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- W2094860060 abstract "In previous work of the first author and others, max-plus methods have been explored for solution of first-order, nonlinear Hamilton–Jacobi–Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods can provide substantial computational-speed advantages, they still generally suffer from the curse-of-dimensionality. Here we consider HJB PDEs where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. The approach to solution will be rather general, but in order to ground the work, we consider only constituent Hamiltonians corresponding to long-run average-cost-per-unit-time optimal control problems for the development. We consider a previously obtained numerical method not subject to the curse-of-dimensionality. The method is based on construction of the dual-space semigroup corresponding to the HJB PDE. This dual-space semigroup is constructed from the dual-space semigroups corresponding to the constituent linear/quadratic Hamiltonians. The dual-space semigroup is particularly useful due to its form as a max-plus integral operator with kernel obtained from the originating semigroup. One considers repeated application of the dual-space semigroup to obtain the solution. Although previous work indicated that the method was not subject to the curse-of-dimensionality, it did not indicate any error bounds or convergence rate. Here we obtain specific error bounds." @default.
- W2094860060 created "2016-06-24" @default.
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- W2094860060 date "2010-01-01" @default.
- W2094860060 modified "2023-10-10" @default.
- W2094860060 title "Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs" @default.
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- W2094860060 doi "https://doi.org/10.1137/070681934" @default.
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