Finite-Time Sliding Mode Control Under Quantization

Abstract

This chapter addresses the sliding mode control for semi-Markovian switching systems (S-MSSs) with quantized measurement under the framework of finite-time interval. The transition between each subsystems obeys a stochastic semi-Markovian process. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with the existing results, the output quantization is considered for finite-time sliding mode control problem via a logarithmic quantizer at the first time. Our aim is to design an appropriate finite-time sliding mode control law to reduce the impact of parameter uncertainty and external disturbance on the overall performance of the system. Firstly, By using stochastic semi-Markov Lyapunov function and key points of observer design theory, the desired sliding mode control law is constructed to guarantee that the trajectory of the system reaches the specified sliding mode surface in the specified finite-time interval. Then, sufficient conditions, including reaching phase and sliding motion phase, are given to satisfy the requirement of finite-time boundedness. Finally, the applicability of the results is verified by a single link manipulator model.