基于非随机信息论的马尔科夫跳变系统可镇定最小信道容量

MINIMUM CHANNEL CAPACITY REQUIRED FOR STABILITY OF MARKOV JUMP SYSTEMS BASED ON NONSTOCHASTIC INFORMATION THEORY

近年来基于信息论的控制方法已成为控制领域关注的热点,很多学者采用随机变量理论来研究控制中的信息问题,即假设未知量服从一定的概率分布.但在实际的控制系统中,未知量常常是不确定变量,因此基于经典信息论的控制方法存在一定局限.为此文章引入一种非随机信息理论,该理论通过构造信息测度表达式来描述不确定变量之间包含彼此信息量的大小,并建立了信息测度与零误差信道容量之间的关系.基于该理论,利用马尔科夫跳变系统参数构造一个空间集合,根据该空间集合性质得到了信息测度与系统参数的关系,并由此进一步推导出马尔科夫跳变系统可镇定时的零误差信道容量约束.

Recently,the control method based on information theory has become a hot topic in control field.Many scholars adopt random variable theory to research the information problems of the control systems,in which the unknown quantities are modelled as random variables.However,in actual control system,unknown quantities are often uncertain variables without statistical structure.So there are some limitations of the control method based on the classical information theory.For this reason,a nonrandom information theory is introduced in this paper.In this theory,the information measure expression is constructed to describe the amount of information contained among each uncertain variables,and the linkage between information measure and zero-error channel capacity is established.Based on this theory,an interval set is constructed firstly with MJLS parameters to obtain the relationship between information measure and system parameters,then the zero-error channel capacity required for stability of MJLS is further deduced.