Data-driven control synthesis for discrete-time semi-Markov jump systems

In discrete-time semi-Markov jump systems, the system matrix for each subsystem is usually determined by the system identification method. For such systems, a large amount of data and computation are generally required to obtain system parameters close to the real ones. This method has a lot of difficulties in practical applications, especially when there are too many subsystems. In contrast, the data-driven method can skip the system identification step and directly design the controller based on the input and output data. Therefore, the data- driven method is investigated to solve the control problem of discrete-time semi-Markov jump systems. Firstly, a data model for discrete-time semi-Markov hopping systems is proposed. Secondly, the controller design method for the semi-Markov jump system with known and partly unknown transition probabilities is carried out using Lyapunov functions. Thirdly, for the practical situation, the time when the jump occurs is unknown; a new algorithm for mode estimation and the application conditions of this algorithm are given. Finally, a discrete-time semi-Markov jump system is constructed with the car model as an example to verify the effectiveness of the proposed method.