Global Asymptotic Stabilization with Smooth High-gain/Low-Gain Transitions: AVA - Adaptive Variance Algorithm

Abstract

This paper presents a state-feedback algorithm with adaptive gains, designed to solve the typical gain tuning trade-off between accurate tracking in a neighborhood of the working points and large control inputs far from their proximity. The main idea is to use a Gaussian function to specify a "trust" region around the working point. For values outside this region, the gain decays exponentially and therefore the actuation input is limited. On the other hand, the variance of the Gaussian is constantly adapted, so that the attractive region around the working point will expand and eventually allow the convergence to the desired value. The stability of the algorithm is analyzed and simulations are used to validate the theoretical results.