A Zonotope-Based Interval Estimation Method for Systems With Nonlinear Equality Constraints

This article studies the problem of interval estimation for systems with nonlinear equality constraints and unknown but bounded uncertainties. An iterative zonotope-based method is presented to compute accurate interval bounds of system states. To manage the nonlinear constraints, we utilize a Taylor expansion and consider the dependence in the remainder. Furthermore, to determine the optimal zonotopic enclosures of the intersection of two zonotopes, the widths of the smallest intervals enclosing zonotopes are used as the size criterion. Numerically efficient linear programming is used for solving the associated optimization problems. A simulation on a ground vehicle example shows that the proposed method can provide accurate interval estimation results.