Unstable systems stabilizing each other through adaptation

Abstract

An asymptotically stable reference model plays a crucial role in the entire literature on adaptive systems. Given a plant with unknown parameters, the objective is to adapt the parameters of a controller so that the behavior of the controlled plant emulates that of the reference model in some sense. This paper addresses the following question, which is markedly different from that encountered in conventional adaptive control: “Can two or more unstable plants adaptively stabilize each other? ”. This is because neither system has a stable model to emulate, and each depends upon the other to stabilize itself. It is not surprising that this seemingly innocuous question has far reaching implications in widely different fields such as biology, psychology, economics and robotics, where it is found to arise frequently.