controls

Course Coordinator:

Prerequisites: ECE 6550

Corequisites: None.

Catalog Description

Optimal control of dynamic systems, numerical optimization techniques and
their applications in solving optimal-trajectory problems.

Course Outcomes

Not Applicable

Student Outcomes

In the parentheses for each Student Outcome:
"P" for primary indicates the outcome is a major focus of the entire course.
“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.
“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( Not Applicable ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

Strategic Performance Indicators (SPIs)

Not Applicable

Course Objectives

Topical Outline

1. Introductory material
a. Review of linear, time-invariant systems
b. Linear, time-varying systems
2. Parameter Optimization
a. Unconstrained Optimization: gradient-descent algorithms and Newton-Raphson methods
b. Optimization with constrains: Lagrange multipliers and the Karush-Kuhn-Tucker method, linear programming and the penalty-function method
3. Optimal Control
a. Unconstrained problems, the calculus of variations, Lagrangian Dynamics
b. The Bolza problem with free final time and fixed final time
c. Problems with and without constraints on the final state
4. Optimal control problems with control-inequality constraints
a. Pontryagin Maximum Principle
b. Bang-Bang Control, Sliding Modes
c. Minimum time problems, minimum fuel and minimum energy problems
5. Optimal Feedback Control
a. Dynamic programming
b. The Hamilton-Jacobi-Bellman Equation
6. Linear systems with quadratic criteria
a. LQR control and the Riccati equation
b. Square root characteristic equation, spectral factorization
7. Supplements (to be covered selectively if time permits)
a. Model Predictive Control
b. Minimum Sensitivity Design and Maximum Accuracy Control
c. Relaxed controls
d. Optimal Control of Systems with Delays
e. Singular Optimal Control