Asynchronous Control For Nonlinear Markov Jump Systems

In the control system,abnormal factors,such as the mutations of links and malfunctions of the working components,often lead to sudden changes in the structures and parameters of the system.In order to ensure the control accuracy of the system,scholars often use Markov process to quantitatively describe these mutations,that is,Markov jump system.In the researche of its control problems,due to the existence of external noise,data losses and other factors,the mode information of the original system can not be obtained in time and accurately.If a synchronous controller is adopted,its mode is inconsistent with that of the original system,which makes the control effect degrading.To make the controller design independent of the accurate mode information of the original system,the concept of asynchronous control is proposed.On the other hand,there are still many problems for nonlinear Markov jump system to be solved urgentily.In this paper,by introducing the hidden Markov model,the asynchronous controllers are designed to make the systems stochastically stable or stochastically finite-time bounded and meet the expected performance index.The main research contents are as follows:For the nonlinear discrete-time Markov jump system with random packet loss and partlly unknown conditional probability matrix,the problem of its finite-time bounded asynchronous robust control is studied via the output feedback control strategy.Based on the mode-dependent Lyapunuo function and matrix inequality method,an algorithm for solving the gain matrix is proposed.The designed controller can ensure the stochastic finite-time bound-edness and l₂-l_? performance index of the closed-loop system.The problem of asynchronous input passive control of nonlinear discrete Markov jump system is considered from the perspective of energy processing.The nonlinear matrix in-equality that satisfies the input passivity is obtained through the Lyapunov function.Then by using the matrix inequality and the controller matrix parameterization method,the al-gorithm for solving the controller gain matrix is proposed and ensure the input passivity of the closed-loop system.The effectiveness of the algorithm is demonstrated by numerical simulation.Then,the problem of robust finite-time asynchronous control for nonlinear discrete Markov jump system with singular perturbation and time delay is studied.Based on aux-iliary variable and the mode-dependent Lyapunov function,the finite-time boundedness and H_? performance of the closed-loop system are analyzed,and an algorithm for solving the gain matrix is proposed and the influence of singular perturbation parameters on the algo-rithm is further analyzed.The asynchronous control problem is considered for Markov jump system with actu-ator saturation.Based on the matrix inequality,an asynchronous controller design algo-rithm that guarantees the stochastic stability of the transformed linear system is proposed and an estimate of the maximum contractive invariant set is given.The numerical simu-lation demonstrates that the designed controller based on the linear system can ensure the stochastic stability of the original Markov jump system.