  This paper proposes a new state estimator for discrete-time nonlinear
dynamical systems with unknown-but-bounded uncertainties and state linear
inequality and nonlinear equality constraints. Our algorithm is based on
constrained zonotopes (CZs) and on a DC programming approach (DC stands for
difference of convex functions). Recently, mean value extension and first-order
Taylor extension have been adapted from zonotopes to propagate CZs over
nonlinear mappings. Although the resulting algorithms (called CZMV and CZFO)
reach better precision than the original zonotopic versions, they carry the
sensitivity to the wrapping and dependency effects inherited from interval
arithmetic. These interval issues can be mitigated with DC programming since
the approximation error bounds are obtained solving optimization problems. A
direct benefit of this technique is the elimination of the dependency effect.
Our set-membership filter (called CZDC) offers an alternative solution to CZMV
and CZFO. In order to demonstrate the effectiveness of the proposed approach,
CZDC is experimented over two numerical examples.
