Adaptive event-triggered output tracking control for Markovian jump systems: A robust H2/H∞ MPC approach

This work focuses on the output tracking control for discrete-time Markov jump systems (MJSs) via a model predictive control (MPC) approach. Not only the mean-square stability (MSS), but also the H2 performance and H∞ performance is considered in the MPC controller design. To save communication resources, a version of adaptive event-triggered mechanism (AETM) is utilized. Different from the traditional static event-triggered mechanism, its threshold coefficient is time-varying and can be adjusted in real-time to fit the system evolution. Moreover, the asynchronous switching between the controller modes and the plant modes is taken into account. The design objective is to synthesis an adaptive event-triggered asynchronous MPC controller such that not only the augmented closed-loop system is MSS with a certain level of H2/H∞ performance, but also the communication burden can be reduced to some extent. It is the first attempt to investigate the output tracking control of MJSs via an MPC approach. By constructing a plant model-dependent Lyapunov function, a set of conditions is derived to determine a desired MPC controller. In addition, two MPC related issues, namely recursive feasibility and closed-loop MSS, are also studied. At last, an illustrative example is given to verify the availability of the theoretical findings.