A dual-mode framework for lifting-based self-triggered model predictive control of linear systems with a guarantee of minimum triggering in steady state

In this paper, we propose a new self-triggered model predictive control (ST-MPC) that stabilizes a class of linear time-invariant systems, under limited communication resource between plant and controller. A remarkable feature of the ST-MPC presented this work is to trigger as little as possible in steady state, by adopting the lifting method in order to realize the dual-mode paradigm in the ST-MPC formulation. In the lifting-based dual-mode framework, the steady-state requirement on minimum triggering can be achieved by driving the system state into a (maximal) positively invariant set constructed based on a large-sized lifted model, for which a new self-triggering mechanism is also proposed to plan a sequence of moments of triggering in transient (that takes place more frequently than in steady state if needed). The solution of a lifting-based discrete-time algebraic Riccati equation (DARE) plays an essential role in the ST-MPC design, whose existence condition and structural properties are thus intensively studied. The recursive feasibility and closed-loop stability are mathematically analyzed, while the validity of the proposed ST-MPC is verified via computer-aided simulation.