Energy-Optimal Maintenance Control for Oscillatory Fusion Plasmas**

Magnetically confined fusion plasmas are intrinsically nonlinear, oscillatory, and noisy systems whose stability is typically maintained using continuous, high-gain control. While effective, such approaches impose a significant parasitic power burden and scale poorly for long-pulse, reactor-relevant operation. This work introduces the Safe-Instability Envelope (SIE), a mathematically grounded control framework in which actuation is temporally concentrated into phase windows of maximal plasma responsiveness rather than applied continuously. For a broad class of oscillatory nonlinear systems with multiple stable attractors, bounded control energy, and stochastic disturbances, we prove that phase-aligned pulsed intervention minimizes expected control energy while maintaining the probability of remaining within a target (“healthy”) basin above a specified threshold. A formal optimality theorem is presented using phase-reduction theory and phase-dependent responsiveness, followed by numerical validation in bistable systems subject to drift and stochastic shocks. Monte Carlo results demonstrate that SIE achieves confinement maintenance with 60–75% lower cumulative control energy than continuous suppression while preserving performance and tolerating bounded transient excursions. The framework provides a unifying theoretical explanation for several empirically successful fusion control practices, including edge-localized mode (ELM) pellet pacing, modulated resonant magnetic perturbations (RMPs), and phase-synchronized electron cyclotron current drive (ECCD). A key implication is that allowing controlled, phase-timed instability can reduce actuator stress and parasitic power without compromising long-horizon stability. These results suggest that Safe-Instability Envelope control offers a scalable, energy-optimal pathway for plasma maintenance in ITER-class, DEMO, and STEP-relevant fusion devices, with direct implications for reducing fusion levelized cost of energy and improving commercial viability.