Exponential almost Sure Stabilization of Nonlinear Delay Differential Systems under Stochastic Optimal Control Driven by Ito Brownian Noise

This study investigates the role of Brownian white noise in stabilizing nonlinear optimal control delay differential equations (OCDDES) that are typically unstable in their deterministic form. The technique applied involves the use of Lyapunov sample exponent and a specialized partial differential equation suggested by Mao, (1997). It is demonstrated that if the noise scaling parameters of the stochastically perturbed equation is finite, then the new stochastic optimal control delay differential equation (SOCDDES ) is self - stabilized in an almost sure exponential sense. This phenomenon does not occur in deterministic optimal control delay differential equations where noise is absent.