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

TL;DR

This paper introduces set-theoretic methods using zonotope bundles and constrained zonotopes for guaranteed state estimation in nonlinear discrete-time systems, ensuring enclosures of true states despite nonlinearities and bounded errors.

Contribution

It develops a novel approach transforming polytopic sets into generator spaces and applies remainder-form decomposition functions for both propagation and update steps in nonlinear systems.

Findings

Guaranteed enclosures of state trajectories are computed for nonlinear systems.

The approach extends mean value methods to nonlinear observation functions.

Set propagation and update are efficiently achieved using zonotope bundle and constrained zonotope representations.

Abstract

This paper proposes novel set-theoretic approaches for state estimation in bounded-error discrete-time nonlinear systems, subject to nonlinear observations/constraints. By transforming the polytopic sets 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 the 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. Finally, 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.