马尔可夫跳变系统的蒙特卡罗仿真

Monte Carlo simulation of markovian jump system

针对跳变系统理论研究中缺少有效的仿真方法,提出了一种适用于跳变系统的蒙特卡罗法。跳变系统蒙特卡罗仿真的关键是马尔可夫链的仿真实现,研究了两种生成马尔可夫链的方法,即利用MATLAB函数randsrc和基于unifrnd函数产生均匀分布的随机数,提出了根据转移概率矩阵P对随机数设置不同的阈值来形成马尔可夫链的算法。根据仿真的结果对转移概率进行了验证,该方法概念清晰,简单易行,可用于切换系统等一般随机系统的研究。

Because there are no effective simulation methods in the theoretical study of jump systems, a Monte carlo method for jump systems is proposed. The key problem of Monte Carlo simulation of the jump system is the realization of the Markov chain. Two methods of generating the Markov chain are presented. One method was to use the MATLAB function randsrc, another was based on the function unfired to generate random numbers with uniform distribution. And various threshouds for the random numbers were set accoding to the transition probability matrix P to produce the Markov chain. The algorithms of the two methods were also provided. An application example was given and the transition probability was verified based on the simulation results. The proposed method is simple and clear in concepts, and can be also used for the study of stochastic systems such as switching systems.