基于LMI的参数随机变化系统的概率密度函数控制

PDF Control of Stochastic Parameter System Using Linear Matrix Inequalities

针对模型参数在有界区域内随机变化的系统,基于平方根B样条模型,提出了输出概率密度函数(Probability density function,PDF)跟踪控制策略.目标是控制系统输出的概率密度函数跟踪给定的概率密度函数.通过B样条逼近建立了输出PDF和权值之间的对应关系,把PDF的跟踪转化为权值的跟踪,同时系统转化为MIMO系统,从而权值向量的跟踪就转化为MIMO系统的跟踪问题,接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件,通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计,得到了系统具有Hinfinity范数界Gamma鲁棒镇定的结果.仿真结果表明本文提出的控制算法是有效的.

This paper presents a probability density function （PDF） tracking control strategy for stochastic parameter system based on a square root B-spline model for the output probability density functions. The objective is to control the PDF of system output to follow a desired PDF. Using the B-spline approximation the tracking problem of PDFs is transferred to the tracking of given weights values which correspond to the given PDF. At the same time, the system is transferred to a MIMO system, whose output is the weight value vector. As a result, the tracking of given weights values is transformed to a tracking problem of a MIMO system. Furthermore, a sufficient condition of the PDF of system output to follow a desired PDF is given and the control strategy is obtained by solving several linear matrix inequalities. A simulated example is used to demonstrate the efficiency of the proposed approach and encouraging results have been gained.