一类严格反馈时滞系统的自适应输出反馈控制

摘要

针对一类单输入单输出的严格反馈时滞系统研究跟踪控制问题.该控制系统包含不确定项、输出约束、未知死区特性和未知时间延迟.首先,设计一个状态观测器来估计无法测量的系统状态;其次,利用径向基函数(radial basis function,RBF)神经网络去逼近未知的系统内部动态;同时,利用障碍李雅普诺夫(Lyapunov)函数确保输出约束及Lyapunov-Krasovskii方法消除时滞项对系统的影响;最后,基于Lyapunov稳定性理论,构造一个鲁棒自适应神经网络输出反馈控制器,并且克服了过参数问题.结果显示,设计的神经网络输出反馈控制器可以保证闭环系统中的所有信号都是半全局最终一致有界的,跟踪误差能收敛到零值小的领域内.文中通过两个例子进一步验证了提出方法的有效性.%This paper investigates the problem concerning tracking control for a class of single input and single output uncertain strict-feedback nonlinear systems, under the condition of the input dead-zone and output constraint with unknown time delays.Firstly, a state observer is established to estimate the unmeasured states.Secondly, radial basis function neural networks are used to approximate the unknown nonlinearity;a barrier Lyapunov function is designed to ensure that the output parameters are restricted and the effects of unknown time-delays are eliminated by choosing appropriate Lyapunov-Krasovskii functions in the design procedure.Finally, based on Lyapunov stability theory, a robust adaptive neural network output feedback controller is constructed.The designed controller overcomes the problem of over-parameterization.It is shown that the designed control scheme can ensure that all the closed-loop signals are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin.Two examples are provided to further show the effectiveness of the proposed approach.