Exponential almost Sure Stabilization of Nonlinear Delay Differential Systems under Stochastic Optimal Control Driven by Ito Brownian Noise
Ijeoma Donatus Anonwa *
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
Augustine Omoghaghare Atonuje
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
John Nwabueze Igabari
Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Almost sure exponential stability, optimal control, deterministic delay differential equation, lyapunov sample exponent, brownian noise, stochastic delay differential equation