Approximate controllability of abstract semilinear stochastic control systems with nonlocal conditions

Divya Ahluwalia,N Sukavanam,Urvashi Arora,Amar Debbouche

doi:10.1080/23311835.2016.1191409

Abstract

This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approximate controllability of semilinear deterministic system, Schauder fixed point theorem has been used. At the end, an example has been presented to illustrate the feasibility of the proposed result.

Highlights

Control theory is an area of application-oriented mathematics which deals with basic principles underlying the analysis and design of control systems
In this paper, we discuss the approximate controllability of semilinear stochastic systems with nonlocal conditions using splitting technique
In this paper, sufficient conditions have been established for the approximate controllability of an abstract semilinear stochastic system with nonlocal conditions using splitting technique

Summary

Introduction

Control theory is an area of application-oriented mathematics which deals with basic principles underlying the analysis and design of control systems. In this paper, we discuss the approximate controllability of semilinear stochastic systems with nonlocal conditions using splitting technique. Arora and Sukavanam (2015) established sufficient conditions for the approximate controllability of second-order semilinear stochastic system with nonlocal conditions using Sadovskii’s Fixed point theorem. For each solution pr(t) of (Equation 3.1) with control r, define the random operator fpr :M0 → M0 as fpr (m) = K(n) where n is given by the unique decomposition (3.7). For approximate controllability of (Equation 2.3), let us introduce some operators and lemmas. We conclude that the semilinear stochastic system (Equation 2.3) is approximate controllable since the corresponding deterministic linear system is approximate controllable. We conclude that the semilinear stochastic system (Equation 2.1) is approximate controllable

Example

Conclusion