Hybrid variables-dependent event-triggered model predictive control subject to polytopic uncertainties

This paper focuses on the model predictive control (MPC) issue where the measurable state is released under an event-triggered mechanism (ETM) to implement MPC over an infinite horizon. A new dynamic ETM (DETM) is devised to conserve network resources, which contains an additive internal dynamic variable (IDV), a multiplicative adaptively adjusting variable, a time-varying weighting matrix and several flexible scalars. The MPC problem is formulated as a ‘min–max’ optimisation problem (OP), where a hard constraint and robust positive invariant set on the predictive state/IDV are considered simultaneously. By resorting to a Lyapunov-like function that depends on the IDV, we put forward an auxiliary OP with matrix-inequality-based constraints. By the feasible solutions of such an auxiliary OP, the feedback gain matrix is designed which ensures the asymptotic stability of the closed-loop system. Two examples are presented to demonstrate the validity of the devised DETM and the DETM-based MPC algorithm. The study verifies that the devised DETM has advantages over an existing counterpart in conserving network resources while achieving the desired performance.