Robust l1 estimation using the Popov-Tsypkin multiplier with application to robust fault detection

Abstract

This paper considers the design of robust l1 estimators based on multiplier theory (which is intimately related to mixed structured singular value theory) and the application of robust l1 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. Specifically, the Popov-Tsypkin multiplier is used to develop an upper bound on an l1 cost function over an uncertainty set. The robust l1 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 (the algorithm of Broyden, Fletcher, Goldfab and Shanno) corrections is developed to solve the minimization problem. The estimation algorithm has two stages. The first stage solves a mixed-norm H2/l1 estimation problem. In particular, it is initialized with a steady-state Kalman filter and, by varying a design parameter from 0 to 1, the Kalman filter is deformed to an l1 estimator. In the second stage the l1 estimator is made robust. The robust l1 estimation 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 l1 estimation methodology proposed in this paper can reduce false alarm rates.