Stability and H_∞ performance of human-in-the-loop control systems through hidden semi-Markov human behavior modeling

In this paper, a stochastic framework of analysis and synthesis is proposed for the stability and H_∞ performance of linear human-in-the-loop (HiTL) control systems which involve both human's discrete internal states and machine's continuous-time dynamics. Initially, a hidden semi-Markov model (HS-MM) is used for the human behavior modeling, which takes into account the random nature of human internal state (HIS) reasoning and the sojourn time of HIS, as well as the uncertainty from HIS observation. Subsequently, by integrating human model, machine model, and their interaction, a hidden semi-Markov jump system (HS-MJS) model is constructed to describe the HiTL control system. By the tools of stochastic Lyapunov functional and linear matrix inequalities (LMIs), a sufficient and necessary condition for the stochastic stability of the HiTL control system via state feedback is then given on the basis of the HS-MJS model. Besides, an LMI-based human-assistance stabilizing control design is developed. For the prescribed disturbance attenuation level, a human-assistance H_∞ controller synthesis method of the HiTL control system is proposed in terms of LMIs. Finally, the developed theoretical results are applied to the steering control of the lane-keeping assistance system.