Coupling Control and Human-Centered Automation in Mathematical Models of Complex Systems

TL;DR

This paper presents a mathematical framework for integrating human factors into control models of complex systems, exemplified through intelligent transportation systems and speed control decision-making.

Contribution

It introduces a novel approach using Hamilton-Jacobi-Bellman equations to incorporate human factors via system Hamiltonian estimations in control problems.

Findings

Mathematically models human-centered control in complex systems.

Demonstrates reduction to Hamilton-Jacobi-Bellman equations with human factors.

Applicable to various dynamic systems beyond transportation.

Abstract

In this paper we analyze mathematically how human factors can be effectively incorporated into the analysis and control of complex systems. As an example, we focus our discussion around one of the key problems in the Intelligent Transportation Systems (ITS) theory and practice, the problem of speed control, considered here as a decision making process with limited information available. The problem is cast mathematically in the general framework of control problems and is treated in the context of dynamically changing environments where control is coupled to human-centered automation. Since in this case control might not be limited to a small number of control settings, as it is often assumed in the control literature, serious difficulties arise in the solution of this problem. We demonstrate that the problem can be reduced to a set of Hamilton-Jacobi-Bellman equations where human factors are incorporated via estimations of the system Hamiltonian. In the ITS context, these estimations can be obtained with the use of on-board equipment like sensors/receivers/actuators, in-vehicle communication devices, etc. The proposed methodology provides a way to integrate human factor into the solving process of the models for other complex dynamic systems.