Robust H/sub 2/ estimation using the Popov-Tsypkin multiplier

Collins, Emmanuel G.; Song, Tinglun

doi:10.1109/cdc.1998.760860

Cited by 3 publications

(2 citation statements)

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“…Proof. The proof is a specialization of the proof of the corresponding theorem in Collins and Song (1998) for nite-horizon cost functionals. Now de ne the uncertainty set U A 2 R n n as U A 4 = f A 2 R n n : A = ?B 0 FC 0 ; F 2 Fg;…”

Section: Bounds On H 2 Performance Over the Uncertainty Setmentioning

confidence: 95%

“…In this section, a generic upper bound on the H 2 performance functional (18) will be developed over the entire uncertainty set for an uncertain system by using a parameter-dependent bounding function approach similar to that proposed by Bernstein (1994, 1995). Then speci c structure is assigned to the bounding function by using the Popov-Tsypkin multiplier (Collins et al 1997, Collins and Song 1998, Kapila and Haddad 1996. The upper bound to be developed can be used in the synthesis of robust H 2 estimators.…”

Section: Bounds On H 2 Performance Over the Uncertainty Setmentioning

confidence: 99%

See 1 more Smart Citation

Robust H Estimation with Application to Robust Fault Detection

Song

Collins

2000

Journal of Guidance, Control, and Dynamics

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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. Hence, this paper considers the design of robust H 2 estimators using a parameter-dependent bounding function approach in conjunction with multiplier theory (which is intimately related to mixed-structured singular value theory). Speci cally, the Popov-Tsypkin multiplier is used to develop an upper bound on an H 2 cost function over an uncertainty set. The robust H 2 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 robust H 2 estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simpli ed longitudinal ight control system. It is shown that the robust fault detection procedure based on the robust H 2 estimation methodology proposed in this paper can reduce false alarm rates.

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Section: Bounds On H 2 Performance Over the Uncertainty Setmentioning

confidence: 95%

Section: Bounds On H 2 Performance Over the Uncertainty Setmentioning

confidence: 99%