Deterministic and Stochastic Dynamics with Hyperbolic HJB-Type Equations

Melnik, R.V.N.

Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis , 10(1-3), 317--330, 2003


The study of deterministic and stochastic dynamic problems in control theory can be reduced to partial differential equations by using Bellman's approach. The resulting PDE-based mathematical models are difficult to solve numerically, and most existing approaches cannot provide accuracy expected in practical applications. It is proposed to approximate the original controlled dynamics with a sequence of PDEs. By applying the Steklov-Poincare operator technique the general form of equations in such a sequence has been established. The derived model can be used in cases that are not covered by standard diffusion processes.