A globally convergent composite‐step trust‐region framework for real‐time optimization

Abstract

Inaccurate models limit the performance of model‐based real‐time optimization (RTO) and even cause system instability. Therefore, a RTO framework that guarantees global convergence in the presence of plant‐model mismatch is desired. In this regard, the trust‐region framework is intuitive and simple to implement for unconstrained problems. Constrained RTO problems are converted to unconstrained ones by the penalty function, and global convergence is guaranteed if the penalty coefficient is large enough. However, a sufficiently large penalty coefficient is hard to determine and may lead to numerical difficulties. This paper addresses this issue and proposes a novel composite‐step trust‐region framework for constrained RTO problems that handles inequality constraints directly. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. A rigorous proof of its global convergence property is given.