Probabilistic stability and stabilization of human-machine system via hidden semi-Markov modeling approach

This paper investigates the probabilistic stability and stabilization issues of human-machine systems (H-MSs) through the use of hidden semi-Markov model (HS-MM) for human behavior modeling. Firstly, an HS-MM is employed to illustrate the sojourn-time-dependent HIS behavior, which considers the stochastic nature of human internal state (HIS) reasoning and the uncertainty from HIS observation. Next, by integrating HIS model, machine dynamic model, and human-machine interaction, a hidden semi-Markov jump system (HS-MJS) model is established to describe the H-MS. The initial machine state is considered to be Gaussian distributed with some given expected value and covariance matrix. By the tools of probabilistic reachable set computation and stochastic Lyapunov functional, a sufficient condition for the stochastic stability of the H-MS with some given confidence level is provided in terms of linear matrix inequalities (LMIs). Moreover, for a prescribed confidence level, an LMI-based human-assistance controller synthesis method is proposed to stabilize the H-MS with the confidence level. Finally, a driver-automation cooperative system is employed to verify the feasibility of the theoretical results.