This paper investigates distributed optimization-assisted output consensus for nonlinear multi-agent systems with mutually incommensurate Caputo orders, unavailable velocity-like states, bounded disturbances, measurement noise, and actuator saturation. A mixed-power exact penalty flow generates practical optimal references from local costs and intermittent neighbor broadcasts. The penalty gain and a smoothing bias bound are determined from a public interval, topology information, and certified local gradient data without prior knowledge of the aggregate optimizer. An autonomous decaying threshold provides event-triggered communication, an initial condition-independent fixed-time practical certificate for the integer-order optimizer, and exclusion of finite-time event accumulation. The physical layer is analyzed with established Caputo quadratic inequalities and agentwise Mittag–Leffler comparison. Fractional reference and command filters, a composite observer, and two-gain anti-saturation compensation form the output feedback controller, while the physical result is formulated as a finite-horizon regional verification certificate. Numerical studies include same-model and communication budget comparisons, a recent method-inspired optimizer benchmark, certificate tightening, and robustness tests for initialization, the fractional order, measurement noise, and the integration step size.

The exponential growth of the digital economy has transformed data centers into major energy consumers, yet their inflexible power consumption patterns and substantial waste heat generation pose significant challenges to grid stability and carbon neutrality targets. Existing energy management strategies often overlook the deep coupling potential between computing workload flexibility, thermal dynamics, and carbon trading mechanisms, leading to suboptimal resource utilization. To address these issues, this study proposes a collaborative low-carbon economic scheduling strategy for data center microgrids. A multiple-dimensional coupling framework is established, integrating a queuing theory-based model for delay-tolerant workload shifting and a heat-determined computing mechanism for active waste heat recovery (WHR). Furthermore, a mixed-integer linear programming (MILP) model is formulated, incorporating a linearized tiered carbon trading mechanism to facilitate source–load coordination. Simulation results demonstrate that the proposed strategy achieves a dual optimization of economic and environmental benefits, reducing total operating costs by 11.7% while minimizing carbon emissions to 6879 kg compared to baseline scenarios. Additionally, by leveraging temperature aware load migration, the daily weighted power usage effectiveness (PUE) is optimized to 1.2607. These findings quantify the marginal benefits of load flexibility under tiered pricing, providing insights for operators to balance service timeliness and energy efficiency in next generation green computing infrastructure.