Computing control invariant sets in high dimension is easy
It addresses the computational bottleneck of computing control invariant sets for high-dimensional systems, which was previously limited by set addition and vertex enumeration.
The paper presents a method for computing control invariant sets for high-dimensional linear systems with constraints, using linear programming conditions based on N-step sets. The method scales to systems with state dimension 30 and input dimension 15.
In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that involve the N-step sets and are posed in form of linear programming problems. Such conditions allow to overcome the complexity limitation inherent to the set addition and vertices enumeration and can be applied also to high dimensional systems. The efficiency and scalability of the method are illustrated by computing approximations of the maximal control invariant set, based on the 10-step operator, for a system whose state and input dimensions are 30 and 15, respectively.