| In modern industrial systems,most systems have multi-time scale phenomena due to their vast and complex.At the same time,their structural parameters often change randomly due to environmental factors.Usually,the system with these two characteristics is modeled as a Markov jump singularly perturbed system.With the increasing Internet penetration into all walks of life,the systems gradually tend to be networked.The analysis and control of networked systems have become one of the hotspots.Given this,based on singular perturbation theory and Markov jump theory,this thesis studies the control method of networked Markov jump singular perturbation systems.The goal is to solve the system control problem with multi-time scale characteristics,random variation characteristics of structural parameters and limited by network transmission.The main work is summarized as follows:1.The nonstationary quantitative control problem of slow sampling Markov jump singularly perturbed systems(MJSPSs)under deception attacks(DAs)is addressed.Firstly,the control input is characterized by nonstationary quantization and randomly occurring DAs.A quantizer is introduced to quantize the control input.At the same time,a Bernoulli distribution sequence is introduced to simulate the random occurrence of DAs.Considering the asynchronous phenomenon and correlation among controller,quantizer and system,a multi-layer structure methodology is applied to design nonstationary controller and quantizer for MJSPSs.Then,the modal dependent Lyapunov function is constructed.Sufficient criteria are established such that the closed-loop system is stochastic mean square exponential ultimately bounded,and the expression of the control gain is given.Finally,the correctness and effectiveness of the theoretical results are proved by a numerical example and an inverted pendulum system controlled by a DC motor.At the same time,the effects of different attack rates on the optimal stability bound of singular perturbation parameters and the effects of different attack intensities on the system’s stability are discussed in the simulation.2.The problem of nonstationary sliding mode control for a class of MJSPSs with uncertainties and nonlinear disturbances under mismatched external disturbances and communication constraints is studied.First,a stochastic communication protocol(SCP)is introduced to alleviate the transmission pressure in the communication network.Under SCP scheduling,only one sensor/actuator has access to the shared network at each time.Unlike the current work,the scheduling rules of SCP here are controlled by a piecewise homogeneous Markov chain which depends on the system and controller modes.Then,based on a sliding mode surface related to singular perturbation parameters,an appropriate non-stationary sliding mode control law is designed.The modal dependent Lyapunov function is constructed.Sufficient criteria in the form of linear matrix inequality(LMI)are obtained to ensure the accessibility of the sliding mode surface and the system’s stability by using the stochastic analysis method.At the same time,the expression of the control gain is given.Finally,a numerical example is given to illustrate the correctness of the theoretical results and the method’s effectiveness. |
