Controller Structure for Optimized Region of Attraction of Polynomial Systems

The problem of optimizing the region of attraction (ROA) of continuous, autonomous polynomial system models is considered in this paper. An increase in the ROA of a favorable equilibrium point is a key step in ensuring the system is robust to the internal and external perturbations that may lead it to deviate from its equilibrium point. For example, in disease control and treatment, an increase in the ROA is desirable to inhibit the growth of a malignant cell. In this work, we propose a feedback nonlinear controller structure to optimize the ROA of a polynomial system model while keeping the nature and position of the favorable fixed point unchanged. The control action allows us to manipulate positions of other fixed points, thus providing an increase in the ROA of the fixed point of interest. We show that an extension of the bi-level optimization algorithm presented by Matallana et al. can be used to optimize the parameters of the proposed controller structure. We compare the resulting ROA of the controlled system with the ROA of the uncontrolled system to assess the effectiveness of the approach.