Prashanth Harshangi

The multiple models, switching, and tuning methodology is used in this paper to identify simultaneously multiple linear time-invariant (LTI) plants. Two model assignment strategies are also presented. These strategies cause the models to organize themselves so that at any given instant only one model adapts to each plant. The choice of the assignment strategy and the performance criteria play an important role in the manner of both the convergence and the switching between models.

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? ”… Show more

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. Show less

It is now well realized [1] that two unstable dynamical systems, attempting to stabilize each other using the error between their outputs for adjusting their parameters, may not always succeed. The fact that adaptation may result in instability makes the mathematical problem a very interesting one. Since similar problems are arising in many other branches of science (e.g psychology, biology, medicine etc), obtaining precisely the conditions under which stability is achieved is also assuming… Show more

It is now well realized [1] that two unstable dynamical systems, attempting to stabilize each other using the error between their outputs for adjusting their parameters, may not always succeed. The fact that adaptation may result in instability makes the mathematical problem a very interesting one. Since similar problems are arising in many other branches of science (e.g psychology, biology, medicine etc), obtaining precisely the conditions under which stability is achieved is also assuming greater importance. This paper may be considered as a first attempt to discuss the many aspects of this intriguing and difficult problem. Work carried out during the past year has shown that the interaction of two n th order systems, results in a 4n th order differential equation, whose stability has to be investigated. Even in the simple case when n = 2, determining necessary and sufficient conditions for stability is a formidable undertaking. However, through extensive simulation studies and the theoretical analysis of special cases suggested by them, numerous insights have been obtained. The objective of this paper is to convey these insights, and discuss wherever possible, their implications to higher order systems. Show less