Singular System Semi-stability And Its Control

A lot of research on the optimal control problem of non-singular systems have been done and widely used in practical work.However,people have found that in actual engineering systems,not all systems are non-singular systems or multiagent network systems,which often appear More are singular systems,which makes the existing theories difficult to apply.Therefore,it is necessary to discuss the semi-stability optimal control problem based on singular systems.This dissertation will discuss the semi-stability of the singular system and its control problems.The method adopted is to decompose the singular system into two systems,one is a fast system and the other is a slow system,which is derived from the equivalence relationship between the fast system and the slow system The semi-stability judgment condition further transforms the semistable optimal control problem of the original singular system into the semi-stable optimal control problem of the slow system obtained by the decomposition of the original system,and gives the semi-stability of the singular system through the obtained Riccati equation Sufficient conditions for optimal control.Finally,this dissertation also discusses the semi-stability of the dynamic ADAS model(aggregate demand-total supply model),and verifies the correctness of the sufficient conditions for judging the semi-stable linear quadratic optimal control of the singular system.The different situations of the coefficient matrix when it is non-singular and singular are discussed,and numerical results are given.