#### Fall 2015 textbook list

The Fall 2015 ECE textbook list is available online for students.

#### Current Prerequisites & Course Offering

For current prerequisites for a particular course, and to view course offerings for a particular semester, see the Virginia Tech Course Timetables.

### ECE 6744 Linear Control Theory (3C)

Advanced introduction to the theory of optimal control of time-varying and time-invariant linear systems; Solutions to the linear-quadratic regulator, optimal filtering, and linear-quadratic-gaussian problems; Robustness analysis and techniques to enhance robustness of controllers.

What is the reason for this course?

This course provides a rigorous introduction to linear optimal control systems. The emphasis is on being able to derive the fundamental properties of these systems as well as to provide an introduction to important theoretical tools such as dynamic programming and least-squares optimization in function spaces.

Typically offered: Spring. Program Area: Systems/Controls.

*Prerequisites: Prerequisites: ECE 5744 or ECE 5754 or ME 5544 or ME 5554 or AOE 5744 or AOE 5754*.

*ECE 6744 is a new course, and ECE 5404 is being deleted. Cross-listed with ME (6544) and AOE (6744).*

### Department Syllabus Information:

**Major Measurable Learning Objectives:**

- Derive the solutions to the Linear-Quadratic Regulator problem and the Linear-Quadratic-Gaussian problem.
- Use linear optimal control techniques to solve problems such as disturbance rejection and tracking.
- Test the robustness of linear control systems to unstructured uncertainty and implement methods to improve robustness.
- Derive the basic equations of the Kalman filter and describe the important stochastic properties of this filter.

Course Topics | |
---|---|

Topic | Percentage |

1. Introduction and Review | 10% |

2. Linear Quadratic Regulator (LQR) | 25% |

a. Derivation from Dynamic Programming Theory | % |

b. Derivation from Least Squares Theory | % |

c. Penalty Matrix Selection | % |

d. Application to Disturbance Rejection and Tracking | % |

3. Robustness | 15% |

a. Singular Values and the Multivariable Nyquist Test | % |

b. Gain and Phase Margin Properties of LQR | % |

c. General Uncertainty Bounds | % |

4. Kalman Filtering | 10% |

a. Stochastic Dynamical Systems | % |

b. Derivation as Linear, Minimum-Variance Estimator | % |

c. Properties | % |

5. Linear-Quadratic-Gaussian Control | 25% |

a. Stochastic Dynamic Programming | % |

b. Derivation of LQR with Additive or Multiplicative Noise | % |

c. Separation Principle | % |

d. Loss of Robustness and Loop-Transfer Recovery | % |

e. Approaches to Robustness with Structured Uncertainty | % |

6. Advanced Topics | 15% |