Decentralized adaptive neural control for high-order stochastic nonlinear strongly interconnected systems with unknown system dynamics

This paper studies the problem of decentralized adaptive neural backstepping control for a class of high-order stochastic nonlinear systems with unknown strongly interconnected nonlinearity. During the control of the high-order nonlinear interconnected systems, only one adaptive parameter is used to overcome the over-parameterization problem, and radial basis function (RBF) neural networks are employed to tackle the difficulties brought about by completely unknown system dynamics and stochastic disturbances. In addition, to address the problem arising from high-order strongly interconnected nonlinearities with full states of the overall system, the variable separation technique is introduced based on the monotonically increasing property of the bounding functions. Next, a decentralized adaptive neural control method is proposed based on Lyapunov stability theory, in which the controller is designed to decrease the number of learning parameters. It is shown that the designed controller can ensure that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are offered to illustrate the effectiveness of the proposed control scheme.