Stability Analysis And Controller Design For Two-Time-Scale Production-Inventory Systems

The problems of H_? control and event-triggered control for two-time-scale productioninventory systems are discussed in this thesis.Two-time-scale is caused by the different review periods in different production process of production-inventory systems.Due to the requirement in the practical systems,the scheme of multi-time-scale is widely concerned.For the multi-rate sampling problem caused by multi-time-scale,the lifting technique is introduced to deal with it,because of simplicity and easy operation.For the problem of the limited network bandwidth,the event-triggered scheme is used to choose the review data,to reduce the burden of network,to reduce the number of decisions and to save the enterprise cost.The main research contents of this thesis contain two parts: the first part is the study ofH_? control problem for the production-inventory systems in the network environment,the second part is the event-triggered control problem for two-time-scale production-inventory systems.The work of this paper is organized as follows:(1)The first chapter gives the introduction,significance and the research status at home and abroad of the production-inventory systems,then introduces the main research contents of this thesis.(2)In the second chapter,the H_? control problem of two-time-scale production-inventory systems with Markovian jumping parameters and time-varying delays is studied.Due to the uncertainty of consumer demand and the difference of stock level,the productioninventory systems is modeled as the switching systems,and the switches among subsystems are described as the Markov process.According to Lyapunov-Krasovskii theory and the switched theory,the condition of exponent stability with a prescribed H_?performance level is derived.Considering the different product rates in different subsystems,the controller is designed such that the systems are exponentially stable with a prescribed H_? performance level .Finally,a simulation example is proposed to illustrate the effectiveness of the proposed method in this chapter.(3)The third chapter researches the event-triggered control problem for two-time-scale production-inventory systems with average dwell time and time-varying delays.Similar to the second chapter,the production-inventory systems are modeled as the switching system,and the switches among subsystems are arbitrary,which satisfy the average dwell time condition.In order to improve the network utilization and reduce the number of decisions,the event-triggered scheme is introduced to choose the review data.According to Lyapunov-Krasovskii theory and the switching theory,the criterion of exponent stability with a prescribed H_? performance level is given,and the method of co-designing the event-triggered scheme and the controller is given.Lastly,A simulation example is selected to verify the effectiveness of the proposed method in this chapter,and to prove the event-triggered scheme in this thesis can be translated into the time-triggered scheme under a condition.(4)In the fourth chapter,we summarize the present research work,and make a prediction about the future work.