输出概率密度函数鲁棒弹性最优跟踪控制

Robust Resilient Optimal Tracking Control for Output Probability Density Function

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。

The robust resilient optimal tracking control problem is studied for a class of dynamic stochastic system. Based on adopting the Bspline neural network model to approach the output probability density function （PDF） and by considering uncertainties of system model and controller, the robust resilient optimal tracking controller is proposed by using the Lyapunov stability theory and linear matrix inequality （LMI） technique. The aim is to make the output PDF track the desired PDF. Through the solution of LMI, the obtained eontrol law can not only realize the perfect tracking, but also make the closed-loop dynamic stochastic system asymptotically stable and the closed-loop value of linear quadratic cost function satisfy a specified upper bound. This approach is easy of implementation and not in need of tuning any parameters.