Event-triggered adaptive neural control for stochastic nonlinear systems using a novel follower-type integral barrier Lyapunov function.

In this paper, the adaptive trajectory tracking control problem for a class of stochastic nonlinear systems is investigated. A novel follower-type integral barrier Lyapunov function (FIBLF) is proposed to construct full-state dynamic constraint boundaries that translate synchronously with the desired trajectory while maintaining a constant bandwidth. Corresponding adaptive neural controllers are designed for both symmetric and asymmetric constraint cases. In addition, a relative-threshold event-triggered mechanism is introduced to reduce redundant control updates and the computational burden. Based on the backstepping design and the online approximation capability of radial basis function neural networks (RBFNNs) for unknown terms, the corresponding control laws and adaptive update laws are constructed. Stability analysis demonstrates that all closed-loop signals are semiglobally uniformly ultimately bounded (SGUUB) in probability. Numerical simulations further validate the effectiveness of the proposed method in terms of trajectory tracking performance, state constraint satisfaction, and a reduction in the control update frequency.