Fuzzy Control And Filtering Based On Hidden Markov Model

In designing controllers and filters for Markov jump systems,external noises,data dropouts,actuator failures and some other abnormal factors often result in a situation that we can not obtain mode information of original systems timely and accurately.To deal with the problem,researchers use the hidden Markov model to detect jump modes of orig-inal systems.With the detected mode,the corresponding controller and filter are devised.On the other hand,Takagi-Sugeno(T-S)fuzzy model plays an important role in solving the nonlinear terms of systems,which can transform complex nonlinear systems into many local linear systems.At present,due to the difficulty in directly obtaining jump mode infor-mation of original systems,results concerning the controller and filter design for T-S fuzzy Markov jump systems are few and there are many open problems to be solved.The paper mainly deals with the controller and filter design problems for T-S fuzzy Markov jump systems based on the hidden Markov model and the desired systems can satisfy some performance indexes simultaneously.Its main works can be summarized as follows:(1)The asynchronous dissipative control problem is studied for T-S fuzzy Markov jump systems.Using the hidden Markov model,we design an asynchronous fuzzy con-troller.Adopting a Lyapunov function and employing matrix inequality transformation methods,we propose a solution to controller gains,which can also ensure the stochas-tic stability of the closed-loop systems with dissipative performance.The study includes both continuous-time and discrete-time systems.(2)The asynchronous guaranteed cost control problem is investigated for T-S fuzzy Markov jump systems.An asynchronous fuzzy controller is constructed with the hidden Markov model.Due to communication constraints,the stochastic quantizer is introduced to quantize transmitted data and thus reduce the quantity of the signals.The proposed algorithm to solve controller gains can ensure the stochastic stability of the closed-loop systems with guaranteed cost performance(3)The asynchronous extended dissipative static output feedback control problem is analyzed for T-S fuzzy switched systems.The intermittent phenomenon during measur-ing the output signal is modelled by a Bernoulli process.The asynchronous static output controller is devised with the hidden Markov model,which can ensure that closed-loop sys-tems are stochastically stable and meet the desired extended dissipative performance.The investigated systems not only cover the T-S fuzzy Markov jump system but also another kind of T-S fuzzy switched systems subject to sojourn probabilities.(4)The asynchronous dissipative filtering problem is considered for T-S fuzzy Markov jump systems.With the hidden Markov model,an asynchronous fuzzy filter is designed.The mode-dependent Lyapunov function is used to analyze the stochastic stability and dissipative performance of the filtering error systems.Two design methods are proposed to solve filter gains.(5)The asynchronous dissipative fault detection problem is studied for T-S fuzzy Markov jump systems.A fault detection filter is constructed by using the hidden Markov model.Based on a Lyapunov function,two approaches to solve fault detection filter gain-s are developed,which can ensure that the fault detection system is stochastically stable with dissipative performance as well.The effectiveness and correctness of the developed approaches are verified by an example simulation.