Guaranteeing Performance Robust Control for Human-Machine Systems With Optimal Human Decision

Human-machine systems (HMSs) are dedicated to integrating intelligent human decisions with machine operations to achieve synergistic operational functionality. We focus on constraint-following control within the HMS, considering potential uncertainties, environmental disturbances, and limited operational space. A hierarchical hybrid control scheme is proposed, consisting of a preemption algorithm and a human decision algorithm. Specifically, the preemption algorithm relies on online state feedback from mechanical system signals, such as position and velocity, which can be implemented in hardware or software; the human decision algorithm takes inputs from electrophysiological signals or language commands. In this development, a Lagrangian density function is constructed that integrates optimal decision making with a uniformly bounded threshold. The intelligent decision-making problem in the HMS is creatively analyzed and mathematically solved leveraging variational calculus, resulting in the analytical expression of the optimal membership function associated with human decisions. Furthermore, a series of numerical simulation experiments are conducted using a bionic upper-limb prosthetic system as an example, and the comparison results demonstrate the superiority and effectiveness of the proposed method.