On stability and error bounds of describing functions for oscillatory control of movements

Abstract

Biological neural circuits are often modeled by neural oscillators consisting of two mutually inhibiting neurons. These oscillators explore the natural dynamics of the body coupled to a dynamic system, to excecute complex tasks, which resembles biological structures in animals. The dynamics of multiple nonlinear oscillators for controlling (non)linear multivariable robotic systems is complex. Although algebraic equations are now available for tuning the oscillators to accomplish a complex task, based on quasi-linear approximations by describing functions, it is essential to infer stability characteristics of the solutions, as well as establish error bounds for the solutions due to the approximation. The paper suggests solutions for these problems, by presenting a method for estimating stability and bounds on the estimated parameter errors.