Synthesis With Guaranteed Cost and Less Human Intervention for Human-in-the-Loop Control Systems

This article studies the problem of synthesis with guaranteed cost and less human intervention for linear human-in-the-loop (HiTL) control systems. Initially, the human behaviors are modeled via a hidden controlled Markov process, which not only considers the inference's stochasticity and observation's uncertainty of the human internal state but also takes the control input to human into account. Then, to integrate both models of human and machine as well as their interaction, a hidden controlled Markov jump system (HCMJS) is constructed. With the aid of the stochastic Lyapunov functional together with the bilinear matrix inequality technique, a sufficient condition for the existence of human-assistance controllers is derived on the basis of the HCMJS model, which not only guarantees the stochastic stability of the closed-loop HiTL system but also provides a prescribed upper bound for the quadratic cost function. Moreover, to achieve less human intervention while meeting the desired cost level, an algorithm that mixes the particle swarm optimization and linear matrix inequality technique is proposed to seek a suitable feedback control law to the human and a human-assistance control law to the machine. Finally, the proposed method is applied to a driver-assistance system to verify its effectiveness.