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A Model-Reference Adaptive Control technique realized with Tap-Delay filters is presented. The adaptive logic is based upon Lyapunov stability with the Lyapunov function consisting of a quadratic sum of system errors and Tap-Delay filter weights. The problem of trajectory control of a robot manipulator consisting of a simple two-link, planar robot with revolute joints is selected to exemplify the method. The Tap-Delay filter allows a straightforward implementation of an inverse modeling control scheme which can be used in the initiation of robot motion, before the model reference system can effectively compensate. The resulting trajectory control systems is, computationally, very simple and requires adaptation of as few as five weights per each joint and measurement of only link angular orientation and rate. Robustness properties are examined and the control technique is evaluated in simulation. The proposed algorithm appears to have considerable potential for application to a variety of nonlinear control problems.