Robust Self-excitation by Biological Oscillators

The vast majority of literature on control theory has focused on stability and certain regulation performances with respect to equilibrium points of dynamical systems. On the other hand, there are many practically important problems that are concerned with control specifications described by periodic motions. This paper makes an initial attempt to investigating the potential of biological oscillators for use as a new feedback control architecture to achieve such objectives. In particular, we use the Lur’e neuron model to construct a biological oscillator and demonstrate by a simple pendulum example that the oscillator is capable of robustly exciting the natural motion of the mechanical system. Interestingly, an oscillator of the same architecture but with a simpler neuron model, similar to those used in artificial neural network literature, does not seem to have the robust self-excitation capability. Practical implications of the result are discussed.