The control of a one degree of freedom exercise machine is considered. The control objective is to cause the user to exercise at a rate which optimizes a modified power criterion. The optimality condition is determined by the muscle mechanics which is assumed to satisfy a linear force-velocity relationship. The parameters of the equation are assumed to be unknown and to vary with the body geometric configuration. The control scheme simultaneously i) identifies the parameters, ii) optimizes the controller, and iii) stabilizes the system to the estimated optimal states. The controller is in the form of a nonlinear dynamic damper such that the controlled system interacts passively with respect to the user. Experimental results show that the force-velocity relationship is strongly position dependent and the scheme is successful in identifying the unknown parameters and in obtaining the optimal exercise regime.