Artificial intelligence has shifted from a software-centric discipline to an infrastructure-driven system. Large-scale training and inference increasingly depend on tightly coupled data centers, high-capacity optical networks, and energy systems operating close to physical and environmental limits. As a result, control over data and algorithms alone is no longer sufficient to achieve meaningful AI sovereignty. Practical sovereignty now depends on who can deploy, operate, and adapt AI infrastructure under constraints imposed by energy availability, sustainability targets, and network reach. This tutorial-survey introduces the concept of AI infrastructure sovereignty, defined as the ability of a region, operator, or nation to exercise operational control over AI systems within physical and environmental limits. The paper argues that sovereignty emerges from the co-design of three layers: AI-oriented data centers, optical transport networks, and automation frameworks that provide real-time visibility and control. We analyze how AI workloads reshape data center design, driving extreme power densities, advanced cooling requirements, and tighter coupling to local energy systems, with sustainability metrics such as carbon intensity and water usage acting as hard deployment boundaries. We then examine optical networks as the backbone of distributed AI, showing how latency, capacity, failure domains, and jurisdictional control define practical sovereignty limits. Building on this foundation, the paper positions telemetry, agentic AI, and digital twins as enablers of operational sovereignty through validated, closed-loop control across compute, network, and energy domains. The tutorial concludes with a reference architecture for sovereign AI infrastructure that integrates telemetry pipelines, agent-based control, and digital twins, framing sustainability as a first-order design constraint.

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