Abstract
The H∞ problem for a nonlinear system is considered. The corresponding dynamic programming equation is a fully nonlinear, first-order, steady-state partial differential equation (PDE). The computation of the solution of a nonlinear, steady-state, first-order PDE is typically quite difficult. We consider an entirely new class of methods for the obtaining the solution of such PDEs. These methods are based on the linearity of the associated semi-group over the max-plus algebra. In particular, solution of the PDE is reduced to solution of a max-plus eigenvector problem for known unique eigenvalue 0. We consider the error analysis for such an algorithm. The errors are due to both the truncation of the basis expansion and computation of the matrix whose eigenvector one computes.
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Research partially supported by NSF grant DMS-9971546.
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This paper is dedicated to Prof. Tyrone E. Duncan
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© 2002 Springer-Verlag Berlin Heidelberg
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McEneaney, W.M. (2002). Error Analysis of a Max-Plus Algorithm for a First-Order HJB Equation. In: Pasik-Duncan, B. (eds) Stochastic Theory and Control. Lecture Notes in Control and Information Sciences, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48022-6_23
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DOI: https://doi.org/10.1007/3-540-48022-6_23
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