Research Of Variable Period Networked Control Systems With Partly Unknown Transition Probabilities

The networked control system is the production of the continuously renovating of computer technology,communication network technology and control disciplines.The networked control system has many benefits such as inexpensiveness,install ability,and maintainability owing to the import of communication networks into control systems.It has also been widely used in the fields of workshop production,mechanical control,and aerospace industry.However,as a data transmission medium,communication networks also cause problems such as network delay and data loss due to their instability.In addition,changes in network resources and load will also make the sampling period of the system different.This paper first considers NCS with a constant sampling period,and studies the H_?controller design problem with random delay and data packet dropout.Based on this,considers NCS with a variable sampling period,and studies the state feedback controller design problem with delay and data packet dropout.The primary coverage of this article includes the following:(1)For a networked control system with random delay,an NCS state feedback controller is designed.The random delay is modeled as a Markov chain with finite states,and some elements of its state transition probability matrix are unknown.By using the principle of Lyapunov stability and stochastic stability,sufficient conditions for the existence of state feedback controllers are proved and obtained.The linear matrix inequality(LMI)is calculated,and the control gain is derived from the matrix factorization theory.Finally,Matlab simulation examples are given to verify that the state feedback controller design method is effective and feasible.(2)For a class of networked control systems with both network delay and random packet dropout,an H_?controller is designed.Considering the delay to determine the short delay,the NCS with packet dropout is modeled as a Markov jump system with three subsystems,and some elements of its state transition probability matrix are unknown.Bernoulli sequences are used to describe the packet dropout.Using the Lyapunov stability principle and random stability principle,the sufficient conditions for the existence of the H_?controller are proved and obtained,and the LMI is calculated to obtain the control gain.Finally,Matlab simulations example are given.The design method is verified and proved to be effective and feasible.(3)A state feedback controller is designed for a class of NCS with time-varying delay and variable sampling period.Consider transforming the variable sampling period into the sum of the constant sampling period and the time-varying delay,so as to establish a discrete system model,and use the matrix factorization method to convert the uncertainty of the network time-varying delay and the sampling period to the uncertainty of system parameters.The analysis method of Lyapunov stability theory is used to prove and obtain the sufficient conditions for the existence of the state feedback controller,and the LMI is calculated to obtain the control gain.Finally,Matlab simulations example are given,and the design method of the state feedback controller verify that it is effective and feasible.(4)For a class of networked control systems with variable sampling period with time-varying delay and packet dropout,a time-varying state feedback controller that relies on the characteristics of data packet dropout is designed.Firstly,a discrete model of the system is established according to the time-varying delay and the variable sampling period.According to the method of matrix factorization,the uncertainty of the sampling period is converted into the uncertainty of the system parameters.The network control system with packet dropout is modeled as a Markov jump system with 4 subsystems and partially unknown probability.The packet dropout situation is described by Bernoulli sequence;Lyapunov stability principle and random stability theory are used to prove and obtain the sufficient conditions for the existence of the time-varying state feedback controller,and calculate the output control gain of the LMI.Finally,Matlab simulation examples are given.The square design method is verified to prove that it is effective and feasible.