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A local iterative approach for solving the stochastic Hamilton‐Jacobi‐Bellman equation (SHJBE) arising in the stochastic control of affine nonlinear systems
Author(s) -
Aliyu M.D.S.
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2393
Subject(s) - affine transformation , mathematics , hamilton–jacobi equation , hamilton–jacobi–bellman equation , nonlinear system , convergence (economics) , optimal control , stochastic control , quadratic equation , mathematical optimization , pure mathematics , physics , quantum mechanics , geometry , economics , economic growth
Summary In this paper, local iterative methods for solving the stochastic Hamilton‐Jacobi‐Bellman equation arising in the stochastic optimal control of affine nonlinear systems are discussed. Superquadratic and quadratic convergence of the methods is established under fairly mild assumptions, and an example is solved to demonstrate the effectiveness of the methods. Finally, as a by‐product, an existence result for the solution to the stochastic Hamilton‐Jacobi‐Bellman equation is also established under the same assumptions.