Observer gain optimization for minimization of minimal robust positively invariant set and invariant set-based fault detection

Abstract

This paper designs observer gains to optimize the minimal robust positively invariant set and uses this set for robust fault detection. First, the sizes of the minimal robust positively invariant set and corresponding minimal residual set are computed based on the Frobenius norm size (i.e., Frobenius radius) of zonotopes. Second, by formulating the size minimization problem as a solvable optimization problem, an observer gain is designed to minimize the minimal robust positively invariant set. Third, by maximizing the relative effect of faults to uncertainties, an observer gain is further designed to optimize robust fault detection performance. At the end, several examples are used to illustrate the effectiveness of the proposed methods.