A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering

Authors:
Wendell H. Fleming;William M. McEneaney
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

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Abstract

The Hamilton--Jacobi--Bellman (HJB) equation associated with the {robust/\hinfty} filter (as well as the Mortensen filter) is considered. These filters employ a model where the disturbances have finite power. The HJB equation for the filter information state is a first-order equation with a term that is quadratic in the gradient. Yet the solution operator is linear in the max-plus algebra. This property is exploited by the development of a numerical algorithm where the effect of the solution operator on a set of basis functions is computed off-line. The precomputed solutions are stored as vectors of coefficients of the basis functions. These coefficients are then used directly in the real-time computations.