Controllability of stochastic semilinear systems

Abstract

Abstract In this paper, we demonstrate that the exact controllability concept is inappropriate for stochastic systems by proving the nonfulfillment of the coercivity inequality. As a result, we explore the concept of C-controllability, which was introduced as a weaker alternative to exact controllability when the controllability problem was first extended to stochastic systems. We establish a sufficient condition for C-controllability in finite-dimensional semilinear stochastic systems driven by a Wiener process and illustrate the result with several examples.

Keywords

• Exact controllability
• C-controllability
• Stochastic system
• Semilinear system