Adaptive self-triggered control for nonhomogeneous semi-Markov jump systems under finite-time interval

In this paper, an adaptive self-triggered control is studied for nonhomogeneous semi-Markov jump systems under finite-time interval, which can satisfy the dual purposes of suppressing interference and saving resources. Specifically, an adaptive self-triggered mechanism is proposed different from the traditional self-triggered mechanism, in which the threshold can be adjusted dynamically to reduce interference and obtain better performance. According to the current sampling data, the next executing time is predicted to effectively avoid Zeno behavior. At the same time, the relation expressions are derived among transition probability, probability distribution function, and probability density function. Taking the transient performance into account, sufficient conditions are proposed for finite-time boundedness of the underlying nonhomogeneous semi-Markov jump systems. In order to save communication resource, the triggered mechanism and the finite-time controller are co-designed. Finally, a physical mass-spring-damper mechanical system is given to verify the effectiveness of the design method.