Fully Distributed Adaptive Resource Allocation With Anytime Feasibility

This article is concerned with distributed adaptive resource allocation over general digraphs with resource-demand constraints. The central aim is to tackle two essential challenges in distributed resource allocation, namely, scalable implementation and anytime feasibility, ensuring continuous satisfaction of constraints. For this purpose, two novel fully distributed optimization algorithms, featuring sum-based and product-based schemes for adaptive gains, are first developed. It is shown that these algorithms offer several advantageous features in terms of fully distributed implementation without global knowledge and algorithm simplicity as well as anytime feasibility guarantees over existing methods. Notably, the incorporation of a double-layer adaptive control law with a damping term into each algorithm prevents the continuous growth of adaptive gains, thus avoiding excessively large system gain values and enhancing practical applicability in real-world scenarios. Furthermore, by constructing appropriate Lyapunov functions, rigorous convergence analysis confirms that both algorithms achieve the optimal resource allocation and global asymptotic convergence. Finally, several simulation case studies are conducted to validate the efficiency of the proposed algorithms.