Unstable systems stabilizing each other through adaptation

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. If simple rules of adaptation were adequate to answer the above question, it would not merit much attention. However, preliminary investigations have revealed that such adaptation often does lead to instability. In fact the answer to the question is far from simple, and depends upon the assumptions made regarding the adaptive subsystems, and the manner in which they interact with each other. This has given rise to a vast spectrum of interesting questions. The objective of this paper is consequently not to provide an exhaustive set of answers, but merely to pose several problems in what the authors hope will be a new area of research, and to present preliminary results concerning some of them.