Extended Data Fig. 7: Effect of thresholds, \({{{{\rm{T}}}}}_{\min }\) and \({{{{\rm{T}}}}}_{\max }\) in Triggered Excitation strategy.

(a-c) Heatmaps showing mean RMS tracking error in Triggered Excitation (e_TE, a), mean RMS control effort (u_RMS, b) and mean kurtosis (κ, c) of the resultant velocity distributions from 100 independent simulations at critical excitation level corresponds to minimum RMS tracking error in Persistent Excitation (\({{{{\rm{e}}}}}_{{{{\rm{PE}}}},\min }\) in Fig. ??l) as thresholds \({{{{\rm{T}}}}}_{\min }\) and \({{{{\rm{T}}}}}_{\max }\) were varied. The dashed line in (a-c) shows the phase transition based on the difference between the tracking error in Triggered and Persistent Excitation. The region inside the line corresponds to parameter space where the tracking error in Persistent Excitation is less than Triggered excitation, whereas outside the region Triggered excitation performs better. (d) Variation of kurtosis, κ (green, left y-axis), and Kullback-Leibler (K-L) divergence (right y-axis) of normal distribution (magenta dashed) and Gaussian mixture model (blue solid) fit to the velocity distribution with sensor noise variance, σ². (e,f) Velocity histograms with kurtosis values are shown for sensor noise variance, σ² = 0.70 and 2, respectively, as indicated by (i) and (ii) in (d). (g) Variation of RMS control effort (u_RMS) with sensor noise variance, σ². The shaded regions in (d,g) denote the respective standard deviations (n = 25 independent simulations per σ²).