Abstract
This project considers specific systems with high-degree nonlinearities and applies the composition of the algorithms described above to solve the reachability problem. The main challenge is to adjust the transformation at most quadratic systems in a way that would make the subsequent Carleman linearization as numerically stable as possible. In the project, we try to first explore 3 typical ODE systems with different characteristics, and then we prove that for any dissipative polynomial ODEs system, there exists a quadratization such that the quadratized system is dissipative as well. Based on this theorem, we later derive that if all the new variables introduced in quadratization can be quadratized by other variables, then the dissipativity of the resulting quadratic system can be ensured.
Yubo Cai 蔡宇博
My research interests include Computational Mathematics, Operation Research, Machine Learning.