Figure 4.

Optimising PID gains as expected sensory log-precisions ${\mu }_{{\gamma }_{\tilde{z}}}$. This example shows the control of the car velocity before and after the optimisation of ${\mu }_{{\gamma }_{\tilde{z}}}$ (before and after the vertical dash dot black line) is introduced. (a) The velocity of the car; (b) The acceleration of the car; (c) The action of the car, with an external disturbance introduced at $t=150$ s; (d) The optimisation of expected sensory precisions ${\mu }_{{\gamma }_{\tilde{z}}}$ and their convergence to an equilibrium state, after which the optimisation is stopped before introducing an external force. The blue line represents the true log-precision of observation noise in the system, ${\gamma }_z={\gamma }_{z^{\prime }}=5$.

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(a)	(b)

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(c)	(d)