Model-Reference Adaptive Moment Control of Uncertain Nonlinear Stochastic Systems

In this paper, a new model-reference adaptive moment control method is proposed to control the first and second moments of an uncertain nonlinear system with additive external stochastic excitation. This method has established a closed-loop control system that calculates an adaptive stochastic nonlinear input by introducing a Lyapunov function and adaptive update law. The proposed adaptive structure is innovative in trying to minimize two errors simultaneously: the moments tracking error and the error between the nonlinear system output and reference model. Furthermore, the proposed method can control the expected and covariance matrices of the states without needing to solve the complicated Fokker-Planck-Kolmogorov differential equation or using the approximate methods. Simulation has been performed on two practical examples, which show a good performance for the designed controller.