The authors study how spiking neurons can control an inverted pendulum. Each spike produces a force acting on the pendulum (like a muscle twitch), and the observed variables (angle and its derivative) are inputs to the neurons (it’s a single layer). The question is how to set the parameters (input gains) so that the system is stable. This is an interesting problem, which is not straightforward, despite the simplicity of the architecture. The authors simply define an error function and derive a gradient descent on parameters, which seems to work. It seems however that the gradient depends on detailed aspects of the system, so it’s not so clear that is a good solution. Nevertheless, it is interesting because it addresses a problem of learning that is not representational but directly related to behavior, in contrast with most modeling studies on synaptic plasticity and learning.