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

Jun Xu, Fanglin Chen

Published 2022-11-23Version 1

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.