In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

中文翻译：

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状态约束不确定随机非线性系统的基于 IBLF 的自适应神经控制

在本文中，自适应神经反步控制方法是为具有全状态约束的不确定随机非线性系统设计的。根据约束边界的对称性，分别研究了受控系统受对称和非对称约束的两种情况。然后，利用反步设计程序和径向基函数神经网络（RBFNN）的学习能力开发了相应的自适应神经控制器。值得一提的是，积分Barrier Lyapunov函数（IBLF）作为一种有效的工具，首次应用于解决上述约束问题。结果，通过所提出的方案避免了状态约束被转换为错误约束。此外，基于 Lyapunov 稳定性分析，证明误差可以收敛到零的小邻域，完整状态不超过给定的约束界限，并且闭环系统中的所有信号在概率上半全局一致最终有界（SGUUB）。最后，提供了数值模拟结果来展示所提出的控制方法的有效性。