Min-Plus Techniques for Set-Valued State Estimation

TL;DR

This paper introduces a novel set-valued state estimation method for nonlinear discrete-time systems using min-plus algebra, avoiding linearization and leveraging dynamic programming for improved filtering accuracy.

Contribution

It develops a min-plus based filtering approach that directly solves the HJB equation for nonlinear systems without linearization, enhancing robustness and computational efficiency.

Findings

Provides a new set-valued estimator for nonlinear systems

Avoids linearization of system dynamics and output equations

Demonstrates effectiveness through theoretical analysis

Abstract

This article approaches deterministic filtering via an application of the min-plus linearity of the corresponding dynamic programming operator. This filter design method yields a set-valued state estimator for discrete-time nonlinear systems (nonlinear dynamics and output functions). The energy bounds in the process and the measurement disturbances are modeled using a sum quadratic constraint. The filtering problem is recast into an optimal control problem in the form of a Hamilton-Jacobi-Bellman (HJB) equation, the solution to which is obtained by employing the min-plus linearity property of the dynamic programming operator. This approach enables the solution to the HJB equation and the design of the filter without recourse to linearization of the system dynamics/ output equation.