Distributed Resource Allocation Algorithm for General Linear Multiagent Systems

We focus on the optimal resource allocation problems with global equality constraints and local convex function inequality constraints over heterogeneous linear multi-agent systems. The distributed resource allocation problem minimizes the total objective function through neighboring information exchange. First, we propose an initialization-free state-based distributed optimization algorithm based on the Karush-Kuhn-Tucker(KKT) conditions and proportional-integral control. In addition, each agent is driven by the gradient(subgradient) of its local objective function and local constraint convex function. In addition, the penalty factor control parameter is changed adaptively. Next, we propose an output-based distributed optimization algorithm that uses a Luenberger observer when the state variable is not accessible. Based on the Lyapunov stability, it is proved that the proposed algorithms converge to the optimal solution to the distributed resource allocation problem. Finally, simulation examples are used to demonstrate the effectiveness of the proposed algorithms.