Min-Plus Techniques for Set-Valued State Estimation

2012/03/13 by Abhijit G. Kallapur, Srinivas Sridharan, Kallapur, Abhijit G. +5
Engineering · #49L20 #90C56 #93E10 #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1203.2846

openalex publication_date 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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