Guaranteed State Estimation via Indirect Polytopic Set Computation for Nonlinear Discrete-Time Systems

Abstract

This paper proposes novel set-theoretic approaches for recursive state estimation in bounded-error discrete-time nonlinear systems subject to nonlinear observations/constraints. By transforming the polytopes that are characterized as zonotope bundles (ZB) and/or constrained zonotopes (CZ), from the state space to the space of the generators of ZB/CZ, we leverage a recent result on remainder-form mixed-monotone decomposition functions to compute the propagated set, i.e., a ZB/CZ that is guaranteed to enclose the set of the state trajectories of the considered system. Further, by applying the remainder-form decomposition functions to the nonlinear observation function, we derive the updated set, i.e., an enclosing ZB/CZ of the intersection of the propagated set and the set of states that are compatible/consistent with the observations/constraints. In addition, we show that the mean value extension result in [1] for computing propagated sets can also be extended to compute the updated set when the observation function is nonlinear.