**4. Conclusions**

Based on the hybrid dynamic traffic system with unknown inputs, a switched unknown-input state observer was designed, and the issues of vehicle density estimation and congestion identification were investigated. We showed that the unknown-inputsobserver was able to reconstruct the vehicle densities of road sections which were not equipped with traffic sensors. This strategy for vehicle density estimation was applied to The Beijing Jingtong freeway. Experimental results demonstrated that the estimated densities matched the actual densities reasonably well, and thus congestion can be identified effectively using ths model.

However, in this study, only simulation data obtained by VISSIM were used to verify the performance of the observer, thus the results have some limitations. Meanwhile, the design of the model parameters did not consider the coupled-street effect. In future work, we will choose a practical road network and collect real data to evaluate and optimize the model parameters. The coupled-street issue will also be addressed.

**Author Contributions:** Y.M. and Z.L. (Zhixiong Li) conceived and designed the experiments; Y.G., B.L., D.L. and M.D.C. performed the experiments and wrote the paper; M.A.S. and Z.L. (Zongzhi Li) revised the paper; M.A.S., D.L., and Z.L. (Zongzhi Li) analyzed the data. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Key Research and Development Program of China (2018YFB1601300 & 2016YFB0100903), JITRI Suzhou Automotive Research Institute Project (CEC20190404), Basic Scientific Research Business Expenses Special Funds from National Treasury (2019-0019, 2019-0092, 2018-9067, 2018-9060, 2017-9038, zx-2017-014), and Australia Research Council (No. DE190100931).

**Acknowledgments:** We would also like to thank the anonymous reviewers, whose meticulous reading and thoughtful comments helped improve this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
