Optimal Control for Non-Homogeneous Linear Systems Driven by Fractional Noises

Abstract

The article considers the problem of optimal control of a non homogeneous linear system driven by fractional noises. Due to the high complexity of the specific problem, we use a scalar valued state variable and also a quadratic objective criterion. The entire analysis could be generalized within a multi dimensional framework. The investigation is restricted within the class of the Markovian controls. Actually, we calculate a sub optimal control for the original problem.

Keywords:

• Fractional Brownian motion (fBm)
• Ito integral
• Malliavin derivative
• Stochastic linear-quadratic (LQ) control

Mathematics Subject Classification:

• 60H05
• 60H07
• 93E20