This article focuses on the numerical estimation of the Region of Attraction of systems with polynomial vector field. The presented approach, based on a recent theoretical work on positively invariant sets, computes the inner Estimates of the Region of Attraction by means of Sum of Squares techniques. This allows the set containment conditions defining the region to be enforced at the expense of requiring iterative schemes since the ensuing optimization features bilinearities in the decision variables. The main contribution consists of two novel algorithms aimed at addressing some of the shortcomings typically associated with the adoption of iterative schemes. The results confirm the advantages of the proposed approaches, particularly as the size of the system increases.
|Title of host publication||2018 7th International Conference on Systems and Control (ICSC 2018)|
|Subtitle of host publication||Proceedings of a meeting held 24-26 October 2018, Valencia, Spain|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||6|
|Publication status||Published - Jan 2019|
Iannelli, A., Marcos, A., & Lowenberg, M. (2019). Algorithms for the estimation of the region of attraction with positively invariant sets. In 2018 7th International Conference on Systems and Control (ICSC 2018): Proceedings of a meeting held 24-26 October 2018, Valencia, Spain (pp. 93-98). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICoSC.2018.8587774