Multiple Objective Optimal Control For Singularly Perturbed Systems

The theory of singularly perturbed systems attracts the attention of researchers for the theoretical significance and practical value from its birth.The optimal problem of singularly perturbed systems increasingly becomes the research hotspot.In this paper,the muti-objective optimal control problem of singularly perturbed systems is concerned,and some new methods and results are presented.The main contents in this paper are as follow:(1)The H? optimal guaranteed cost control problem for linear systems is concerned.Firstly,the H? optimal guaranteed cost control based on state-feedback for normal linear systems is studied,and the design algorithm for state-feedback controller is presented.Then,two numerical examples are used to illustrate the correctness and effectiveness.Secondly,the H? optimal guaranteed cost control based on state-feedback for linear systems with multiple time delay and disturbance is studied,and the design algorithm for state-feedback controller is presented.Finally a numerical example is used to illustrate the correctness and effectiveness of the results.The new Lyapunov function which is built in this process is one of innovation points of this paper.(2)The optimization for the upper bound of perturbed parameter in singularly perturbed systems is concerned based on the genetic algorithm.Firstly,the stability problem for singularly perturbed systems is discussed based on the linear matrix inequality.Then,the stand form for the optimal problem for perturbed parameter is presented.And then the optimal algorithm is presented based on the genetic algorithm.Finally two numerical examples are used to illustrate the correctness and effectiveness of the results.The use of the genetic algorithm into the field of singularly perturbed systems is one of innovation points of this paper.(3)The multiple objective optimal control for singularly perturbed systems is concerned.Firstly,the stability problem for the singularly perturbed systems is concerned under the passive constraint based on the linear matrix inequality.Then the design problem for the state-feedback is studied and the quadratic performance is also concerned.Finally,a numerical example is used to illustrate the correctness and effectiveness of the results.