Multiplier-Based, Robust H∞ Estimation with Applications to Robust Fault Detection

This paper uses the Popov-Tsypkin multiplier (which has intimate connections to mixed structured singular value theory) to design robust H∞ estimators for uncertain, linear discrete-time systems and considers the application of robust H∞ estimators to robust fault detection. The key to estimator-based, robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs, which in turn requires the design of robust estimators. The robust H∞ estimation problem is formulated as a Riccati equation feasibility problem in which a cost function is minimized subject to a Riccati equation constraint. A continuation algorithm that uses quasi-Newton (BFGS) corrections is developed to solve the minimization problem. The algorithm is initialized with an H∞ estimator designed for the nominal system. The initializing multiplier matrices are obtained by solving a linear matrix inequality. The robust H∞ estimator framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simplified longitudinal flight control system. It is shown that the robust fault detection procedure based on the robust H∞ estimation methodology proposed in this paper can reduce the false alarm rate.