MPC for Sampled-Data Linear Systems: Guaranteeing Constraint Satisfaction in Continuous-Time

Model Predictive Controllers (MPC) designed for sampled-data systems can be shown to violate the constraints in continuous time. A reformulation of the initial problem will guarantee constraint satisfaction throughout the intersample period. Polytopic inclusions of the continuous trajectory are used in this technical note to establish additional constraints leading to a linearly constrained quadratic optimization problem. Continuous time asymptotic stability and continuous-time positive invariance are proven for the reformulated problem.