On Terminal Set and Cost for Stability-aware MPC for Sampled-data Linear Systems with Continuous-time Constraint: A Lifting Approach

In this paper, we address the problem of con-structing a stability-aware model predictive control (MPC) for continuous-time optimal control problem in the sampled-data setting, with which continuous-time constraints of input and state are satisfied. To this end, we first approximate the continuous-time problem in discrete time with fast sampling, from which we derive a sufficient condition on state and input of the sampled-data system for satisfaction of continuous-time constraints. The lifting technique is then employed to represent the discretized model with the input-hold constraint as an augmented time-invariant model. Investigating several properties of the (multi-rate) linear quadratic regulator for this lifted system, we suggest a specific form of the terminal cost and terminal set of the proposed MPC, with which stability and recursive feasibility of the proposed MPC are theoretically guaranteed.