<p>Operations in contested mission environments require a balanced composition of competency, authority, and responsibility, underpinned by comprehensive operational awareness in order to provide the context, insight and foresight is required for effective command. While human intervention would be necessary directly acting or supervising some operational tasks, other tasks can only be accomplished by non-human intelligent entities, autonomously sensing, processing, deciding and acting within and between different operational domains and dimensions. Human-Autonomy Teams are Complex Adaptive Systems, able to accurately and rapidly sense, process and interpret relevant events and circumstances in order to sustain and improve decision-making and action, enabling wide-ranging appreciation of and influence on agents and effects in the Operating Environment. This calls for technologies that are able to autonomously engage with its environment, without continuous human supervision. Based on recent studies and with the support from other fields of study, we devised a number of elements of cognitive command and decision-making in a special case of complex Multi-Domain Operations. Emergent, Dynamic, Global and Evolutionary (EDGE) operations require flexible, adaptive, and high-performance human and technological (hybrid) cognitive capabilities, sustaining comprehensive operational awareness and situation understanding. This work formulates future work towards a future-oriented Essence of Human-Autonomy Command in EDGE operations, comprising strategic capability elements with equal relevance and applicability on human and Autonomous Adaptive Agents. It will be grounded in adaptive and versatile command and execution principles, supported by hierarchical knowledge structures, where the Human-Autonomy Command approach is superior regarding managing and maintaining operational availability, versatility, and efficiency.</p>