Stochastic Stability Analysis and Synthesis of a Class of Human-in-the-Loop Control Systems

There have been a wide variety of practical control applications having human in the loop in today's society, such as automobile systems, health care, and energy management. In this article, a Markov jump system with controlled and hidden modes (MJSCHM) is employed to model a class of human-in-the-loop (HiTL) control systems which passively monitor human internal state (HIS) and take appropriate control actions to the human and the machine. By means of the MJSCHM, the human model, the machine model, and their interaction can be integrated in a probabilistic framework. In the MJSCHM, a controlled hidden Markov model (CHMM) is used for the human behavior modeling, which takes into account the random nature of HIS reasoning and the uncertainty from HIS observation, as well as the effect of control input for the human on the HIS. The stability analysis and human-assistance control design for linear discrete-time HiTL systems are addressed using the stochastic Lyapunov functional and linear matrix inequality (LMI) technique. Necessary and sufficient condition for stochastic stability of the HiTL system is first developed on the basis of the MJSCHM model. An LMI approach to the human-assistance control design is then proposed such that the HiTL system is stochastically stable. Finally, simulation results on a driver-assistance system are presented to illustrate the effectiveness of the proposed methods.