具有输入和输出约束的高阶随机系统神经网络控制

Adaptive neural control for uncertain high-order stochastic nonlinear systems with input and output constraints

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.

This paper presents the problem of adaptive neural tracking control for a class of high-order nonlinear systems subject to stochastic disturbances.It is the first time that input and output constraints are introduced into the design of controllers of higher-order systems,and it is assumed that unknown system dynamics are unknown.First,the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation nonlinearity,and barrier Lyapunov functions are designed to ensure that the output parameters are restricted.Second,for high-order nonlinear systems,radial basis function(RBF)neural networks are employed to tackle the difficulties caused by completely unknown system dynamics and stochastic disturbances.At each recursive step of backstepping design,only one adaptive parameter is constructed to overcome the over-parameterization.At last,based on the Lyapunov stability method,the adaptive neural control method is proposed,which decreases the number of learning parameters.It is shown that the designed controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the tracking error converges to a small neighborhood of the origin.The simulation studies are provided to further illustrate the effectiveness of the proposed method.