Robust ` 1 Estimation with Applications to Robust

This paper considers the design of robust`1 estimators based on multiplier theory (which is intimately related to the mixed structured singular value theory) and the application of robust`1 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. Speciically, the Popov-Tsypkin multiplier is used to develop an upper bound on an`1 cost function over an uncertainty set. The robust`1 estimation problem is formulated as a parameter optimization problem in which the upper bound 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 estimation algorithm has two stages. The rst stage solves a mixed-norm H 2 =` 1 estimation problem. In particular, it is initialized with a steady-state Kalman lter and by varying a design parameter from 0 to 1, the Kalman lter is deformed to an`1 estimator. In the second stage thè 1 estimator is made robust. The robust`1 estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simpliied longitudianl ight control system. It is shown that the robust fault detection procedure based on the robust`1 estimation methodology proposed in this paper can reduce false alarm rates.