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Control invariant set is critical for guaranteeing safe control and theproblem of computing control invariant set for linear discrete-time system isrevisited in this paper by using a data-driven approach. Specifically, samplepoints on convergent trajectories of linear MPC are recorded, of which theconvex hull formulates a control invariant set for the linear system. Toapproximate the convex hull of multiple sample points, a convex piecewiselinear (PWL) fitting framework has been proposed, which yields a polyhedralapproximation with predefined complexity. A descent algorithm for the convexPWL fitting problem is also developed, which is guaranteed to converge to alocal optimum. The proposed strategy is flexible in computing the controlinvariant set in high dimension with a predefined complexity. Simulationresults show that the proposed data-driven approximation can compute theapproximated control invariant set with high accuracy and relatively lowcomputational cost.

Data-driven approximation of control invariant set for linear system based on convex piecewise linear fitting