Singular Adaptive Sliding Mode Control For Markovian Systems

Since the 1960 s,Markovian jump systems have been used in engineering systems widely,and its related directions have been concerned by the control field.Such as the control problem of singular Markovian system,robust stability of Markovian system and so on.In addition,the switching rate of Markovian jump system depends on its jump parameters,that is,the research on the known,partially known or completely unknown jump parameters is necessary.In addition,as a kind of effective control method,the advantage of sliding mode control method is that it has excellent robustness to the change of parameters and external disturbances.In this paper,the sliding mode control is used to investigate Markovian jump systems with partially known transition rates and uncertain Markovian jump systems with generally uncertain transition rates.Then some research results are obtained.The main work of this article is arranged as follows:1.For a class of Markovian jump systems with partially known transitions rates,matched nonlinearity and external disturbances,the adaptive integral-type sliding mode control problem is investigated by singular system method.Firstly,according to the singular system method,the integral sliding mode surface is designed,and the corresponding singular Markovian jump system is obtained by the sliding mode dynamics theory.Next,the sufficient condition which is in the form of linear matrix inequalities are given to guarantee the stochastic admissibility of the obtained singular Markovian jump system.Then,the adaptive parameters are used to construct adaptive sliding mode control law to ensure the reaching conditions of state trajectory to the integral-type sliding mode surface.Finally,the effectiveness of the results is verified by a simulation case.2.For uncertain Markovian jump systems with generally uncertain transition rates,nonlinear function and unknown disturbance,the stochastic admissibility of the resulting singular Markovian jump systems and the reaching conditions of the state trajectory are investigated by the adaptive sliding mode control systematically.Firstly,the singular Markovian system is constructed based on singular system method in view of the uncertainty of the system.Then,the sufficient conditions are given to guarantee the stochastic admissibility of the obtained system,and the existence of the sliding mode surface is also verified;On this basis,an adaptive sliding mode controller is constructed to guarantee the reaching conditions of the state trajectory to the constructed sliding mode surface.Finally,the solvability of the obtained results is verified by a numerical case.