Welcome to the world of System Identification! This course will explore the fascinating realm of understanding, modeling, and optimizing complex and industrial systems. System Identification is a crucial discipline that finds applications across various fields, including engineering, control systems, fault detection, and more. By the end of this course, you will have the skills and knowledge needed to tackle various challenges related to system modeling and parameter estimation.
This course will equip you with the tools to model linear and nonlinear systems, understand the key concepts in system identification, and apply them to practical, real-world scenarios. We encourage active participation and engagement throughout the course to deepen your understanding of these topics.

Prerequisite: Control Theory, Linear Algebra, Statistics and Probability, MATLAB (or Python)



Dr Mahdi Aliyari

Dr. Mahdi Aliyari 

Associate professor
Department of Electrical Engineering, Control Systems
Member of APAC research group
K. N. Toosi University of Science and Technology

  • Introduction to System Identification

Characteristics, Applications (Prediction, Simulation, Control, Fault Detection, etc.), Linear or Nonlinear? Parameter Identification or Modeling? Selection: Input, Model Structure, Complexity, Real-time vs. Offline, Black Box, White Box, Gray Box, Evaluation Metrics.

  •  Static Linear System Identification

Linear Parameter Estimation and Optimization Methods: Least Squares (LS), Statistical Analysis, Regularization, Bias-Free Estimation, Minimum Variance Estimation, BLUE (Best Linear Unbiased Estimation), Cramer-Rao Lower Bound, Rao-Blackwell Theorem, Recursive Least Squares (RLS), Forgetting Factor (FRLS), Multiforgetting Factor (MFRLS), Computational Complexity, Problems, and Solutions, Prediction Error.

  • Minimizing Prediction Error for Parameter Estimation

Kalman Filter (KF) and Its Applications in Linear Parameter Estimation, Extended Kalman Filter (EKF) Selection, Noise Covariance Matrix, Adding Artificial Noise, Orthogonalized Images, Orthogonalized Regression (Ridge Regression), Orthogonal Least Squares (OLS), Orthogonalized Recursive Methods.

  • Linear Dynamic System Identification

Input Signal Selection for Sufficient Excitation in Dynamic Identification, Linear Dynamic System Identification Models with and without Feedback, Time Series Models (FIR, ARX, ARMAX, OE, BJ, PEM), AR, MA, ARMA Models, Instrumental Variables, Consistency, ARX Model Problem, Minimizing Prediction Error as Optimization Goal, Optimal Parameter Estimation in ARMAX Models, Nonlinear or Iterative Optimization Methods, ELS, GLS Methods, Recursive Iterative Methods for Parameter Estimation (RELS, RGLS, RIV, RPEM), Data Splitting for Validation and Testing, Training Data.

  • Closed-Loop System Identification

Identifying Closed-Loop Systems, Multi-Input Multi-Output System Identification, and System Identification in State Space.

  • Static Nonlinear System Identification

The Transition from Linear to Nonlinear Identification, Reasons and Challenges.

  • Introduction to Nonlinear Parameter Optimization

Local Optimization Methods: Gradient-Based and Non-Gradient-Based, Gradient-Reliant Optimization Methods, Absolute Optimization Methods, Population-Based Optimization Methods, Evolutionary Optimization Methods, Multi-Objective Optimization Methods, and Their Application in Identification.

  • General Approximators, Nonlinear Models Based on Basis Functions, Parameter Training, Parameter Presence Classification in Outputs, and Choosing Appropriate Training Methods.
  • Neural Networks, Neuron Philosophy, Introduction to Neuro Science, MLP and RBF Networks, Their Applications in Identification, Dynamic Neural Networks, and Deep Learning Networks.
  • Parameter Learning in Neural Networks, Training Structure, Optimal Structure Selection, Initial Weight Selection, Parameter Drift, Training Termination Time.
  • Fuzzy Concepts Review, Fuzzy Models, Application in Identification, Linear Local Models (LLM), Parameter Identification, Incremental Clustering of Data and Its Applications in Structure Determination, Neural-Fuzzy Models and Their Evolution.
  • Nonlinear Dynamic System Identification

Hammerstein and Wiener Models, NOE, NARMAX, NARX, Nonlinear Input-Output Models.

  • Nonlinear Dynamic System Identification Using Neural Networks and Its Application in Adaptive Controllers, Jacobian System.
  • Nonlinear Dynamic System Identification Using Fuzzy and Neural-Fuzzy Models and Its Application in Adaptive Controllers, Jacobian System.
  • Interpretability in Identification and Its Application in Understanding System Behavior.
  • Parameter Estimation in Linear and Nonlinear Dynamic Systems.
  • System Identification with a Combination of Linear and Nonlinear Models.
  • Exploration of Some Real-World System Identification Applications.
  • Dimension Reduction Techniques in Identification.

Main Reference:

  • Nonlinear System Identification: From Classical Approaches to Neural Networks, Fuzzy
    Models, and Gaussian Processes, O. Nelles, 2020

Other References:

  • System Identification: Theory for Users, L. Ljung, 2nd Editions, 1999.
  • System Identification, by T. Soderstrom and Petre Stoica, 1989.
  • System Identification: A Frequency Domain Approach, by R. Pintelon, J. Schoukens, 2001.
  • Recent selected papers