Fig. 4.

Control model for the mirror game. (A) A reactive–predictive controller produces output motion υ₁ that tracks the input motion υ₂. The controller has a reactive unit (integral feedback, f₁) that compares υ₁ with υ₂, and a predictive unit that generates an expectation of the future motion. (B) Two reactive–predictive controllers in a mirror configuration, where the output of one is the input of the other. (C) A single controller tracks an input signal with jitter. Here the predictor has a single frequency, ω. (D) Mirrored controllers converge to precise jitterless motion. Initial conditions are A₁(0) = 2, A₂(0) = 0, υ₁(0) = 0, υ₂(0) = 0. (Insets) Predictor amplitudes A₁ and A₂ converge, so that controllers end up agreeing on future motion. Here k₁ = k₂ = 1, g₁ = g₂ = 10. (E and F) Same as C and D for a predictor with five frequencies (ω₁,…,ω₅ = 0.025, 0.05, 0.075, 0.1, 0.125). F shows the motion of mirrored controllers, after a transient time, in response to initial conditions A_i,1(0) = A_i,2(0) = 0,υ₁(0) = 0,υ₂(0) = 1. E is the motion of a single controller receiving the motion of F as input.