Stochastic Systems


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: CEE/ISYE/MATH 3770

Corequisites: None.

Catalog Description

Advanced techniques in stochastic analysis with emphasis on stochastic
dynamics, nonlinear filtering and detection, stochastic control and
stochastic optimization and simulation methods.


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. Introduction
a. Stochastic dynamic problems in control and robotics
b. Review basic probability
2. Probability and stochastic analysis
a. Random walks and Brownian motion
b. Stochastic integrals and martingales
c. Stochastic differential equations and Ito calculus
3. Stochastic Systems
a. Stochastic stability
b. Evolution equation: Kolmogorov and Fokker-Planck
4. Optimal Estimation
a. Static estimation: linear and nonlinear
b. Explicit solutions and approximations
5. Stochastic Control
a. Optimal stochastic control: Full information case
b. Optimal stochastic control: Partial information case
c. Separation principle and LQG-design
d. Dynamic programming, value functions, verification theorem
6. Applications in Robotics and Control
a. Sensor measurements
b. Localization and sensor fusing