N -Step MPC: A Staged Requirements-Dependent Mixed Time/Event-Triggered Encoding–Decoding Approach

This article focuses on the problem of $N$ -step model predictive control (MPC) under a mixed time/event-triggered encoding-decoding strategy for polytopic uncertain systems with hard constraints. A staged requirements-dependent mixed time/event-triggered mechanism (MTEM) is proposed. When the system state is outside the terminal constraint set (TCS), the time-triggered pattern is implemented to meet the staged requirement of improving control performance. When the system state is in the TCS, an event-triggered pattern is used to fulfill the staged requirement of conserving resources. The event-triggered pattern contains an adaptively adjusting variable related to the "distance" of the system state from the TCS core, which helps meet the relative staged requirements in the TCS. The staged requirements-dependent MTEM-based encoding-decoding strategy improves the communication security while saving computational resources for encoding and decoding, as well as network resources. Based on two offline optimization problems (OPs), the TCS and the approximate robust one-step sets are designed, respectively. The control laws outside the TCS are obtained by an online OP. A mixed time/event-triggered encoding-decoding-based $N$ -step MPC algorithm is proposed based on three OPs. The algorithm's feasibility and the input-to-state stability of the closed-loop system are analyzed. Two examples are presented to illustrate the effectiveness and superiority of the proposed MTEM and MPC algorithm in saving resources while ensuring control performance.