Weak Control for Human-in-the-loop Systems

TL;DR

This paper introduces a control framework for human-in-the-loop systems where decision makers are weakly controlled, allowing them to choose actions within admissible sets, ensuring system stability and optimizing human costs.

Contribution

It proposes a novel set-valued control approach for human-in-the-loop systems with weak control, maintaining stability and enabling learning-based optimization.

Findings

System stability is maintained regardless of human decisions.

A learning algorithm effectively reduces human decision costs.

Numerical experiments demonstrate the approach's effectiveness.

Abstract

In this letter, we propose a control framework for human-in-the-loop systems, in which many human decision makers are involved in the feedback loop composed of a plant and a controller. The novelty of the framework is that the decision makers are weakly controlled; in other words, they receive a set of admissible control actions from the controller and choose one of them in accordance with their private preferences. For example, the decision makers can decide their actions to minimize their own costs or by simply relying on their experience and intuition. A class of controllers which output set-valued signals is proposed, and it is shown that the overall control system is stable independently of the decisions made by the humans. Finally, a learning algorithm is applied to the controller that updates the controller parameters to reduce the achievable minimal costs for the decision makers. Effective use of the algorithm is demonstrated in a numerical experiment.