6.435 | Spring 2005 | Graduate

System Identification


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.


6.241 and 6.432.

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.


  1. 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
  2. Background
    • Random Variables and Stochastic Processes
    • Signals and Systems and Related Topics
    • Model Parameterization and Prediction
  3. Nonparametric Identification
    • Impulse and Step Response
    • Correlation Methods
    • Spectral Analysis
  4. Linear Regression
    • Least Square Estimation
    • Statistical Analysis of LS Methods
    • Determining Model Dimension
  5. Input Signals
    • Commonly used Signals: Spectral Properties
    • Persistent Excitation
  6. 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
  7. Algorithms
    • Computing the Estimates
    • Recursive Estimation
    • Kalman Filter Interpretation
  8. Identification in Practice
    • Aliasing due to Sampling
    • Closed Loop Data
    • Model Order Estimation
  9. Bounded but Unknown Disturbances
    • Identification in the Worst Case
    • Optimal Algorithms
    • Optimal Inputs
    • Robustness Consideration
  10. Adaptive Control * Certainty Equivalence * Stability Issues in Time-varying Systems * Stability of an Adaptive Systems