Linear time logic control of linear systems with disturbances

TL;DR

This paper develops a method for controlling linear systems with disturbances using finite abstractions, aiming to improve the design process by bridging the gap between the systems and their abstractions.

Contribution

It introduces a novel approach to control linear systems with disturbances by ensuring the finite abstractions accurately reflect the original systems' specifications.

Findings

Finite abstractions can be effectively used for control design with disturbances.

The proposed method bridges the gap between linear systems and their finite abstractions.

Control specifications are preserved in the abstraction process.

Abstract

The formal analysis and design of control systems is one of recent trends in control theory. In this area, in order to reduce the complexity and scale of control systems, finite abstractions of control systems are introduced and explored. In non-disturbance case, the controller of control systems is often generated from the controller of finite abstractions. Recently, Pola and Tabuada provide approximate finite abstractions for linear control systems with disturbance inputs. However, these finite abstractions and original linear systems do not always share the identical specifications, which obstructs designing controller (of linear systems) based on their finite abstractions. This paper tries to bridge such gap between linear systems and their finite abstractions.