Filtering condition of multi layered neural network for minimum-phase stochastic nonlinear system

In this paper, we present an adaptive control method for minimum-phase stochastic nonlinear systems using neural networks. State feedback linearization is widely used for converting a nonlinear system to a canonical linear system on a distribution of the corresponding Lie algebra. However, in a stochastic environment, even the minimum phase linear system derived by feedback linearization is not controlled robustly. Thus, it is necessary to make an additional condition for observation of a nonlinear stochastic system, called the perfect filtering condition. Based on the proposed stochastic nonlinear observation condition, we propose an adaptive control law using neural networks. Computer simulation results show that the stochastic nonlinear system satisfying the perfect filtering condition is controllable and that the proposed neural adaptive controller is more efficient than a conventional adaptive controller.