Many engineering systems exhibit natural dynamics that can be exploited for efficient operation, as exemplified by robots based on passive dynamic walking [1]. However, standard control approaches often struggle to stabilize these behaviors across varying operating conditions. Recent advances in robotic locomotion have started to address this challenge, enabling the stabilization of entire families of efficient periodic motions [2]. In practice, dissipation (e.g., friction at the joints or aerodynamic drag) can drive the system away from these naturally efficient behaviors and quickly degrade performance. In this talk, we present a hardware and control co-design framework that integrates data-driven control methods to compensate for dissipative effects along families of periodic orbits. We first highlight recent work on identifying Poincaré maps for stabilizing periodic orbits in both dissipative and Hamiltonian systems [3, 4]. Building on this, we discuss strategies for learning efficient forcing inputs and switching mechanisms that enable transition between distinct operating conditions [5]. These approaches are demonstrated on benchmark dynamical systems and robotics platforms. We conclude by discussing how joint hardware and controller design can more effectively exploit natural dynamics, ultimately maximizing the performance of complex engineering systems. [1] Steve Collins, Andy Ruina, Russ Tedrake, and Martijn Wisse. Efficient bipedal robots based on passive-dynamic walkers. Science, 2005. [2] Davide Calzolari, Cosimo Della Santina, and Alin Albu-Schaffer. Exciting families of passive gaits in an elastic quadruped via natural motion manifold control. The International Journal of Robotics Research, 2024. [3] Jason J Bramburger, J Nathan Kutz, and Steven L Brunton. Data-driven stabilization of periodic orbits. IEEE Access, 2021. [4] Owen M Brook, Jason J Bramburger, Davide Amato, and Urban Fasel. Data-driven stabilisation of unstable periodic orbits of the three-body problem. IEEE Access, 2025. [5] Nicolo Botteghi, Owen Brook, Urban Fasel, and Federico Califano. Interconnection and damping assignment passivity-based control using sparse neural odes. arXiv:2512.06935, 2025.