Min-Plus Techniques for Set-Valued State Estimation

Details Min-Plus Techniques for Set-Valued State Estimation Min-Plus Techniques for Set-Valued State Estimation

2012-03-13

arxiv.org/abs/1203.2846v1

Mathematics

Optimization and Control

7 pages, 4 figures

Scientific paper

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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