Multiobjective Control Design for Human-Machine Systems with Safety Performance Constraints

This article studies the problem of multiobjective control design for a class of human-machine systems (HMSs) with safety performance constraints containing state constraints and input constraints. The HMSs under consideration not only monitor the human but also need to take proper actions to both the human and machine. A model of controlled hidden Markov jump system (CHMJS) is applied to represent the HMSs. Based on the CHMJS model, a sufficient condition for the practical mean square stability of the unconstrained HMSs is first derived using a stochastic Lyapunov functional. A sufficient condition for ensuring the safety performance constraints of the HMSs is also deduced by employing reachability analysis and set invariance theory. Subsequently, a bilinear matrix inequality-based control design is presented to guarantee both the practical mean square stability and safety performance constraints of the HMSs. A multiobjective optimization problem (MOP) is then formulated to determine a feedback controller for the human and a human-assistance controller for the machine such that both the practical mean square stability and safety performance constraints as well as the less human intervention can be satisfied. An algorithm that mixes the multiobjective particle swarm optimization and linear matrix inequality technique is developed to solve this MOP. Finally, a lane departure example is given to illustrate its effectiveness.