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Nonlinear n-th Cost Cumulant Control and Hamilton-Jacobi-Bellman Equations for Markov Diffusion Process

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1 Author(s)
Won, Chang-Hee ; IEEE Member, Department of Electrical and Computer Engineering, Temple University, Philadelphia, PA 19122, USA

A general nonlinear stochastic system with non-quadratic cost function is considered for cost cumulant control of a Markov diffusion problem. The Hamilton-Jacobi-Bellman equation for the n-th cost moment case is derived as a necessary condition for optimality. The n-th cost cumulant Hamilton-Jacobi-Bellman equation derivation procedure is given. Second, third, and fourth cost cumulant Hamilton-Jacobi-Bellman equations are derived using the proposed procedure. The solutions of the nonlinear cost cumulant control problem is discussed using the state dependent Riccati equation method.

Published in:

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Date of Conference:

12-15 Dec. 2005