System Identification

Overview

System identification is the process of building mathematical models of dynamical systems from measured input-output data. In model-based control engineering, the quality of the controller or observer depends directly on the accuracy of the plant model. System identification provides the essential link between real-world experiments and the mathematical models used for control design.

The classical approach to system identification uses parametric models — such as ARX, ARMAX, Output-Error, and Box-Jenkins structures — whose parameters are estimated by minimizing the prediction error (Prediction Error Method, PEM). A complementary approach is subspace identification (N4SID, MOESP, CVA), which directly estimates state-space models from input-output data using singular value decomposition, without requiring iterative optimization or prior specification of a model structure.

Our research focuses on system identification for periodically time-varying (LPTV) systems and multirate systems, where sensors operate at different sampling rates. The key innovation is cyclic reformulation, which transforms the time-varying identification problem into an equivalent linear time-invariant (LTI) problem. A novel state coordinate transformation then recovers the original system parameters from the identified cycled system. This approach works with arbitrary (non-periodic) input signals and does not require special input design.

In our research, system identification connects to multiple topics: the identified models serve as the basis for multi-rate observer design and controller synthesis, model inaccuracies in identified models can be compensated using the Model Error Compensator (MEC), and LMI optimization is used in subsequent controller and observer design based on the identified model.

Blog Articles on System Identification

For detailed explanations with mathematical formulations, MATLAB code examples, and references to key literature, see the following blog articles:

Comprehensive guide:

• System Identification: From Data to Dynamical Models — A Comprehensive Guide — Covers classical parametric methods, subspace identification, kernel-based approaches, LPTV and multirate system identification, and connections to data-driven control. Includes links to all research papers, MATLAB codes, and videos.

Individual topics:

• System Identification: Obtaining Dynamical Model — Introduction to the basic concepts and workflow of system identification.

• Cyclic Reformulation-Based System Identification for Periodically Time-Varying Systems — System identification for LPTV systems using cyclic reformulation. Based on IEEE Access 2025.

• System Identification Under Multirate Sensing Environments — Identifying plant models when sensors operate at different sampling rates. Based on JRM 2025.

Key Papers

• H. Okajima, Y. Fujimoto, H. Oku and H. Kondo, "Cyclic Reformulation-Based System Identification for Periodically Time-Varying Systems," IEEE Access, 2025. Paper

• H. Okajima, R. Furukawa and N. Matsunaga, "System Identification Under Multirate Sensing Environments," Journal of Robotics and Mechatronics, Vol. 37, No. 5, pp. 1102–1112, 2025. Paper (Open Access)

MATLAB Code

• Multi-Rate System Code — Code Ocean

• MATLAB Fundamental Control LMI — GitHub

Related Pages

• Multi-rate System — Multi-rate system analysis, observer and controller design

• State Estimation — Observer design using identified models

• Model Error Compensator — Compensating model inaccuracies in identified models

• Linear Matrix Inequality — LMI optimization for controller/observer design based on identified models

• Publications — Full publication list

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