Set-Membership Filtering for Discrete-Time Systems With Nonlinear Equality Constraints

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.