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

TL;DR

This paper introduces a data-driven method to approximate control invariant sets for linear systems using convex piecewise linear fitting, enabling efficient computation in high dimensions with guaranteed convergence.

Contribution

It proposes a novel convex PWL fitting framework and descent algorithm for approximating control invariant sets from trajectory samples, improving efficiency and scalability.

Findings

High accuracy in approximating control invariant sets

Low computational cost compared to traditional methods

Effective in high-dimensional systems

Abstract

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.