Recent demands on improved system efficiency and reduced system emissions have driven improvements in hydraulic system architectures as well as system supervisory control strategies employed in mobile multi-actuator machinery. Valve-controlled (VC) architectures have been in use for several decades and have seen moderate improvements in terms of system efficiency. Further, throttle-less concepts such as displacement-controlled (DC) actuation have been recently proposed and successfully demonstrated efficiency improvements in numerous prototypes (wheel-loaders, excavators, and skid-steer loaders) of different sizes. The combination of electric or hydraulic hybrid systems for energy recovery (for a single actuator) with VC actuation for the rest of the actuators has also been recently deployed by original equipment manufacturers (OEMs) on some excavator models. The combination of DC actuation together with a series hydraulic hybrid actuator for the swing drive has been previously proposed and implemented as part of this work, on a mini-excavator. This combination of highly efficient DC actuation with hydraulic hybrid configuration allows drastic engine downsizing and efficiency improvements of more than 50% compared to modern-day VC-actuated systems. With a conservative, suboptimal supervisory control, it was previously demonstrated that over 50% energy savings with a 50% downsized engine over the standard load-sensing (LS) architecture for a 5-t excavator application. The problem of achieving maximum system efficiency through near-optimal supervisory control (or system power management) is a theoretically challenging problem, and has been tackled for the first time in this work for DC hydraulic hybrid machines, through a two-part publication. In Part I, the theoretical aspects of this problem are outlined, supported by simulations of the theoretically optimal supervisory control as well as an implementable, near-optimal rule-based supervisory control strategy that included a detailed system model of the DC hybrid hydraulic excavator. In Part II, the world's first prototype DC hydraulic hybrid excavator is detailed, together with machine implementation of the novel supervisory control strategy proposed in Part I. The main contributions of Part I are summarized below. Dynamic programming (DP) was employed to solve the optimal supervisory problem, and benchmark implementable strategies. Importantly, the patterns in optimal state trajectories and control histories obtained from DP were analyzed and identified for different working cycles, and a common pattern was found for engine speed and DC unit displacements across different working cycles. A rule-based strategy was employed to achieve near-optimal system efficiency, with the design of the strategy guided by optimal patterns. It was found that the strategy replicates optimal system behavior with the same rule for controlling engine speed for different cycles, but different rules for the primary unit (of the series-hybrid swing drive) for different cycles. Thus, in terms of practical implementation of a rule-based approach, the operator is to be provided with a family of controllers from which one can be chosen so as to have near-optimal system behavior under all kinds of cyclical operation.