Nonlinear predictive control employing Carleman bilinearization and fixed search directions

This work is concerned with the predictive control of nonlinear systems using the Carleman bilinearization technique. Given a nonlinear system model with sufficient regularity, a bilinear approximation can be obtained by means of Carleman's technique. After discretizing the continuous time model, several algorithms exist to tackle the bilinear model predictive control (BMPC) problem. More specifically, the present work exploits the combination of Carleman's approximation with a fixed search directions algorithm previously proposed within the context of BMPC. Simulations are carried out in order to compare predictive controllers designed using bilinear and linear plant models, but acting on the original nonlinear system. Moreover, the fixed search directions algorithm is compared with the use of a standard interior point optimizer. As a result, the proposed method is shown to provide improvements in terms of either stability, constraint satisfaction or reduced computational effort.

Automated summary

This paper focuses on predictive control of nonlinear systems using the Carleman bilinearization technique. By combining Carleman's approximation with a fixed search directions algorithm, improvements in stability, constraint satisfaction, and reduced computational effort are observed. Simulations show that the proposed method outperforms traditional methods in various aspects.