Variance Assignment for a Class of Stochastic Non-linear Systems

In this paper, a new variance assignment method has been proposed for stochastic non-linear systems which are described by stochastic differential equation. The variance governs the shape of the probability density function if the stochastic distribution is Gaussian. It means that the variance assignment is a special case for stochastic distribution control if the control law can be designed to force the probability distribution of investigated stochastic non-linear system as Gaussian. Motivated by Ornstein-Uhlenbeck process and Fokker-Planck-Kolmogorov equation, the backstepping design has been adopted for system stabilisation and the desired variance can be formulated using the free design parameter in the control law. Therefore, the variance assignment can be achieved and the closed-loop system is bounded in probability sense. In addition, the entropy assignment is also discussed as a generalised study of variance assignment. The simulation is given to validate the proposed control algorithm where the effectiveness has been demonstrated.