Research On Sliding Mode Control For Markov Jump Systems

The sudden structure change will happen in the realistic industrial system when it is in running. The complicated systems can be effectively described by Markov jump systems. Besides, parameter uncertainties and external disturbance will lead to the instability of the system performance. However, the sliding mode control method can address the intricate systems, which have parameter uncertainties and disturbance. The problem of sliding mode control for Markov jump systems has been widely considered. However, many current works are based on the ideal assumptions, for instance the system states are available and the actuator works well. This paper investigates the sliding mode control for Markov jump systems with some complicated conditions.The actuator faults and environment factors will lead to the instability of the control systems with in the realistic industrial systems. In order to overcome these problems, the authors designed a novel sliding mode controller to tackle the Markov jump systems, which have unknown nonlinearity, unknown disturbance and partly unknown transition probabilities. A novel sliding mode controller based state observer is designed. Then the condition of the stability for sliding mode dynamics can be obtained. The problem of observer-based adaptive sliding mode control for nonlinear Markov jump systems was discussed. The problem of adaptive sliding mode control for Markov jump nonlinear systems with actuator faults was investigated. A sliding mode controller is designed such that the stability for sliding mode dynamics is received when the system state trajectories are driven onto the sliding mode surface. When the system state trajectories cannot be attracted to the designed sliding mode surface, the stochastic stability of the closed-loop system should be provided. The issue of robust adaptive sliding mode control for nonlinear uncertain neutral Markov jump systems was studied. A novel adaptive sliding mode controller is constructed to guarantee the stochastic stability of the closed-loop system. Finally, a numerical example or practical example is given to demonstrate the effectiveness of the proposed control method.