The control of a one degree of freedom exercise machine is considered. The control objective consists in making the human user exercise in a manner that maximizes his consumption of power. The optimality condition is determined by the muscle mechanics which is assumed to satisfy a force-position-velocity relationship. In general, the parameters of this relationship are unknown and vary with the configuration of the exercise machine. As a consequence, the control scheme must simultaneously i) identify the user's strength characteristic, ii) optimize the controller, and iii) stabilize the system to the estimated optimal state. In this paper we present control systems in the form of a nonlinear dynamic or static dampers that make the controlled system interact passively with the user. Adaptive and self-optimizing control strategies are discussed, which achieve the control objectives described above. Results of a clinical study are presented which corroborate many of the assumptions used in this paper and verify the efficacy of the proposed control schemes.