Systematic model bank determination approach for nonlinear systems using gap metric and stability margin

Abstract

This paper introduces a novel systematic approach for designing multimodel controller tailored to nonlinear systems. Our methodology focuses on the precise selection of local controllers, aligning their performance with specific requirements while minimizing redundancy. We achieve this through a two-fold process: first, the creation of an initial multimodel bank using the Self-Organizing Map (SOM) algorithm. Then, we employ gap metrics to assess the similarity between linear subsystems and hierarchical agglomerative clustering to group local models. This process leads to the identification of model sets for aggregation. Finally, we use stability margins as a guidance to get the reduced bank to elaborate the multimodel controller, ensuring robust stability. The main advantages of our method lie in the elimination of redundancy, simplification of the controller structure and the guarantee of robust stability. Three highly nonlinear processes are studied to demonstrate the efficiency of the proposed multimodel control approach.