PARCIS: Parameterized Robust Control Invariant Sets

Introduction

Given a discrete time affine system: where:

• x is state, wished to be restricted to a safe polyhedron \mathbb{X}={x \in \mathbb{R}^n| H_x x \le h},
• u$$ is control, with admissible set being a polyhedron \mathbb{U}={u \in \mathbb{R}^m| H_u u \le h_u},
• w is additive disturbance belonging to a polytope \mathbb{W}={w \in \mathbb{R}^n| H_w w \le h_w}.

The tool computes a robust control invariant set in $$\mathbb{X}$$.

Dependencies

• Pypolycontain package
• Gurobi version 8.0 or later.

Reference

The tool is partially based on the method in the following paper: Raković SV, Kerrigan EC, Mayne DQ, Kouramas KI. Optimized robust control invariance for linear discrete-time systems: Theoretical foundations. Automatica. 2007 May 31;43(5):831-41.: