Enhancing Output Feedback Robust MPC via Lexicographic Optimization

In this article, a novel approach to hierarchical implementation of output feedback robust model predictive control is proposed for the linear polytopic uncertain model. One optimization problem for minimizing the performance index is followed with the other assessing estimation error set (EES). The two problems are posed in a lexicographic order. Since in the latter problem, the controller parametric matrices are retaken as the degrees of freedom for the optimization, a much less conservative EES is calculated. Therefore, by applying the new approach, the control performance can be greatly improved as compared with the earlier schemes without lexicographic optimization. The proposed approach is proven to be recursively feasible, and the closed-loop stability is specified by the notion of quadratic boundedness. The result is verified through two numerical examples.