On Barriers in State and Input Constrained Nonlinear Systems

TL;DR

This paper investigates the structure of the boundary of the admissible state-input space in constrained nonlinear control systems, introducing a barrier surface characterized by a minimum-like principle to understand system safety limits.

Contribution

It provides a local description of the admissible set boundary, including the construction of a barrier surface using a minimum-like principle, advancing the understanding of constrained control.

Findings

Characterization of the boundary of the admissible set

Identification of two disjoint parts of the boundary

Construction of a barrier surface via a minimum-like principle

Abstract

In this paper, the problem of state and input constrained control is addressed, with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied \emph{for all times}. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.