A local iterative approach for solving the stochastic Hamilton‐Jacobi‐Bellman equation (SHJBE) arising in the stochastic control of affine nonlinear systems. (14th December 2017)

• Record Type: Journal Article
• Authors: Aliyu, M.D.S.
• Other Names: Chachuat Benoît guestEditor.; Sager Sebastian guestEditor.
• Is Part Of: Optimal control applications and methods. Volume 39:Number 2(2018)
• Page Start: 997
• Page End: 1010
• Publication Date: 2017-12-14
• Subjects: affine nonlinear system -- bounded continuous function -- Hamilton‐Jacobi‐Bellman equation -- secant method -- stochastic optimal control -- quadratic convergence; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2393
• Languages: English
• ISSNs: 0143-2087

Abstract

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.