期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 54, 期 10, 页码 2480-2486出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2009.2029403
关键词
Nonlinear equality constraint; state constraint; state estimate ellipsoid; set-membership filtering; time-varying linear matrix inequality (LMI) optimization based approach
资金
- Engineering and Physical Sciences Research Council (EPSRC) of the U.K. [EP/C007654/1]
- National Nature Science Foundation of China [60874059, 60604027]
- Engineering and Physical Sciences Research Council [EP/C007654/1] Funding Source: researchfish
- EPSRC [EP/C007654/1] Funding Source: UKRI
In this technical note, the problem of set-membership filtering is considered for discrete-time systems with nonlinear equality constraint between their state variables. The nonlinear equality constraint is first linearized and transformed into a state linear equality constraint with two uncertain quantities related to linearizing truncation error and base point error. S-procedure method is then applied to merge all inequalities into one inequality and the solution to the unconstrained set-membership filtering problem is provided. The set-membership filter with state constraint is finally derived from projecting the unconstrained set-membership filter onto the constrained surface by using Finsler's Lemma. A time-varying linear matrix inequality optimization based approach is proposed to design the set-membership filter with nonlinear equality constraint. A recursive algorithm is developed for computing the state estimate ellipsoid that guarantees to contain the true state. An illustrative example is provided to demonstrate the effectiveness of the proposed set-membership filtering with nonlinear equality constraint.
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