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Ordinary least-squares (OLS) for estimating partially observed LTI systems

This repository contains MATLAB scripts that implement the numerical examples in the following paper:

  1. Zheng, Y. and Li, N. (2020). Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories, preprint.

Instructions

To run the scripts in this repository, you only need a working MATLAB installation. We implement four types of OLS methods and the celebrated Ho-Kalman algorithm Ref. [1]

  • OLS using mutliple independent trajectories, where all data points are utilized (our method)
  • OLS using multiple independent trajectories, where only the last data point of each trajectory is used; Ref [2]
  • OLS using a single trajectory; Ref [3]
  • OLS + prefilter using a single trajectory; Ref [4]

References

  1. Ho, Β. L., and Rudolf E. Kálmán. "Effective construction of linear state-variable models from input/output functions." at-Automatisierungstechnik 14.1-12 (1966): 545-548
  2. Sun, Y., Oymak, S., & Fazel, M. (2020, July). Finite sample system identification: Optimal rates and the role of regularization. In Learning for Dynamics and Control (pp. 16-25). PMLR.
  3. Oymak, S., & Ozay, N. (2019, July). Non-asymptotic identification of lti systems from a single trajectory. In 2019 American Control Conference (ACC) (pp. 5655-5661). IEEE.
  4. Simchowitz, M., Boczar, R., & Recht, B. (2019). Learning linear dynamical systems with semi-parametric least squares. arXiv preprint arXiv:1902.00768.

Troubleshooting

If you have any trouble running the scripts in this repository, please email Yang Zheng.

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