Information-transmission rates in manual control of unstable systems with time delays.

In analyzing the human-machine interaction (HMI), a human-centered approach is needed to address the potential and limitation of human control, especially in the control of high-order or unstable systems. However, there is no quantitative measure of the human performance or cognitive workload in these difficult HMI tasks. We propose to characterize the HMI as information flows quantified by the information-transmission rate in bits per second (b/s). Using information- and control-theoretic approaches, we derive the minimum rates of information transmission in manual control required by any deterministic controller to stabilize the feedback system. Furthermore, we suggest a method adopted from time-series analysis to estimate the information-transmission rate from human experiments. We show that the relationship between the empirically estimated information rates and the minimum bounds allows for the quantitative indication of the potential and limitation of human manual control. We illustrate our method in the control of an inverted pendulum with time delays.