Coupling control and human factors in mathematical models of complex systems

Abstract

It is known that with the increasing complexity of technological systems that operate in dynamically changing environments and require human supervision or a human operator, the relative share of human errors is increasing across all modern applications. This indicates that in the analysis and control of such systems, human factors should not be eliminated by conventional formal mathematical methodologies. Instead, they must be incorporated into the modelling framework. In this paper we analyse mathematically how such 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 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 factors. 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 factors into the solving process of the models for other complex dynamic systems.