On DC Programming and Set-based State Estimation

Abstract

Difference of convex (DC) programming has been employed in set-based state estimation to mitigate wrapping and dependency effects caused by interval arithmetic. These effects produce undesirable overestimation in sets, affecting the precision of the estimated sets in different magnitudes. Although DC programming is a promising technique, it may not be as intuitive as the interval approach. Moreover, some key methods currently proposed for constrained zonotopes (CZs) have not been completely discussed, making hard its use for beginners. Therefore, this paper proposes a discussion about the implementation of some techniques to define multivariate DC functions. The complexity orders are here derived, and one of the presented methods is an extension of zonotopes to CZs. Afterwards, each method is applied to a numerical example under different test conditions. The state estimation results are analyzed, justified and compared with some CZ-based state estimators.