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Some observations on the activity of terminal constraints in linear MPC

We analyze the activity of terminal constraints in stabilizing MPC for linear systems with state and input constraints. In particular, we show that the set of initial states for which the terminal constraints are inactive (or weakly active), is always compact but may or may not be convex. In addition, we illustrate that the set where terminal constraints are (strongly) active may be nonempty, even for arbitrarily long prediction horizons. This observation is important for the design of stabilizing MPC schemes without terminal constraints.