Safety Control of Monotone Systems with Bounded Uncertainties

TL;DR

This paper develops a control strategy for discrete-time monotone systems with uncertainties, ensuring the system remains within a safe state space, demonstrated on traffic network management.

Contribution

It introduces a novel constraint programming approach leveraging monotonicity to design safety controls without requiring state measurements.

Findings

Control strategies based on finite control sequences ensure safety.

Safety control does not require real-time state measurement under certain assumptions.

Validated on urban traffic network to prevent congestion.

Abstract

Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control strategy for a discrete time monotone system with bounded uncertainties such that the evolution of the system is guaranteed to be confined to a safe set in the state space for all times. By exploiting monotonicity, we propose an approach to this problem which is based on constraint programming. We find control strategies that are based on repetitions of finite sequences of control actions. We show that, under assumptions made in the paper, safety control of monotone systems does not require state measurement. We demonstrate the results on a signalized urban traffic network, where the safety objective is to keep the traffic flow free of congestion.