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

Set-based state estimation for discrete-time constrained nonlinear systems: an approach based on constrained zonotopes and DC programming