An approach to model-referenced adaptive control systems

This paper considers the model-referenced adaptive control problem. An adaption technique that is extremely simple to implement is derived analytically. The simplicity of this technique gives it a distinct advantage over other techniques that have been described in the literature and makes it attractive for practical applications. A direct approach to the problem is taken, employing the state-space point of view. By solving the differential equations of the reference model and the adaptive control system, an expression is obtained showing the explicit functional dependence of the performance error on the adaptive parameters. Manipulation of the expression for performance error yields the adaption equations which are subsequently shown to be very simple to implement. To illustrate the theory developed in this paper, a simple example is discussed and a stability analysis employing Lyapunov's second method is undertaken.