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Reachability Analysis and Safety Synthesis of a Class of Human-Computer Collaborative Driving Systems

This work investigates the safety problem for a class of human-computer collaborative driving (H-CCD) systems by the approach of reachable set computation. The H-CCD system under consideration can monitor the human internal state (HIS) and then provide a proper human-assistance control law to the vehicle. Firstly, a yaw-sideslip bicycle model is employed to describe the lateral dynamics of the vehicle in which a human driver is maintaining the center of gravity of the vehicle at the middle of a lane and trying to keep the vehicle away from road boundaries. Subsequently, a hidden Markov model (HMM) is used for human behavior modelling, which takes into account the random nature of HIS reasoning and the uncertainty from HIS observation. By integrating a vehicle model, a human model, and their interaction, a hidden Markov jump system (HMJS) model is constructed to describe the H-CCD system. By the tools of reachable set computation and linear matrix inequalities (LMIs), a sufficient condition for the reachability of the H-CCD system to a prescribed safe set is given on the basis of the HMJS model. An LMI approach to the human-assistance control design is then proposed such that the H-CCD system is safe in the sense of expectation. Finally, theoretical results are verified by a numerical simulation.