Dynamic Event-Triggered Fixed-Time Practical Distributed Optimization and Output Consensus of Incommensurate Nonlinear Fractional-Order Multi-Agent Systems with Input Saturation

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.