Hierarchy Control Of Markov Jump Systems

Markov Jump Systems(MJSs)are an important subclass of Hybrid Dynamic Sys-tems(HDSs).The main characteristic of this system is that its state space is composed of Euclidean space Rn and discrete finite event set S.The switching between modes of the finite set is governed by a Markov process.MJSs are widely used in some com-plicated systems whose parameters have abrupt changes,such as abrupt environmental disturbance,subsystems interconnection changes,systems random failures and so on.This kind of systems are more closed to the actual situation,therefore the researches on MJSs have an important significance.Most of the researches on MJSs in recent years are based on the cases that the system transition rate(or probability)matrix is unknown or has a norm bound.The modes of these systems are assumed to be accurately known.However,in the modeling process of actual systems,due to the quantization errors or the influence of the network channel noise,we can only get the range of the actual mode if the thresholds of some modes are much closed to each other,and can not get the true value,which leads to the system modes indistinguishable.This will bring difficulties to the research of the system stability and controller design.Based on the above,the main research works are as follows.(1)In this dissertation,we consider the case that some modes of the MJSs can not be got accurately,and propose a hierarchy control method.This method combines the modes whose reference thresholds are closed and can not be precisely distinguished,and treat as a cluster.Then we define each cluster as an element of a new discrete finite set.In this way,we can get a new discrete space which is a partion of the original modes set.A priori distribution between the true mode and the observed modes is given and this distribution is the only way to distinguish modes within a cluster.When the distribution is satisfied,the stochastic variable taking values in the new discrete space is a Markov process.(2)In this dissertation,we study the stability,H? control performance for the Markov Jump linear systems with partial mode imprecisely known.The relationship between original transition rate(or probability)matrix and the transition rate(or prob-ability)matrix of the new mode variable is given.A new system is constructed based on the new Markov process.The relationship of stability between the original system and and the new system is analyzed.The mode related controllers are designed to make sure the original system reach stable state,which achieve a hierarchy control.(3)Event-triggered mechanism can reduce the frequency of pocket transmission,save network resources and reduce energy consumption.In this paper,we focus on the event-triggered control problem for Networked Markov Jump Systems(NMJSs)with partial modes imprecisely known.The event-triggered control problem for the discrete closed-loop system is equivalently converted into the control problem for a discrete markov jump system with time-varying delays.As partial modes of the system are not unknown exactly,the stability of the system is analyzed by the above hierarchy control method and the delay system method,and the design of the system controllers is given.