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Authors & Affiliations
Luke Eilers, Jean-Pascal Pfister
Abstract
Energy efficiency and robustness to noise for long-distance communication are often cited as reasons to the question of why the brain uses digital communication in the form of spiking neurons [1,2]. However, a quantitative and systematic analysis of the advantages and disadvantages of spikes in terms of communication, computation or control is still missing.
Here, we approach the question from a control perspective and systematically compare event-based control with analog control. In particular, we view motor neurons as controllers that act on muscle fibers through their twitch response kernel [3]. The goal of the controller is to produce the appropriate event-based or analog stimulation that is convolved with the twitch response kernel to produce a specific target force trajectory. The stimulation is either proportional or leaky integral with respect to the error between the produced force and the target force. The target cost given by the deviation from the target and the control cost add up to the total cost. Since both controllers are convolved with the same twitch response kernel, we use a common definition for the respective control costs. This allows us to compare the costs between event-based and analog control in a fair way.
Our numerical simulations show that event-based control generally outperforms analog control in terms of cost when the frequency of the oscillating target signal is high and hence fast tracking is required. Here, we consider the total costs optimized over the free parameters of the controllers. While the difference between the two types of control is small in the case of proportional control, analog control gets worse if we consider leaky integral control instead. On the contrary, event-based control is more robust and performs well in both cases. Thus, we find that event-based control is advantageous in regimes where integral control is beneficial, i.e., when noise or delays are present. In addition to the better performance in terms of optimal total cost, event-based control is more robust to the choice of its free parameter and the optimal parameter is easier to find. Therefore, event-based control is preferable in settings where the system parameters, e.g., target frequency or noise, are unknown or subject to change. Overall, our results support the idea that the spiking nature of motor neurons is not only beneficial for the long-distance communication from soma to muscle fibers but also for the muscle control itself.