System Theory for Communication and Control

(3-0-3-4)

CMPE Degree: This course is Elective for the CMPE degree.

EE Degree: This course is Elective for the EE degree.

Lab Hours: 0 supervised lab hours and 3 unsupervised lab hours.

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

Course Coordinator: Erik I Verriest

Prerequisites: ECE 3550

Corequisites: None.

Catalog Description

Study of the basic concepts in linear system theory and numerical linear
algebra with applications to communication, compution, control and signal
processing. A unified treatment.

Textbook(s)

Lie Groups, Lie Algebras, and Representations-An Elementary Introduction, A Polynomial Approach to Linear Algebra

Course Outcomes

  1. Detect and exploit mathematical structure to solve complex problems (exact and approximation) in systems theory.
  2. Apply common proof techniques to verify the validity of (simple) conjectures.
  3. Apply basic principles (such as feedback) in a broad context of engineering.
  4. Exploit geometric structure and symmetries in system and signal models to reduce hard problems to simpler ones.
  5. Synthesize complex processes with elementary building blocks.
  6. Solve engineering problems through teamwork.

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. ( P ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( LN ) 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. ( LN ) An ability to communicate effectively with a range of audiences

4. ( LN ) 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. ( M ) 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. ( P ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( P ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

Strategic Performance Indicators (SPIs)

Not Applicable

Course Objectives

Topical Outline

Introduction
Matrix algebra and algebraic structures
State equations for multi-variable linear systems
Reachability and Observability Properties
Range space, reachability, and minimum norm solution
Null space, observability, and last squared error solution
Finite state systems and linear modular systems: cyclic codes
Solutions of State Equations
Eigen problem
Stability
Quadratic forms
Adjoints
Elements of Polynomial System Theory (Algebraic System Theory)
Rings and modules of polynomials
Functional Models and Shift Spaces
Linear Systems Analysis and Design
Systems on Lie Groups (Applications to Control and Computation)
Matrix Lie Groups
Lie algebras and exponential mapping, BCH-formula
Basic Representation Theory
Applications in attitude control, switched systems and ODE-solving
Linear Systems in Disguise
Carleman Linearization
Perspective systems (Applications in computer vision)
Quaternions (Applications in Robotics, Control and Signal Processing)
Design in Control and Communication
State feedback design
State observer design
Stabilization and convergence of numerical algorithms
Motion planning and steering
Synchronization in communication systems
Simulation and Modelling
Shift-register synthesis
Subspace identification algorithm
Parametrization and sensitivity
Elementary notions of optimization