Scalable Computation of Controlled Invariant Sets for Discrete-Time Linear Systems with Input Delays

TL;DR

This paper introduces an efficient method for computing maximal controlled invariant sets in discrete-time linear systems with input delays, incorporating disturbance preview information to enhance safety guarantees while maintaining scalability.

Contribution

It proposes a novel approach that relates delayed systems to auxiliary delay-free systems, enabling scalable computation of invariant sets even with disturbance preview information.

Findings

Method efficiently computes invariant sets for systems with input delays.

Incorporating disturbance preview improves safety guarantees.

Approach scales better than naive higher-dimensional system methods.

Abstract

In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system (without delay) with the same state-space dimension of the original system in consideration and to relate the maximal invariant set of the auxiliary system to that of the original system. When the system is subject to disturbances, guaranteeing safety is harder for systems with input delays. Ability to incorporate any additional information about the disturbance becomes more critical in these cases. Motivated by this observation, in the second part of the paper, we generalize the proposed method to take into account additional preview information on the disturbances, while maintaining computational efficiency. Compared with the naive approach of constructing a higher dimensional system by appending the state-space with the delayed inputs and previewed disturbances, the proposed approach is demonstrated to scale much better with the increasing delay time.