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

Abstract

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.