具有输入饱和的严格反馈系统的约束控制

Constrained Control for Strict Feedback Systems with Input Saturation

摘要: 针对具有全状态约束和输入饱和的非线性严格反馈系统，提出了一种自适应神经网络跟踪控制方案。文中利用反步递推和神经网络逼近相结合的方法设计自适应控制器。在设计过程中，首先，利用高斯误差函数构建一种连续可导的非对称饱和模型。其次，通过选取正切型障碍李雅普诺夫函数处理状态约束问题，即确保全状态约束不被违背。对比已有对数型障碍李雅普诺夫函数和积分型障碍李雅普诺夫函数，正切型的障碍李雅普诺夫函数是一种即可以处理具有约束的系统又可以处理没有约束的系统的函数。再次，通过定理证明闭环系统的所有信号是一致最终有界的，误差信号保持在零的小邻域内，并且不违反全状态约束。最后，由仿真结果验证所提方案的有效性和可行性。

Abstract: An adaptive neural network tracking control scheme is proposed for nonlinear strict feedback systems with full state constraints and input saturation. The adaptive controller is designed by combining the backstepping technique and neural network approximator. In the design process, firstly, a continuous differentiable asymmetric saturation model is constructed by using Gaussian error function. Secondly, tangent Barrier Lyapunov functions (tan-BLFs) are selected to deal with the state constraint problems, that is to ensure that the full-state constraint is not violated. Com-pared with existing logarithm-BLFs and integral-BLFs, tan-BLFs are the BLFs that can deal with both constrained and unconstrained systems. Thirdly, it is proved by the theorem that all the signals in the closed-loop systems are uniformly ultimately bounded, and the error signals are kept in the small neighborhood of zero, and full state constraints are not violated. Finally, the simulation results show that the proposed scheme is effective and feasible.