  Control invariant set is critical for guaranteeing safe control and the
problem of computing control invariant set for linear discrete-time system is
revisited in this paper by using a data-driven approach. Specifically, sample
points on convergent trajectories of linear MPC are recorded, of which the
convex hull formulates a control invariant set for the linear system. To
approximate the convex hull of multiple sample points, a convex piecewise
linear (PWL) fitting framework has been proposed, which yields a polyhedral
approximation with predefined complexity. A descent algorithm for the convex
PWL fitting problem is also developed, which is guaranteed to converge to a
local optimum. The proposed strategy is flexible in computing the control
invariant set in high dimension with a predefined complexity. Simulation
results show that the proposed data-driven approximation can compute the
approximated control invariant set with high accuracy and relatively low
computational cost.
