## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

## Required Textbook

Ljung, Lennart. *System Identification: A Theory for the User*. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1998. ISBN: 0136566952.

## Prerequisites

## Grading Policy

Grades in this course will be based on Homework. We will have approximately 6 sets, a set every 2 weeks. The final 2 sets will be project-like. **Any** use of written solutions from previous terms is **not** permitted. If you have access to such solutions, keep them out of reach! Violations will be dealt with severely.

Collaborations with other students are permitted on the first 4 homework sets, as long as you work out the homework by yourself. For the last two sets, we will have a separate policy. Discussions with the TA about the homework are permitted and encouraged.

## Outline

- Introduction to System Identification
- What is System Identification?
- What are the rules of the game?
- How can we derive Algorithms?
- How do we evaluate the Algorithms?
- Stochatic vs. Non-stachastic Formulation

- Background
- Random Variables and Stochastic Processes
- Signals and Systems and Related Topics
- Model Parameterization and Prediction

- Nonparametric Identification
- Impulse and Step Response
- Correlation Methods
- Spectral Analysis

- Linear Regression
- Least Square Estimation
- Statistical Analysis of LS Methods
- Determining Model Dimension

- Input Signals
- Commonly used Signals: Spectral Properties
- Persistent Excitation

- Parameter Estimation
- Minimizing Prediction Error
- Identifiability, Consistency, Biase
- Least Squares
- Relations between Mimimizing the Prediction Error and the MLE, MAP
- Convergence and Consistency
- Asymptotic Distribution of Parameter Estimates
- The Instrumental-Variable Method

- Algorithms
- Computing the Estimates
- Recursive Estimation
- Kalman Filter Interpretation

- Identification in Practice
- Aliasing due to Sampling
- Closed Loop Data
- Model Order Estimation

- Bounded but Unknown Disturbances
- Identification in the Worst Case
- Optimal Algorithms
- Optimal Inputs
- Robustness Consideration

- Adaptive Control * Certainty Equivalence * Stability Issues in Time-varying Systems * Stability of an Adaptive Systems