Distributed Constraint-coupled Resource Allocation: Anytime Feasibility and Violation Robustness

TL;DR

This paper introduces a distributed algorithm for resource allocation that guarantees feasibility at all times and is robust to external disturbances, with proven convergence and applicability to both inequality and equality constraints.

Contribution

It proposes a novel anytime-feasible distributed algorithm using control barrier functions, ensuring continuous feasibility and robustness in real-time resource allocation.

Findings

Algorithm converges to the optimal solution while maintaining feasibility.

Incorporates virtual queues to handle external disturbances and restore constraint satisfaction.

Proves linear convergence rate for the extended equality constraint case.

Abstract

This paper considers distributed resource allocation problems (DRAPs) with a coupled constraint for real-time systems. Based on primal-dual methods, we adopt a control perspective for optimization algorithm design by synthesizing a safe feedback controller using control barrier functions to enforce constraint satisfaction. On this basis, a distributed anytime-feasible resource allocation (DanyRA) algorithm is proposed. It is shown that DanyRA algorithm converges to the exact optimal solution of DRAPs while ensuring feasibility of the coupled inequality constraint at all time steps. Considering constraint violation arises from potential external interferences, a virtual queue with minimum buffer is incorporated to restore the constraint satisfaction before the pre-defined deadlines. We characterize the trade-off between convergence accuracy and violation robustness for maintaining or recovering feasibility. DanyRA algorithm is further extended to address DRAPs with a coupled equality constraint, and its linear convergence rate is theoretically established. Finally, a numerical example is provided for verification.