Stochastic safety analysis and synthesis of a class of human-in-the-loop systems via reachable set computation

This paper investigates the stochastic safety analysis and synthesis issues for a class of linear human-in-the-loop (HiTL) systems based on hidden semi-Markov human behavior modeling and stochastic reachable set computation. Firstly, by considering the random property of human internal state (HIS) reasoning and the uncertainty from HIS observation, a hidden semi-Markov model (HS-MM) is employed to describe the HIS behavior. A discrete-time hidden semi-Markov jump system (HS-MJS) model is then constructed to depict the HiTL control system, which can integrate human model, machine model, and their interaction in a stochastic framework. The safety constraints are described through a polyhedral set of the machine state. Subsequently, based on the HS-MJS model, a sufficient condition for the stochastic safety of the HiTL control system is provided in terms of linear matrix inequalities (LMIs) via reachable set computation. A human-assistance safety control design is derived on the basis of LMIs. Moreover, for some given safe confidence level, a stochastic safety criterion and an LMI-based human-assistance controller synthesis method are proposed for the HiTL control system by computing the probabilistic reachable set. Finally, a lane-keeping assistance system is employed to verify the feasibility of the theoretical results.