Dual Set Membership Filter With Minimizing Nonlinear Transformation of Ellipsoid

In this article, we propose a dual set membership filter for nonlinear dynamic systems with additive unknown but bounded noises, and it has three distinct advantages. First, the nonlinear system is translated into the linear system by leveraging a semi-infinite programming, rather than linearizing the nonlinear function. The semi-infinite programming is to find an ellipsoid bounding the nonlinear transformation of an ellipsoid, which aims to compute a tight ellipsoid to cover the state. Second, the duality result of the semi-infinite programming is derived by rigorous analysis; then, a first-order Frank–Wolfe method is developed to efficiently solve it with a lower computation complexity. Third, the proposed filter enjoys stability for some special nonlinear dynamic systems and succeeds the advantages of the classic linear set membership filter. Finally, two illustrative examples in the simulations reveal the effectiveness of the dual set membership filter.