A type of distribution control method for nonlinear stochastic systems

© 2017, Editorial Department of Journal of Drainage and Irrigation Machinery Engineering. All right reserved. Most nonlinear control systems are inevitably subject to random disturbances, such as systematic measurements and random noises(random vibrations or shocks) in practice, which affect the control of nonlinear systems. In this paper, a stochastic distributed control method is designed for nonlinear systems subject to random perturbations. In this method, the relationship between steady-state response probability density distribution and control target of a nonlinear stochastic system is studied. The control design is divided into two steps: firstly, the actual model with stochastic perturbation is transformed into the nonlinear system Hamiltonian model; then the output of the controlled system sa-tisfies with a prescribed probability density distribution by using a technique for solving exact stationary solution of a nonlinear stochastic system. The convergence of control system is achieved by introducing the Lyapelov function in which the output of a closed-loop nonlinear stochastic system can converge to a pre-defined steady PDF to ensure the closed-loop stability of the controlled system. The results show that the proposed method is effective and can make the controlled system be able to track a pre-defined target steady probability distribution.