Zero-latency tracking of predictable targets by time-delay systems†

When a ball rolls in front of a car there is a 200 ms time delay before the driver's foot starts to move from the accelerator pedal to the brake pedal. This 200 ms reaction time is typical of all human movements. However, we have found that humans can track predictable targets with zero-latency. In an effort to explain this anomaly, we have developed a control technique that has general applicability. Our scheme allows a time-delay system to track targets with zero-latency whenever the target movement is continuous, smooth, and predictable. In this paper, we explain our control scheme, present our model for the human eye movement system, and suggest other possible applications, For this control scheme the target-selective adaptive controller constructs an adaptive signal that depends on the frequency, amplitude and waveform of the target movement, as well as on the time delay and dynamics of the plant. When this adaptive signal is applied to the time-delay system it allows zerolatency tracking and improved dynamic performance. Figure 1 shows this scheme applied to a general state-variable feedback control system with a time delay in the forward path. The system input r^t), is composed of two parts : the reference source, rs(t) and the adaptive signal, ra(£). When r3(t) is not a known target waveform, ra(£) is turned off ; r^t) then equals rs(t) and the closed-loop transfer function becomes 7(8) _ hT(sI - A^bJSC exp ( - ST) ( ' exp ( - sr) The exp ( — sr) term in the numerator is a pure time delay that remains in spite of the feedback. The similar term in the denominator produces the phase lag that reduces the allowable gain. Of the other symbols, Y(s) represents